Annu. Rev. Fluid Mech. 2000. 32:165–202Copyright q 2000 by Annual Reviews. All rights reserved
0066–4189/00/0115–0165$12.00 165
LABORATORY STUDIES OF OROGRAPHIC
EFFECTS IN ROTATING AND STRATIFIED FLOWS
Don L. Boyer and Peter A. DaviesEnvironmental Fluid Dynamics Program, Department of Mechanical and AerospaceEngineering, Arizona State University, Main Campus, Tempe, Arizona 85287-6106;e-mail: [email protected] of Civil Engineering, University of Dundee, Dundee, United Kingdom; DD14HN; e-mail: [email protected]
Key Words atmospheric sciences, oceanography, geophysics
Abstract This article reviews some aspects of the roles that laboratory experi-ments have played in the study of orographic effects in the Earth’s atmosphere andoceans. The review focuses on, but is not restricted to, physical systems for whichthe effects of both background stratification and rotation are important. In the past,such laboratory studies have been largely decoupled from attempts to make quanti-tative comparisons with the results of numerical-model studies or observations fromfield programs. Rather, they have been used mostly in the important task of betterunderstanding the physics of rotating and stratified flows. Furthermore, most labora-tory experiments concerned with the effects of orography on either homogeneous orstratified rotating fluids have considered laminar flows, whereas their counterpartflows in the atmosphere and ocean are turbulent. We argue that laboratory investi-gations are likely to be more useful in addressing critical environmental problems ifthe studies are more closely allied with numerical-modeling efforts. The latter, in turn,should be tied to field projects, with the overall objective of improving our ability topredict the behavior of natural systems. In this same spirit, we conclude that far moreattention should be given to the laboratory simulation of the turbulent characteristicsof natural flows. The availability of rapidly developing technology to acquire andanalyze laboratory data provides the capability necessary to support the increasinglyimportant roles that laboratory experiments can play in understanding and predictingthe behavior of our natural environment.
1. INTRODUCTION AND SCOPE
Determining the dynamical effects of the interaction between an obstacle and amoving fluid is a classic problem in fluid dynamics. For example, the lift anddrag characteristics of a flow past an airfoil are of fundamental importance inaerodynamics. For low-speed flows (i.e. small Mach numbers), the nature of the
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flow depends on a single dynamical parameter, the Reynolds (Re) number, ensur-ing that the dynamical basis of wind tunnel testing is relatively straightforward.
The counterpart problem in geophysics, as exemplified by the goal of deter-mining the nature of atmospheric or oceanic motions and their transport propertiesover mountain ranges or other topographic features in their respective environ-ments, is far more complex. Many factors contribute to this complexity, including(a) the importance of the Earth’s background rotation and stratification, (b) spatialand temporal variations in the mean background flow, (c) turbulence in the back-ground motion on wide ranges of temporal and spatial scales, (d) complexbathymetry with a wide range of spatial scales, (e) variation in the dynamicaleffect of the Earth’s rotation with latitude (i.e. the beta effect), ( f ) the complexexchange of properties such as momentum and energy across the air-sea interface,and (g) seasonal changes in the characteristics of the atmosphere and/or oceans.These difficulties are compounded by the sheer vastness of the atmospheric andoceanic domains of interest, the limited availability of measurement systems, thecost of data acquisition, and the general problems associated with sampling flowsthat are inherently variable in space and time. Thus, the very basic requirementof defining adequately the initial state of the system and the appropriate boundaryconditions is a major problem for modelers of natural flows.
It has long been recognized that orographic1 effects are fundamental on themesoscale and larger (e.g. global) scale, in determining the nature of atmosphericand oceanic motions and their transport properties. In this connection, it is notedthat the terms global scale and mesoscale refer conventionally to independentdimensional-length-scale ranges that are typically 100–1000 km and 10–100 km,respectively. For atmospheric flows, the former range (typified by the lateraldimensions of low-pressure systems) matches well the appropriate Rossby radiusof deformation NH/f, where N and f are the buoyancy (Brunt-Vaisala) and Coriolisfrequencies, respectively, and H is a vertical dimension of the flow. Thus, bydefinition, mesoscale atmospheric-flow features have scales much less than theRossby radius. However, this is not the case with typical counterpart oceanicflows, for here the Rossby deformation radius is much smaller (between 100 and300 km in tropical seas to ,10 km in subpolar regions) than in the atmosphereand is therefore of the same order as the mesoscale. An interesting and clarifyingdiscussion of this point and its implications for the numerical modeling of meso-scale processes can be found in the work of Røed (1996).
Recognizing that the principal long-range goal of research in the general areasof dynamical meteorology and physical oceanography is the development ofimproved prediction capabilities, it is clear that the effort to achieve such a goalmust be focused on the improvement of numerical models. Currently, however,these models do not handle well the combination of rotation, stratification, steep
1Orography is defined as terrain features having large characteristic length scaler such asmountain ranges which in turn affect the dynamics of large-scale motions of the geograph-ical system being investigated.
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topography, and complex terrain. Furthermore, for reasons delineated above, themodels do not have adequate data available from field measurements (a) to defineinitial and boundary conditions and (b) to check the validity of the model pre-dictions. Additionally, the numerical models require improved information onsubgrid scale processes to better parameterize these physical mechanisms.
Laboratory experiments have been used, for example, to parameterize small-scale flow processes of complex terrain for atmospheric models (Baines 1995,Hunt 1995) and for boundary mixing and sediment transport in oceanic models(Hogg et al 1978, Simpson et al 1982, Simpson & Tett 1986, Ivey 1987). Whereaslaboratory studies have made some contributions to the development of prognos-tic models, it is our thesis here that an increasingly important role can be playedby laboratory experiments in the development of more realistic numerical models.As is already clear to the reader, the contribution of laboratory model studies willbe emphasized herein, not only to set reasonable limits on the scope of the reviewbut also to reflect the specialized interests of the authors.
One important difference between virtually all of the past laboratory experi-ments on orographic effects in rotating (homogeneous or stratified) flows andtheir atmospheric and oceanic counterparts is that the motion fields in the formerare laminar and those in the latter, turbulent. This is apparent from a simple Renumber comparison between the model and geophysical flows. For typical lab-oratory model studies, the Re number is relatively small and is characteristic oflaminar flows; that is, Re 4 UD / m & 103, where U is the characteristic velocity,D a typical horizontal-length scale, and m the molecular kinematic viscosity ofthe working fluid (generally water). The Re numbers for even modest-sized geo-physical topographic features are exceedingly large, and the associated flows areclearly expected a priori to be turbulent.
Much debate has centered on estimating appropriate values of the eddy vis-cosities of natural flows so that the Re and Ekman numbers of the laboratorymodel under consideration represent adequately the physics of the orographicaction of the natural flow. These considerations allow comparisons to be madebetween laboratory results and environmental flows, but it must be recognizedthat questions remain over differences between the transport properties in themodel and natural flows. Thus, the introduction of the eddy viscosity conceptcan, at most, lead only to qualitative comparisons between the model andprototype.
Historically, laboratory model studies on topographic effects were not directedtoward the modeling of the flow in a specific geographical location. Furthermore,the laboratory observations provided only qualitative information or relativelycrude quantitative measures of well-specified, idealized flows. Although somelaboratory model studies have fulfilled the crucial role of providing data that canbe compared profitably with analytical-model predictions to obtain better process-based understanding, comparisons have typically not been made to date in anymeaningful quantitative way with relevant field data or numerical-model predic-tions. Thus, it could be argued that past laboratory experiments on topographic
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effects have not contributed crucially to forecasting quantitatively the behaviorof the atmosphere and oceans when they are influenced by orography.
The development of improved prognostic numerical models is hampered sig-nificantly by at least two important factors. First, these models require satisfactoryparameterization schemes for incorporating the physics of subgrid-scale processesinto the model. Second, there is a need to have data sets that have sufficientresolution in time and space to test the validity of the numerical model in question.Laboratory experiments can play a significant role in both of these areas. Ofcourse, the dynamical behavior of the Earth’s atmosphere and oceans evolvesunder the influence of a myriad of physical processes that are not readily isolated.With recent technological developments, laboratory experiments that can isolatevarious physical processes can also be used to obtain benchmark data sets for thenumerical models. The view that laboratory experiments will play an increasinglyimportant role in the development of prognostic numerical models is a persistenttheme of this review.
The authors have chosen to limit the scope of the review and have not included,for example, relevant experimental work on topographically affected rotatingflows carried out in nongeophysical contexts; attention has been restricted solelyto flows in the Earth’s atmosphere and oceans (thereby excluding the formidableliterature on orographic effects in the Earth’s core). Useful points of entry intothe topic under discussion are previous reviews contributed by others on spe-cialized aspects; of particular note in this regard are the reviews of topographiceffects in atmospheric (Smith 1979), oceanic (Hogg 1980, Roden 1987), andlaboratory (Maxworthy & Browand 1974, Baines & Davies 1980) flows.
Finally, we note that the terms orographic and topographic are both usedthroughout the paper, to reflect their traditional, rather variable usage in this areaof research. Because the review is restricted to those large-scale flows in theatmosphere and oceans that are affected significantly by the Earth’s rotation, ourprimary adoption of the term orographic in the title of the paper is consistent withthe distinction made by Baines (1995).
2. SIMILARITY PARAMETERS
The general problem of a stratified current interacting with a topographic featurein a rotating frame of reference, as occurs in, for example, the oceans or atmo-sphere, is associated with a large number of contributory factors such as (a)nonlinear background stratification, (b) vertical and horizontal shear in the undis-turbed (‘‘free-stream’’) flow, (c) complex bottom and lateral topography associ-ated with a wide range of spatial scales, (d) time-dependent background flowswith some of the time scales well defined (e.g., tidal motions) and others illdefined (e.g. advecting storms), (e) the advection of eddies with a wide range oflength and time scales, ( f ) phase changes associated with precipitation processesin the atmosphere, and (g) mixing associated with boundary turbulence (generated
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Figure 1 Physical system; schematic diagram of stratified shear flow past an obstacle inthe presence of background rotation.
by Kelvin-Helmholtz instabilities and internal wave breaking in the oceans, andboundary turbulence, convective motions, storms, and Kelvin Helmholtz effectsin the atmosphere).
Because modeling simultaneously all of the above effects is not feasible, ageneric problem of topography effects in rotating and stratified fluids is definedby the system sketched in Figure 1; for now, the laboratory model is assumedlaminar and characterized by a fluid of kinematic viscosity m. Here, a unidirec-tional, ‘‘free-stream’’ shear flow U(z,t) is defined by
U(z, t) 4 U ` u (z) ` U sin(x t), (1)0 d l o
where U0 is the characteristic free-stream speed, ud(z) is the deviation from theconstant value U0, and U1 and x0 are the magnitude and frequency, respectively,of the time-dependent component of the flow. The background stratification ofthe undisturbed fluid is taken to be quantified by the density profile q(z), with thecorresponding buoyancy (Brunt-Vaisala) frequency being given by N(z); N0 istaken as the characteristic buoyancy frequency of the undisturbed density profileand is defined as N0 4 (gDq/q0H)1/2, where Dq is the density difference between
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the bottom and top of the undisturbed fluid, q0 is the mean density of the undis-turbed fluid, and g is the acceleration caused by gravity. The depth of the fluidlayer is taken as H, and the characteristic vertical, streamwise, and h, D, and Wgive lateral scales of the topography are given by h, D, and W, respectively. Thetop (z 4 H) of the fluid layer is taken as the free surface in oceanic applicationsand as a level well above that at which topographic influences are felt in theatmosphere.
The dynamical and geometrical parameters governing this generic laboratoryphysical system can be defined by using dimensional analysis via the BuckinghamPi theorem (e.g. Fox & McDonald 1992). A suitable set of governing parameterscan be shown as follows:
temporal Rossby number
Rossby number
shear parameter
Burger
Ekman number
geometrical
x0(Ro ) 4 ,t fUo(Ro) 4 ,fD
du /dzd(A) 4 ,f2 2N H0(Bu) 4 ,2 2f D
m(E) 4 ,
2fHh h h
, , .H D W
(2)
For some applications it is convenient to formulate some of these parameters inalternate groupings, namely the Froude (Fr) number and the Re number, definedas Fr 4 U0 / N0h and Re 4 U0D / m, respectively, although it is noted that theseare not independent of the parameters given in Equation 1. At this stage, theargument of similarity between natural and laboratory flows must invoke consid-erations of the eddy viscosity mE in the determination of the Ekman number inthe atmosphere or the oceans. Below, we propose that future laboratory studiesconsider the use of turbulent background flows, so that eddy viscosity effects maybe simulated directly in the laboratory.
To limit this work to those atmospheric and oceanic situations in which back-ground rotation and stratification are both important, the following parameterrestrictions are specified a priori:
Ro & 0(1), Ro K 0(1), A & 0(1), Bu & 0(1)(3)6E K 1, h/H & 0(1), h/D ; 0(1), h/W ; 0(1).
It is well known that atmospheric and oceanic flows are hydrostatic on the scalesbeing considered herein. To simulate such conditions in laboratory modelsrequires consideration of the vertical-momentum equation, specifically the param-
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eter restrictions required for the inertial terms to be negligible compared with thepressure gradient and buoyancy terms. It can be shown (see Boyer et al 1999)that, for unsteady flow, hydrostatics at the lowest order is achieved under theconditions
2 2h RotK 1,1 2D Bu
and (4)2h Ro Rot 6K 1.1 2D Bu
For steady flows, hydrostatics requires
2 2h RoK 1. (5)1 2D Bu
Equations 4 and 5 are based on the assumption that the vertical velocity equalsthe topographic slope multiplied by the undisturbed horizontal speed. Thishypothesis, however, does not account for stratification effects, which lead tosmaller vertical-velocity scales. We conclude that Equations 4 and 5 are overlystrong criteria.
Restricting the laboratory flows to those that are approximately hydrostaticindicates that the parameter h/D in Equation 2 does not appear in either thegoverning equations or the boundary or initial conditions. This eliminates thenecessity of matching the ratio of the vertical- to horizontal-length scales in thelaboratory. This critical result allows for the distortion (increase) of the vertical-length scale in the model. Because larger-scale natural systems for which rotationand stratification are dynamically important have inherently small vertical-to-length-scale-ratios, the above result is welcome; otherwise, laboratory modelscould not be practically constructed.
3. EXPERIMENTAL FACILITIES AND TECHNIQUES
3.1 Laboratory Facilities
As noted previously, laboratory investigation of the motion field resulting fromthe translation of an obstacle through a homogeneous incompressible fluid in anonrotating system is relatively straightforward through the use of wind or watertunnel facilities that establish a uniform flow past the obstacle in question. Alter-natively, a tow tank can be used (usually with water as the test fluid) to investigatethe flow field resulting from the translation of the obstacle through the fluid, whichis otherwise at rest. The development of laboratory facilities to investigate themotion of rotating and stratified flows past obstacles is far more difficult. Boyer(1970) extended the wind tunnel concept to homogeneous, rotating liquid flowsby developing a small rotating water tunnel. This facility provided an acceptably
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uniform free-stream flow but, as with any such facility, difficulties were experi-enced. One was the requirement of establishing a uniform pressure gradient acrossthe test section because, in rapidly rotating flows that are geostrophic, the pressuregradient acts across rather than along streamlines. Because the tunnel has to beplaced on a turntable, there is a practical maximum length of facility that can beconstructed. It is thus difficult to establish a really accurate uniform flow, becausethe limited channel length does not allow the flow to become fully established.No attempts have been made to develop a rotating stratified tunnel of the abovetype because the added problem of not mixing the fluid, along with the challengeof establishing a uniform free stream, makes this approach difficult at best.
Investigators, beginning with Taylor (1923), have thus used the tow-tankapproach to investigate the motion past obstacles in rotating and stratified fluids.Towing facilities have been constructed in either circular (as that of Taylor) orrectangular geometrys (Zhang & Boyer 1993). For such cases, the test cell is firstfilled with an appropriately stably stratified fluid and then brought slowly to arigid-body rotation to avoid mixing. The rectangular facility allows for a lineartranslation of the obstacle relative to a rotating observer but has one significantdrawback, namely its limited length and the size restrictions associated with plac-ing it on a turntable. This constraint results in the problem of establishing a fullydeveloped flow at some time during the traverse. Additionally, care must be takento assure that the lateral wall and channel end effects do not unduly influence themotion field through the generation of secondary flows (Boyer & Biolley 1986).Some experiments are carried out with a circular tank by towing the obstaclealong a circular path at some central radius in the tank. The principal concernswith this approach are that, in the long term, the obstacle will pass through itswake and, additionally, the free stream is one having radial shear and circularstreamlines.
An alternative approach for establishing a fluid motion relative to a fixed rotat-ing observer is to again fill a circular or annular tank with an appropriately strat-ified fluid in rigid-body rotation, for example, anticlockwise, with Coriolisparameter f/2. A relative azimuthal motion can then be established by impulsivelyincreasing (decreasing) the turntable rotation rate. This leads to a clockwise (anti-clockwise) transient flow relative to the tank and can be used to investigate theinfluence of topographic features affixed to the tank on the flow. The primarydrawback of this approach is that the free stream is continually spinning up (down)so that a time-independent free-stream velocity is not generated. Furthermore, aswith towing systems, the azimuthal nature of the background flow includes aradial shear. This method has been exploited (Perenne et al 1997) to establish aperiodically varying free stream akin to a tidal flow and the passing of storms;that is, the turntable rotation rate is modulated in a periodic way about the constantrotation rate f/2. Boyer et al (1999) have shown that this temporal change in theturntable rotation leads to ‘‘non-oceanic’’ (i.e. acceleration) terms in the governingequations that are negligible for sufficiently large test cell radii and small char-acteristic horizontal-length scales of the topography.
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Source-sink techniques are suited particularly well to rotating fluid motionsystems because of the ability of a rapidly rotating system to generate predictableinterior-velocity fields from weak boundary forcing (Hide et al 1968). Boyer &Chen (1990) have used this technique for circular geometries, whereas Davies &Osborne (1999) have extended the method to generate a two-layer shear flow ina rectangular geometry. For anticlockwise rotation in circular-tank geometry, themethod entails establishing a circularly symmetric source along the wetted periph-ery of the tank and a similar sink along some interior radius. Owing to the influ-ence of the Coriolis acceleration and the dynamical balance between these termsand those of inertia, pressure, and viscosity, the continuous operation of thesource-sink system leads to a fully established cyclonic jet flow relative to arotating observer. The insertion of topographic features into the path of the jetcan then be used to investigate current-topography interactions. It is found that,although stable flows can be generated, these flows may be barotropically and/orbaroclinically unstable, leading to horizontal wavelike motions along the jet axis.Reversing the source and sink leads, of course, to an anticyclonic jet. Boyer et al(1993) have used this technique to demonstrate some of the qualitative featuresof the deflection of the Antarctic Circumpolar Current (ACC) by the bathymetryof the sea floor of the Southern Ocean and to simulate well the principal featuresof the path of the ACC.
Relative motions in a rotating annular or circular tank have also been estab-lished by exerting an azimuthal shear stress on the fluid surface by differentiallyrotating a rigid lid placed along that surface, relative to the background rotationof the tank itself (Pedlosky 1971, Spence et al 1992). Maxworthy (1977), Davieset al (1991), and Pfeffer et al (1993) have carried out topographic steering exper-iments by using this technique for barotropic and baroclinic f-plane flows. Asdescribed in Section 4.3, Narimousa & Maxworthy (1987, 1989) have alsoexploited this approach in their laboratory investigation of the effects of ridgesand other topographic features on a sloping bottom forced by the motion of wind-driven, along-shore coastal currents; these studies considered two-layer flows andwere directed primarily at studying the issue of the influence of various topo-graphic features on the phenomenon of coastal upwelling. The principal drawbackof this approach is that of the circular geometry with radially dependent forcing;the rotating rigid lid continuously introduces vorticity into the fluid interior (whichmay not occur in the natural system).
Drainage flows or katabatic wind systems constitute another class of flows forwhich the effects of orography are exceedingly important. For problems in whichthe background wind field is negligible, these drainage flows can be investigatedin the laboratory by developing an apparatus in which the temperature of thelower bounding surface can be controlled to mimic the radiative cooling of theEarth’s surface. For large-scale katabatic winds, as occur over the Antarctic con-tinent in winter, background rotation is important in determining their behavior.Such thermally driven flows can be established in the laboratory by placing themodel topography in question in a rotating test cell filled with a fluid (which may
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or may not be stratified) in rigid-body rotation. Then cooling the surface in acontrolled way can generate downslope winds, and their deflections by the orog-raphy can be investigated. The principal drawback of this approach is that theinduced velocities are generally very small, so that the flows are laminar, whereasthe counterpart natural flows are turbulent.
Background flows of stratified fluids in rotating systems can also be establishedby (a) the formation of surface gravity currents trapped along the periphery of arotating test cell, (b) the differential heating of fluid in an annulus, as initiated byFultz et al (1959) and Hide (1958), and (c) the establishment of mean flows bygradients in the turbulent Re stresses (Zhang et al 1997). For reasons of economy,these methods of establishing currents in the presence of background rotation arenot considered further.
Turntables used in the above investigations vary in size from small facilities(typically 1 m in diameter) through medium (e.g. the 5-m SINTEF table in Trond-heim, Norway) to larger (e.g. the 13-m diameter, 1.2-m deep tank of the CoriolisLaboratory platform in Grenoble, France). Although the large facilities have onlymodest advantages over the smaller ones for laminar flows, for the turbulent-flowstudies suggested in Section 5.2, the larger facilities are essential in attainingsufficiently large Re numbers required to achieve turbulent-flow conditions.
Large facilities also allow for the less obtrusive placement of measuring instru-ments within the fluid with the expectation of (a) less disturbance than withsmaller platforms and (b) improved instrument signal-to-noise characteristics.Thelatter property has been illustrated well by the direct force measurements collected(Chabert d’Hieres et al 1989, 1990) with a specially designed force transducerattached to a large translating circular cylinder in a rotating homogeneous fluid,with good quality lift and drag data being obtained over a range of Ro even aftersystematic removal of parasitic force components from the raw data. For thetruncated obstacle group of experiments (Chabert d’Hieres et al 1990), the dataextended to higher values of Ro and Re the drag and lift force data inferred byMason (1975, 1977) from obstacle pendulum trajectories in stratified and homo-geneous rotating fluids.
Extensive regions of complex terrain can also be inserted into the workingchamber of such large facilities to carry out hydraulic-model studies encompass-ing different processes within particular geographical zones of interest (e.g. theEnglish Channel and Norwegian shelf). Such site-specific studies provide predic-tions of flow patterns and contaminant distributions in areas either under consid-eration for or being exploited commercially by offshore or coastal engineeringoperations (McClimans & Johannessen 1998). Even with the large horizontalscales allowed by the facilities above, geometric-scale distortion cannot beavoided for coastal studies (where such effects are expected to be accentuated)or deep-ocean applications. Relatively high operating costs, coupled with prob-lems in minimizing spurious effects associated with local wind stress generationand evaporation, mean that the large-scale facilities of the above type are used
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OROGRAPHIC EFFECTS IN FLOWS 175
most effectively for classes of topographic problems in which the overridingadvantages of large scales offer significant and unique scientific benefits.
3.2 Techniques
Measurement techniques for rotating-fluid systems have been recently catalogedcomprehensively by Weidman (1989), although most fluid flow measurementtechniques developed recently for nonrotating-fluid systems are relatively welladapted also to rotating frames. The presence of background rotation, however,may provide technical challenges for some of the intrusive flow visualization andmeasurement techniques that are commonly used in nonrotating-fluid experi-ments. The tendency for Taylor columns to form around suspended probes andaccess holes for instrumentation can be troublesome with homogeneous workingfluids.
In the area covered by this review, the most significant technological advancesin recent years have been in data acquisition in general and video-based automatedparticle-tracking techniques in particular. The latter have enabled reliable synoptictwo-dimensional velocity, vorticity, and divergence fields to be obtained on afairly routine basis; particle image velocimetry (PIV) methods have also beendeveloped commercially to an advanced stage such that they are routinely usedacross a range of rotating-fluid problems including those concerned with topo-graphic effects. Many of the above techniques have been developed (either ser-endipitously or by design) by individual research groups (see, for example, Read1993, Baines & Hughes 1996, Coates & Ivey 1997) concerned with particularclasses of flow problems, although some [like the DigImage particle-tracking andconcentration software package (Dalziel 1992) and the correlation image velo-cimetry (CIV) system (Fincham & Spedding 1997)] have been successfullyexploited commercially within the geophysical fluid dynamics community. Theadvantages of the techniques are clear; they permit, at modest investment, theautomatic acquisition of formidable amounts of reliable, synoptic, digitized veloc-ity data in specified illuminated planes within the flow, with no significant dis-turbance to the flow. Spatial and temporal resolution of the data acquisition andanalysis functions of the techniques are sufficiently good that both laminar andturbulent flows can be investigated, thereby permitting the processing of the datato obtain meaningful vorticity fields and turbulence quantities. Rapid-scanning-hardware techniques have been developed (see Sadoux et al 1999) to extend themethods and obtain full three-dimensional velocity and vorticity fields of theflows under consideration.
Concurrent technical advances have also taken place in video-based concen-tration field measurement techniques and associated instrumentation, particularlysuited to stratified-flow investigations (Davies 1992). Such advances are relativelyeasily adapted to rotating frames, although, when such techniques require watercooling for Argon-ion laser sources (for laser-induced fluorescence measure-ments, for example), only the largest rotating-turntable facilities like the Coriolis
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platform may be appropriate. The problem of providing on-board water coolinghas been solved by using instead an optical slip ring assembly to couple the laserbeam from the laboratory frame to the rotating platform (Coates & Ivey 1997),although the task constitutes a significant technical challenge.
4. OROGRAPHICALLY INFLUENCED FLOWPHENOMENA
4.1 Mountains, Ridges, and Seamounts
Mountain ranges and isolated mountains are well known to affect atmosphericmotions and, in turn, weather and climate. On the global scale, barriers such asthe Himalayas and the Rocky Mountains interact with the westerlies to establishthe locations of the principal high- and low-pressure regions of the NorthernHemisphere. On the mesoscale, extended mountain complexes such as the Alpsare known to influence strongly the regional and local weather and climate, asexemplified by the frequent occurrence of cyclogenesis in the lee of the Alps inthe Gulf of Genoa (Buzzi & Tibaldi 1978). Although key features of this influenceare the deforming effect of the mountain complex on the approaching ‘‘parent’’low-pressure systems and the perturbations exerted by the orography on the flowaloft, the conditions for which strong lee cyclogenesis occurs continue to attractinterest. A review of the ALPEX program—the multinational field and modelingprogram undertaken to study the alpine cyclogenesis phenomenon—is given inGARP (Global Atmospheric Research Program 1986).
Satellite image anthologies of cloud patterns (Scorer 1987) show evidence ofthe enormous range of flow types generated by the passage of air over mesoscaleand global-scale mountainous terrain, with particularly dramatic illustrations ofatmospheric wake flows behind isolated islands and groups of islands; see thereviews by Gjevik (1980) and Etling (1989, 1990a,b). On the scale of the indi-vidual mountain groups within an extended complex of mesoscale extent, airflows and constituent contaminants are steered in a complex fashion by the effectsof local orography, background rotation, and density stratification.
It is well known that oceanic seamounts (either isolated or in groups) arecapable of amplifying tidal flows and generating anticyclonic rectified currents.In addition, they are known (a) to serve as sites for boundary mixing, internal-wave train excitation, and eddy generation and (b) to influence localized domingof isopycnals as a result of flow deflection and distortion (Roden 1987). Sea-mounts present less than complete obstructions to the flow, and the tendency ofcurrents to go over and around the topography has special significance for thedistributions of biological species and sedimentary material inhabiting their flanksand near wake (Roberts et al 1974, Boehlert & Genin 1983, Boehlert 1988,Bograd et al 1997). Most significantly, there is abundant evidence (Warren 1963,Eide 1979, Owens & Hogg 1980, Vinje 1982, Martin & Drucker 1997) that large,
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localized, bottom topographic elements such as seamounts or seafloor depressionscan distort the flow to form Taylor column-type features (see below) over thetopographic disturbance.
In general terms, topographic features of mesoscale or global scale are able toexert a dynamic control over vertical distances much greater than their own heightas a consequence of the Proudman-Taylor theorem (Proudman 1916, Taylor 1923)and the associated flow phenomenon of the Taylor column. For the limiting caseof very slow, steady, uniform motion in a homogeneous, rapidly rotating fluid,the flow is constrained by the Proudman-Taylor theorem to be strongly two-dimensional and geostrophic. Thus, the incident fluid not only flows around anyisolated, bottom topographic feature but also deflects at all heights as if by animaginary, upright, solid-cylinder circumscribing it. Numerous analytical studies(of which the classical contributions are those of Jacobs 1964, Ingersoll 1969,and Hogg 1973) have sought to remove the inherent degeneracy in the Proudman-Taylor theorem by retaining ageostrophic terms in the equations of motion. Recenttheoretical work by, for example, Chapman & Haidvogel (1992) and Goldner &Chapman (1997) with tall seamounts enables meaningful comparisons to be made(at least within certain parameter ranges and for specific flow features) betweentheoretical predictions and laboratory and field data on Taylor columnlike flows.
Numerous laboratory modeling studies on Taylor column effects have beencarried out for small but finite Rossby and Ekman number homogeneous flowspast truncated cylinders, depressions, cones, or smooth isolated or wall-attachedobstacles occupying only a fraction of the fluid depth. Such studies (for exampleby Hide & Ibbetson 1966, Hide et al 1968, Vaziri & Boyer 1971, Maxworthy1977, Heikes & Maxworthy 1982, Griffiths & Linden 1983, Boyer et al 1984,Foster & Davies 1996) have not only established the main features of the three-dimensional interior flows above isolated obstacles for rapidly rotating, homo-geneous fluids, but some of the studies have also provided data against whichnumerical models can be validated (Mason & Sykes 1979, 1981, Boyer et al1984, Verron & Le Provost 1985). Both beta- and f-plane studies have beenconducted, although the laboratory data in the latter category are significantlymore extensive.
Figure 2, taken from Boyer et al (1984), demonstrates the dramatic effect theProudman-Taylor effect can have on rotating flows. Figure 2a is a schematicdiagram of the physical system in which a homogeneous rotating flow was forcedto advect past a depression (hole). Figure 2b, c, and d show streaklines (stream-lines) found in the horizontal center plane of the water tunnel for depressions ofincreasing depth. Note that the depression acts as a stronger obstacle to the flowas its depth is increased, with Figure 2d illustrating a near ‘‘perfect’’ Taylorcolumn.
The above laboratory studies for homogenous fluids show consistently that thepresence of rapid background rotation is associated with (a) strong steering ofthe upper-level flow by the bottom topography and (b) the downstream generationof inertial waves. The general notion of topographic steering (see, for example,
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Figure 2 Midchannel streaklines for flow over a cylindrical depression. (a) Schematicdiagram of system. The parameter values are Ro 4 4.9(10)12, E 4 7.2(10)14, (Re 468), R/H 4 0.73, and, for (b) 2h/H 4 0.25, (c) 0.75, and (d) 1.50. (From Boyer et al1984).
Hide 1971) of mesoscale flows in the atmosphere and oceans leads naturally toconsiderations of flows that are not only rotating but also have background strat-ification. To date, studies of rotating stratified flows past solid obstacles have beenconfined primarily to laboratory investigations of steering attenuation above (and/or eddy generation downstream of) isolated three-dimensional obstacles (Davies1972, Davies & Rahm 1982, Boyer et al 1987). The study by Davies (1972)established that, for a linear stratification with constant buoyancy frequency N0,the vertical steering attenuation length scale is D( f /N0) for flows in which Ro K
1 and Ek K 1. Further laboratory studies (Boyer et al 1987, Davies et al 1990)for isolated topographies (cone and cosine-squared and truncated cylinders) con-firmed the relevance of this attenuation scale and demonstrated furthermore that,at a given reference elevation above the bottom topography, the degree of stream-line distortion (steering) decreases with (a) increasing Ro for constant Bu and Ekand (b) increasing Bu for constant Ro and Ek. A natural extension of the studiesto nonlinear density gradients was carried out experimentally by Davies & Rahm(1982) and analytically by Foster et al (1990), with results consistent with theabove findings (after suitable redefinition of the buoyancy frequency scale N toaccommodate the variation of N with depth).
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Since the time of the GARP review (Baines & Davies 1980) on laboratoryinvestigations of topographic effects in rotating and stratified fluids, relativelylittle effort has been expended (save for the studies cited above) on the determi-nation of interior-flow details above a topographic disturbance for steady, uni-form-incident flows. Indeed, as the references indicate, subsequent studies in thisarea have concentrated largely on wake flows and the effects of time dependenceand/or spatial nonuniformity in the incident flow.
The study by Boyer et al (1987) for linearly stratified, rotating flow past rela-tively steep isolated obstacles occupying only a fraction of the fluid depth indi-cated that increasing density stratification, by suppressing vertical motion andinhibiting flow over the obstacle, causes vortex shedding to occur behind theobstacles of base diameter D at smaller values of the Re number [Re (4 UD/m)]than in the counterpart weakly stratified cases. Interestingly, however, the dataindicated that the Strouhal (St) number (St 4 nD/U, where n is the eddy sheddingfrequency) of the vortex shedding was not affected significantly by changes inRo and Bu. Such vortex shedding wake flows are seen to be limited in verticalextent to the layer of fluid below the peak of the topography; however, for param-eter values for which vortex shedding does not occur (essentially low-Ro, low-Bu combinations), the downstream disturbance is able to propagate vertically asa lee wave pattern. The crucial observation made by Boyer et al (1987) in thisregard is that, on the horizontal scale of the obstacle, the amplitude of the wavepattern varies in the cross-stream direction. Specifically, the amplitude on theright side of the obstacle (facing downstream) is significantly higher than on theleft side, evidently as a result of the anticyclonic deflection of streamlines overthe obstacle and their consequent displacement to the right as they reach the wake.
A different type of wake flow is observed in homogeneous, rapidly rotating(order unity Ro) flows when the disturbance field is generated by a shallow, three-dimensional obstacle (Richards et al 1992) corresponding in the meteorologicalcontext to a broad hill in the atmospheric boundary layer. Laboratory studies forsuch a flow reveal that the background rotation of the system affects significantlythe conditions for separation of the flow by the hill. For a given obstacle, con-ditions for separation (manifested by the generation of a trailing vortex) are shownto depend primarily on the value of Ro, with higher values of Ro favoring sep-aration and lower values associated with complete suppression of separation.
Spatially nonuniform incident flows have received increased attention in thissubset of laboratory models in recent years, partly as an obvious extension of thework done on the uniform-flow cases cited above and partly in response to newfield measurement data showing upstream velocity shear to be dynamically impor-tant for particular and specific oceanographic and meteorological flow/topographyinteractions (see, for example, Heywood et al 1990). The combined analytical/laboratory study by Davies et al (1991) on the motion of a steady, horizontal,linearly stratified, rotating shear flow U(z) over and around a truncated three-dimensional obstacle illustrates the influence of the shear parameter A (see Sec-tion 2) in modifying the vertical decay of the topographic disturbance from the
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uniform-flow counterpart cases discussed earlier. The study confirmed that thevertical penetration height of the topographic influence decreases with increasingshear for otherwise identical external conditions, evidently as a result of concom-itant increases with height (z) in the value of the local Rossby number Ro(z)above the obstacle. It is noted here, in passing, that a further large body of quan-titative work exists on incident shear flows and topography (see, for example,Leach 1981, Li et al 1986, Pfeffer et al 1989) for cases of baroclinic flow in arotating, differentially heated annulus. Since the time of Fultz (1951), this typeof annulus facility has played a central role (Hide 1969, Hide & Mason 1975) insimulating global-scale atmospheric flows. In consequence, differentially heatedannulus flows have attracted a sizeable literature in which a rich variety of flowtypes and nonlinear behavior have been exposed (Read 1993). In view of theserather specialized developments, the authors have, with regret, chosen to defer toothers the task of summarizing the achievements in this important area of rotatingstratified flow.
The U.S. Office of Naval Research supported a multidisciplinary research pro-ject earlier this decade with the objective of obtaining a better understanding ofthe physical and biological effects (and their interaction) of an isolated seamounton its local current environment. The seamount chosen for the study was Fieber-ling Guyot (located in the eastern north Pacific). The field component of the studyincluded a moored array of current and temperature sensors that were deployedin the vicinity of the seamount (Eriksen 1995). During preliminary field studiesit became apparent that, because of the presence of tidal motions, the assumptionthat had typically been made by most numerical and laboratory modelers up untilthat time of a uniform, rectilinear, steady-approach flow was not to be realized,even approximately, at Fieberling. In addition, the assumption that Fieberling wasisolated was brought into question by the proximity of a number of neighboringseamounts including Hoke Guyot.
Within this program, laboratory model experiments were conducted for theidealized configuration of a linearly stratified, rotating system in which theapproach flow to the seamount consisted of an oscillatory flow superimposed ona uniform rectilinear motion in the same direction. Experiments by Zhang &Boyer (1993) showed that such a configuration leads to a rectified anticyclonicflow around the seamount, the strength of the flow being greatest near the peakof the topography and decaying with increasing depth. These observations werein good qualitative agreement with oceanic measurements at Fieberling. Owingto the effects of stratification, the mean flow generated in the region above themodel was found to be very weak. Codiga (1993) conducted similar laboratoryexperiments (with the exception that the uniform background flow was sup-pressed) and found that wave motions were trapped to the topography and wereobserved to advect anticyclonically around the island. Finally, Zhang & Boyer(1991) investigated the matter of the influence of the velocity field in the vicinityof the seamount caused by the presence of neighboring seamounts. Experimentswere conducted for a range of seamount orientations and separation distances.
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Figure 3 Infrared image (see text) of flow past the tip of Cumbrae island, western Scot-land. Distance from the island tip to the offshore edge of the eddy is ;1 km. (From Davies& Mofor 1990).
The influence of neighbors was found to be greatest when the models were bothin line with the free stream.
4.2 Islands and Island Groups
Evidence of interest in oceanic flows around islands (Hogg et al 1978) is foundin the numerous multidisciplinary field study programs (see, for example, CAN-IGO, Bryden & Webb 1998, Stansfield et al 1995, Heywood et al 1990) that havelooked (or are looking currently) at the island flow deformations and their con-sequences for (a) the distribution of naturally occurring biological and chemicalspecies and (b) the fate of contaminants released as a result of anthropogenicactivity. Figure 3 shows an infrared image of a tip eddy formed by tidal flow past
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an island in a shallow coastal channel, with the structure of the eddy beingrevealed by a cold water stream tracer (black) discharging upstream of the islandtip separation site (from Davies & Mofor 1990).
Important areas of interest are (a) oceanic wake flow structures downstreamof islands and island groups, including mutual interactions of individual wakesfrom separate islands, (b) topographically induced distortions to the downstreampycnocline, with localized upwelling and vertical mixing, and (c) boundary mix-ing and the so-called island mass effect. For shallow-water tidal environments(see later), the island boundary-mixing problem is conveniently discussed in termsof island stirring (Simpson et al 1982, Simpson & Tett 1986). Particular issuesrelating to flow distortion by island groups involve the degree to which the groupbehaves kinematically and dynamically as a single ‘‘envelope’’ topographicobstruction to the incident flow—a concept familiar to atmospheric-flow modelersdealing with complex mountain terrain. If the flow through the gaps between theconstituent islands is dynamically important, a number of key modeling chal-lenges are exposed. Save for the wake flow cases discussed below, all of theabove aspects require significantly more investment in modeling effort.
Until ;20 years ago, relatively few investigations had attempted anythingother than qualitative flow visualizations of wake flows in rapidly rotating fluidsystems, with the studies by Boyer (1970) and Boyer & Davies (1982) remainingthe benchmark categorizations for the idealized case of an upright circular cyl-inder in a homogeneous rotating flow (see also, Heywood et al 1990, 1996). Sucha geometry is the obvious one with which to start any modeling investigation ofwake flows behind solid obstacles, because there is a wealth of classical com-parative data already available for the non-rotating counterpart cases (see, e.g.,Tritton 1988). In fact, for deep-water islands like Aldabra (Heywood et al 1990),the upright cylinder is quite a satisfactory topographic idealization, so far as thedownstream wake is concerned.
The studies by both Boyer (1970) and Boyer & Davies (1982) demonstratedthat, in contrast to the nonrotating cases in which the cylinder Re number Rec
(4 UDc /m) is the only controlling dynamical parameter for a cylinder of diameterDc, the flow around an identical cylinder in the rotating frame is determinedinstead by the individual values of both Ro and Ek. Furthermore, across Ro:Ekparameter space the wake flow types associated with the rotating cases havedefinitive structures not observed in the nonrotating counterparts. Qualitatively,such differences are manifested primarily in departures from axial symmetry forregimes in which attached eddy pairs (steady and unsteady) are formed by flowseparation or when eddy shedding takes place. The study by Boyer & Davies(1982) indicated evidence of tuning of the eddy shedding frequency with thebackground rotation frequency, although further quantitative experiments are stillneeded to establish the validity of this finding.
Further laboratory investigations (Boyer & Kmetz 1983, Boyer et al 1984,1987, Chabert d’Hieres et al 1989) of the full cylinder geometry (i.e. the cylinderextending throughout the fluid depth) with homogeneous fluids have established
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that rapid background rotation causes separation and vortex shedding to occur atcritical values of the Reynolds number significantly higher than those for thecorresponding nonrotating cases. Furthermore, for shedding flows, the presenceof rotation results in the formation of an asymmetrical wake flow in whichcyclonic eddies dominate their anticyclonic counterparts—an observationexplained by Hopfinger (1989) in terms of the Rayleigh stability criteria. Asso-ciated theoretical studies by Merkine & Solan (1979), Merkine (1980, 1985),Walker & Stewartson (1972), and Matsuura & Yamagata (1985) offer qualitativesupport for some of these results.
Davies et al (1990) have presented experimental results on the flow past acylinder in a rotating, linearly stratified fluid. Both transient and fully developedflow states were investigated in these studies, and the fully developed flows wereshown to be of three main types, delineated respectively as attached eddy pairs,transitional, and vortex wakes. The boundaries between each flow type are evi-dently determined primarily by the values of the Reynolds and Burger numbersof the flow. The weakening effects of density stratification on characteristic fea-tures of rapidly rotating homogeneous flows are seen to be twofold: first, thewake asymmetries associated with the homogeneous flows are destroyed by thestratification, and, second, the retention times of starting eddies, the eddy growthtimes, and the isolated eddy formation times no longer tune with the background-rotation time scale but to scale with the advective time scale of the motion andthe aspect ratio of the cylinder.
An important distinction has to be made between steep and shallow islandtopography, particularly for oceanic islands where both wind flow and oceanicdynamics are closely coupled. For example, tall volcanic oceanic island groupssuch as Hawaii, the Canaries, and the Azores present significant barriers to inci-dent wind fields [with consequent effects on rainfall distribution and distinctivemicroclimate on the islands themselves (Rodriguez 1994)] and oceanic currents.Significantly, the blockage to the wind field produces shadow zones in the lee ofthe individual islands in the group, with spatial variations in surface wind stresson the affected ocean. The consequences for localized oceanic upwelling may besignificant (e.g. Barton et al 1998, Lumpkin 1998), particularly where interpre-tations are required of remotely sensed sea surface temperature images showingzones of anonymously high or low temperatures downstream of islands or islandgroups.
A different mechanism invoked (see, for example, Wolanski et al 1984) toexplain the formation of such patterns has been upwelling by Ekman pumpingafter flow separation of the surface oceanic current by the island itself. However,for some sites (such as Rottnest Island, Australia), upwelled zones are observedin the lee of the islands even under conditions in which separation is not deemedto occur (Alaee 1998); in such circumstances, a model depending on upwellingfrom the generation of a secondary circulation in the plane normal to the directionof flow (as a result of flow curvature-induced centrifugal action) has been invokedwith some success (Alaee et al 1999) to interpret direct field data taken near
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Rottnest. Encouraging results from the application to this site of the HAMSOMthree-dimensional primitive equation numerical model (Backhaus 1985) havealready been obtained but the general topic of upwelling in the lee of deep andshallow water islands suffers significantly from a lack of data from parametric,quantitative laboratory model experiments. Field data from the waters surround-ing the Aldabra atoll (Heywood et al 1990, 1996) indicate that deep-ocean-modelstudies of such an island should consider (Davies & Osborne 1999) the role ofthe upstream shear in the incident current as well as the two-layer density con-figuration of such a flow if plausible mechanisms for pycnocline elevation and/or doming are to be achieved.
Wakes associated with shallow water flows past islands (Pattiaratchi et al 1986,Tomczak 1988, Wolanski et al 1984, Wolanski 1986) are known to possess par-ticular characteristics not encountered in the deep-sea prototype cases discussedthus far, not least because of (a) the increased role played in the former environ-ments by friction and (b) the enhanced influence of the ambient turbulence gen-erated by flow over the surrounding rough sea floor. For some locations, thedensity structure of the water column is also a dominant constraint. As a result,several authors have proposed that background rotational effects are not dynam-ically significant for determining the structure of the shallow-water wake flows,even for a fully vertically mixed environment. Instead, the wake structure appearsto be described satisfactorily by the value of a so-called wake parameter P (4UoH
2/KzD, with Uo being the incident fluid velocity, H and D the fluid depth andisland horizontal dimension, respectively, and Kz the vertical-eddy viscosity).Recent elegant laboratory data (Chen & Jirka 1995) on shallow, nonrotating flowpast a circular cylinder shed new light on the flow details in the near wake; openquestions remain about the modifications that might be caused to such flows(particularly the large far-field coherent structures within the wake) by back-ground rotation.
The problem of eddy-topography encounters is particularly relevant to themotion of advected or self-propelled isolated eddies past seamounts and islandgroups. In the oceanic context, there is an interest in the fate of meddies—isolatedlenses of Mediterranean water thought to be generated by topographic action atcanyons or capes along the Iberian coast (Bower et al 1997)—as they encounterseamounts and island groups in the Canary Basin. Field measurements (Shapiroet al 1995) reveal evidence of disintegration of such flows by collisions withseamounts; an active laboratory-modeling program by one of the authors (Davies)of this review is currently underway to investigate the details of such a collisionover a range of conditions.
4.3 The Coastal Zones
The continental shelf is the transition zone between the coastline and the openocean. The biological and physical processes and their interaction are particularlyimportant in this region because the shelf break and coastal zone (a) are the home
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for most of the world’s salt water fish stocks, (b) are being used increasingly asa source of mineral resources, (c) are being used extensively for transportation,and (d), owing to the high population density along coastal regions, are associatedwith significant levels of pollution from a variety of sources. The coastal zone isalso the conduit for the transport of material (e.g. nutrients and particulate matterof natural or man-made origin) from regions near the coastline to the open oceanand the reverse.
Coastal regions are among the most complex of marine environments, owingto (a) the nature of the irregular coastlines and complex bathymetry (steep andtall) and (b) the internal, lateral, and surface forcing by tides, surface waves,winds, background currents, and buoyancy on a wide range of space and timescales. The resulting coastal circulation patterns include both persistent and time-variable fronts, intense currents with strong spatial dependence, internally gen-erated mesoscale variability, large, horizontal water mass contrasts, strong verticalstratification, and regions of intense turbulent mixing in both the surface andbottom boundary layers.
Headlands, promontories, capes, ridges, and canyons interrupt the continentalslope/shelf break/shelf region at irregular intervals. It is generally agreed that theregions associated with these topographic features are characterized by (a)enhanced turbulence, upwelling, and internal wave generation, (b) increasedacross-shelf/-slope material transport, and (c) coastal-trapped wave modification.Field programs addressed to better understanding the circulation patterns andphysical processes in regions of the coastal zone having sharp topographic con-trasts have some inherent shortcomings. For example, owing to the complexityof the oceanic environment and to the high costs of making measurements in thefield, data can be taken at only a limited number of locations and for limitedperiods of time. This precludes the acquisition of good synoptic, time-dependentdata sets. In addition, many physical processes are acting simultaneously (e.g.winds, tides, and advecting mesoscale structures), making it difficult to ascribe aspecific cause to an observed effect. An improved understanding of these complexcoastal processes will depend on the continuing development and refinement ofnumerical models coupled with the acquisition of adequate field data to test themodels. Laboratory experiments have the potential for playing increasinglyimportant roles in this process.
To first order, major coastal current systems such as the California currentsystem, extending as far as and beyond the shelf break, follow the coastal ‘‘wall,’’but the locations of structural features of the current (such as upwelling filaments)are correlated well with the positions of the main topographic (cape) features.[Interestingly, for the counterpart Iberian coastline and eastern boundary currentsystem, modeling studies show that topographic control of upwelling filamentsis not of primary importance (Røed 1996)]. In the near shore zone, large headlandsand promontories steer tidal flows in a characteristic manner (Geyer & Signell1990, Geyer 1993) to generate separated eddies and secondary circulations that
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contribute significantly to coastal dispersion processes. Numerical models of theseprocesses indicate that background rotation cannot be ignored in the determinationof the flow distortion by the cape; see, for example, (a) the study of recirculatedflow in the lee of Bass Point by Denniss et al (1995) and (b) the generic studyby Verron et al (1990) of geostrophic flow past a Gaussian cape. Coastal-flowphenomena associated with the combined action of tidal currents, shallow water,and bottom topography (e.g. Komen & Riepma 1981) have attracted very littlelaboratory modeling effort thus far.
The distortion of coastal currents by capes, ridges, and submarine canyons hasbeen considered in a number of laboratory experiments. Baines (1983), for exam-ple, considered the generation of internal waves by tides in a narrow canyon fora nonrotating fluid and showed that the observed wave motion in the canyon wasforced by the incident barotropic tide from the deep ocean as well as the internalwave reflected back into the canyon from its open mouth.
Narimousa & Maxworthy (1987, 1989) conducted laboratory experiments onsimulated upwelling and downwelling favorable wind stresses in the vicinity ofridges and canyons in coastal-zone geometry. In these experiments a two-layerfluid was brought to anticlockwise solid rotation (i.e. Northern Hemisphere) in acircular tank having a uniform sloping bottom (shallow topography at tank edge);capes and ridges were placed along the test cell periphery. The interior flow wasthen initiated by the clockwise rotation of a rigid circular lid covering the entirefluid surface. This drove an upwelling favorable flow near the coastal region forwhich the front between the fluids of different densities could rise to the surface.
The experiments then indicated that the wake pattern downstream of the par-ticular obstacle being considered. Figure 4a and Figure 4b show the types ofpatterns observed by neutrally buoyant particles and dye tracers, respectively. Theinterested reader is referred to Narimousa & Maxworthy (1989) for further details.
Perenne (1997) and Perenne et al (1997) investigated, by laboratory experi-ments and a numerical model (Haidvogel et al 1991), the characteristics of abarotropic oscillatory motion in the vicinity of a canyon interrupting an otherwisecontinuous slope/shelf-break/shelf geometry; see also Boyer et al (1999). Theforcing flow considered was an oscillatory along-shelf background motion tosimulate time-dependent forcing at subtidal and tidal frequencies. The mean flowfield was characterized by a rectified flow along the canyon boundaries whichthen streamed out along the shelf break on the right side of the canyon, facingtoward the deep ocean (Northern Hemisphere rotation).
Finally, a number of recent model studies (Jacobs et al 1999) have consideredthe motion of buoyancy-driven surface and intermediate water currents along theshelf edge and have demonstrated, in line with related theoretical treatments byCondie (1993) and Willmott & Collings (1997), that the shelf break orographycan play a significant role in determining current behavior and frontal location.Recent model studies (Guo et al 1999) show that buoyancy-driven, intermediate-water currents suffer only local perturbations when they encounter isolated sea-
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Figure 4 Laboratory experiment on the effects of a model ridge (Rg) on upwelling favor-able flow. (a) Neutrally buoyant tracer particles and (b) dye tracers. The rotation directionis signified by X and the shear stress direction by s (see text). The symbols cc and Pcdesignate cyclonic circulation and pinched-off eddies, respectively. (From Narimousa &Maxworthy 1989).
mount features located close to the shelf edge, with minimal density mixing andno significant destabilization or permanent downstream deformation.
4.4 Topographic Effects on the General Circulation
Only a limited number of studies have addressed the question of the laboratorysimulation of the effects of topography on the general circulation of the atmo-sphere or oceans, although it is recognized that substantial efforts are being madethroughout the international scientific community to develop numerical modelsof the general circulation in both the atmosphere and oceans. The economic bene-fits of improved weather and climate forecasting in the atmosphere and currentprediction in the oceans are clear, and thus it is anticipated that the public will
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continue to give this area of inquiry a favored status. Major numerical modelingefforts, for example, are in progress at the European Center for Medium-rangeWeather Forecasting (ECMWF), the U.S. National Center for AtmosphericResearch (NCAR), and the Geophysical Fluid Dynamics Laboratory in Princeton,NJ. It is beyond the scope of this article to provide a literature review in this area.
Early examples of laboratory experiments in this area include those of Baker& Robinson (1969), who designed and developed a rotating spherical shell facilityto model large-scale oceanic circulations. Boyer et al (1993) developed a labo-ratory model aimed at simulating the effects of the bathymetric features of thesouthern ocean in determining the path of the ACC. The bathymetry of the oceanfloor was modeled in a circular test cell containing a homogeneous or linearlystratified working fluid. The model used the source-sink methods discussed aboveto simulate a zonal wind stress that varies inversely with the distance from theAntarctic continent. Planetary beta effects were neglected because the topographicbeta term was shown to dominate over large portions of the model area. Themodel prediction of the streamline deflections gave excellent qualitative agree-ment with the observations. One interesting finding of the study was that thelaboratory experiments demonstrated clearly the importance of two narrow frac-ture zones, the Eltanin and Udintsev, across the mid-ocean ridge near 1358 Wlongitude. Without these fractures, the experiments show that the ACC wouldfollow the mid-ocean ridge moving toward the southwestern coast of South Amer-ica. With the fractures, the model shows that the ACC, after passing through thefractures, moves directly toward the Drake Passage, as shown by numerous fieldstudies.
Boyer & Chen (1987) also developed an f-plane laboratory model to simulatethe general circulation of the Northern Hemisphere as affected by Greenland, theRocky Mountains, and the Himalayas. The model was contained in a rotatingcircular tank filled with a linearly stratified fluid, and the westerlies of the North-ern Hemisphere were simulated by attaching the various model mountain rangesto thin radial supporting arms, which could then be rotated in a clockwise senserelative to the rotating tank; beta effects were neglected. The model simulatedqualitatively such semipermanent features of the Northern Hemisphere circulationas the Aleutian and Icelandic lows, the ridges and troughs in the vicinity of theRocky Mountains and Tibet, and the shedding of the ‘‘southwest eddy’’ in thelee of Tibet.
Owing to the fact that the beta effect cannot be simulated in a continuouslystratified rotating fluid, it is anticipated that laboratory simulations of global-scaleatmospheric and oceanic effects of topography will not be a line of inquiry receiv-ing a great deal of attention in the near future.
4.5 Buoyancy-Driven Motions
Solar heating of the Earth’s surface during the daytime and the cooling by infraredradiation at night can be important factors in determining the behavior of the windpatterns near the Earth’s surface, particularly where significant orographic effects
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Figure 5 Time development of nocturnal drainage flow as measured in the city of Phoe-nix, AZ, during the Phoenix Air Flow Experiments (PAFEX) (Pardyjak, private commu-nication, 1999). The results show that the characteristic drainage speed is of the order of1 ms11. The plot is for the speed only and does not indicate the flow direction.
are present and when the Earth’s rotation affects the flow. Here only the coolingcase is considered.
Chen et al (1993) developed a laboratory model for simulating the global-scalekatabatic wind system that occurs on the Antarctic continent during the Australwinter. Schwerdtfeger (1984) gave a review of the weather and climate in Ant-arctica and points out, for example, that such wintertime drainage flows are asso-ciated with some of the largest wind velocities occurring any place in the world.The Chen et al (1993) laboratory model consisted of an accurately scaled modelof the Antarctic continent placed at the center of a rotating circular test cell andsubjected to prescribed internal cooling. The working fluid was either homoge-neous or linearly stratified. At parameter values appropriate to the atmosphere,the experiments showed that the cooling led to a surface drainage flow and anaccompanying polar cyclone that had characteristics qualitatively similar to atmo-spheric observations (Schwerdtfeger 1984) and numerical-model results (Parish& Bromwich 1987).
The ‘‘Valley of the Sun,’’ which encompasses the metropolitan Phoenix area,is a region for which the synoptic-scale wind fields are quite weak during muchof the year. During these times, the diurnal heating-cooling cycle of the Earth’ssurface, which is caused by solar heating in the daytime and radiative cooling atnight, drives convective upslope and downslope katabatic winds, respectively.These buoyancy-driven winds are important factors in understanding and even-tually predicting the nature of the distribution of urban pollutants during thesetimes of weak synoptic winds. Recent field experiments nicely depict such time-dependent drainage flows (see Figure 5, from Pardyjak, private communication,1999). Based on these measurements, the characteristic speed of the drainage
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flows can be estimated at ;1 m/s. Furthermore, the horizontal scale of the valleybeing studied is ;50 km. This leads to an Ro number on the order of unity, withthe conclusion that background rotation is likely to be a contributing factor indetermining the gross features of this flow. Chen et al (1999) have also conductedlaboratory experiments (nonrotating) for a similar flow, but for the region aroundNogales, AZ, and Nogales, Sonora, Mexico.
As with other topographically influenced flows, the velocity and length scalesassociated with the laboratory experiments lead to laminar flows in the models,whereas the associated flows in nature are clearly turbulent. This leads to theconclusion that laminar laboratory experiments give only some qualitative senseof many of these complex phenomena, because the transport coefficients for heatand momentum are significantly different in the laboratory experiments but,owing to turbulence, have similar values in the atmosphere. The challenge to thelaboratory experimenter is thus to produce a simulation for which the drainageflows are turbulent.
5. TRENDS IN LABORATORY EXPERIMENTATION
5.1 Benchmarks for Numerical Models
An example of the need to have adequate data from actual fluid flows to developnumerical models is the recent study of Haidvogel & Beckman (1995), in whichpredictions from a number of numerical coastal circulation models were comparedfor seemingly identical experiments, i.e. the physical systems, including topog-raphy, fluid-forcing, and basic size and shape of the domain were the same foreach numerical model. The problem was to determine the mean-velocity field fora coastal model whose bottom topography consists of a long shelf, shelf-break,and continental-slope region of constant cross-section, incised by a single isolatedcanyon. The fluid was forced by an oscillatory, along-isobath wind stress whosemagnitude was independent of the cross-isobath coordinate. The numerical mod-els considered included the Geophysical Fluid Dynamics Laboratory ModularOcean Model [GFDLM (Bryan 1969, Cox 1984)], the Miami Isopycnic Coordi-nate Ocean Model [MICOM (Bleck et al 1992)], the Princeton Ocean Model[POM (Blumberg & Mellor 1987)], the Spectral Element Model [SEM (Iskan-darani et al 1995)], and the SPEM model (Haidvogel et al 1991, Hedstrom 1994).For the homogeneous case, the results for the residual (mean) flows were foundto agree quite well qualitatively, but not quantitatively. For example, the maxi-mum pointwise, time-mean current speeds varied by a factor of 2.4 and the resid-ual transports by a factor of 5.2.
The introduction of stratification further increased model-model differences,to the extent of showing substantial qualitative differences. These differences arecaused by various assumptions and simplifications used in writing the equationsof motion and boundary conditions, the specification of the vertical coordinate
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OROGRAPHIC EFFECTS IN FLOWS 191
Figure 6 Schematic diagram of laboratory model to study the effect of along-isobathmotions on the flow in the vicinity of a submarine canyon.
system, the discretization in space and time, the treatment of the advective terms,and subgrid parameterization. This study suggests that significant improvementsmust be made in the models before they can be applied with confidence to realcoastal regions.
Laboratory experiments can provide data sets from real fluid flows that canthen be used by the numerical models as benchmarks or tests of the models. Asan example, Figure 6 is a schematic diagram of a laboratory experiment for inves-tigating the oscillatory (or impulsive), along-isobath flows past a model submarinecanyon. The experiments are conducted by first establishing a rigid-body rotationof the working fluid and then modulating sinusoidally the turntable rotation rate.This establishes an oscillatory, along-shelf, background motion relative to anobserver fixed to the canyon. By seeding the fluid with neutrally buoyant particles,illuminating the flow with a horizontal light sheet at the desired elevation, record-ing the particle motions with a video camera, and analyzing these motions byusing the particle-tracking software Digimage, one can obtain the resulting time-dependent motion field. Figure 7a is an example of the mean horizontal velocityobtained by averaging the time-varying fields over 10 oscillatory cycles; theobservation level is at the shelf break, and the remaining parameter values aregiven in the legend. A statistical analysis of these systems leads to the conclusion
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Figure 7 Mean horizontal flow obtained at shelf-break level for parameter values Rot 40.05, Ro 4 0.1, Bu 4 10.0, E 4 1.3(10)14, h/H 4 0.08, h/D 4 0.5, and h/W 4 0.62;(a) laboratory experiment and (b) SEOM numerical model.
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that the maximum rms value of the fluctuation occurs along the left side of thecanyon (i.e. where the mean velocity is the greatest).
Haidvogel (private communication, 1999) has developed a Spectral ElementOcean Model (SEOM) of the laboratory experiment depicted in Figure 6. TheSEOM solves the oceanic primitive equations, which are essentially the incom-pressible Navier-Stokes equations simplified by the hydrostatic and Boussinesqapproximations. A unique feature of the model is its spatial discretization, whichrelies on isoparametric and conforming hexahedral elements (cubes with curvedsurfaces) with the field variables being continuous across the element edges,whereas the higher-order derivatives are not continuous. Horizontally, the spectralelement grid is unstructured; the elements’ shapes, sizes, and connectivity areadjusted to suit the dynamical scales of interest and geometrical constraints of theproblem. Within each element, the solution is approximated with a high-orderLagrangian interpolant whose collocation points are the Gauss-Lobatto roots ofthe Legendre polynomials. SEOM has several desirable features for high-resolution, idealized process modeling, including accuracy, low-implicity dissi-pation, and high scalability on parallel computers (Haidvogel & Beckmann 1999).
Figure 7b is the time–mean-velocity field predicted by the SEOM model byaveraging the time-varying velocity fields over 10 oscillation cycles; the param-eter values are the same as for Figure 7a. There is generally good qualitativeagreement between the laboratory results and the numerical predictions. Forexample, both show jetlike mean flows on the left and upper-right sides of thecanyon and a flow from the mouth to the head of the canyon. The numericalmodel does not reproduce some details of the laboratory flow. Furthermore, somefeatures of the numerical model, such as the jet along the right side of the canyonand along the shelf break to the left and right of the canyon, are not apparent inthe laboratory model. These laboratory–numerical-model differences representchallenges for the numerical studies, because the good repeatability of the result-ing laboratory data suggests that one can have substantial confidence in the lab-oratory measurements.
For any such laboratory models to be useful as benchmarks, it is essential thatthey provide levels of uncertainty related to the various measured questions con-sidered. This aspect of experimental work on the motion of rotating and stratifiedfluids past complex topography has not had a great deal of attention in the past,but it is surely critical if the quantitative comparisons of the laboratory and numer-ical flows are to be meaningful. A metric method also needs to be developed toassess the performance of different models vis-a-vis the data.
Although it is natural to begin the laboratory–numerical-model comparisonswith laminar flows, it is clear that, in the future, these flows must both be turbulent.The critical matter related to the comparison is that the laboratory model providesdata from an actual fluid motion. Finally, it should be noted that laboratory mea-surements in no way are substitutes for numerical-model comparisons with fielddata. More confidence, however, can be ascribed to numerical models that have
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first been tested by comparisons with synoptic data in space and time—dataobtained from actual fluid flows.
5.2 Turbulence Modeling
Until recently, most laboratory experiments concerned with the effects of topo-graphic features (say models with isolated seamounts) on the motion of rotatingflows (homogeneous incompressible or stratified) focussed on such matters as thedeflection and distortion of the mean background flow. Field studies on topo-graphic effects, such as the U.S. Office of Naval Research’s project (Erickson1995) conducted at Fieberling Guyot, showed clearly that, for certain geograph-ical locations, the overall motion field is dominated by fluctuations near a zeromean rather than some mean background current. For the Fieberling case, thetemporal fluctuations are predominantly tidal (see Ericksen 1991 and Brink 1995).These observations led to a number of laboratory studies on the interaction ofunsteady background currents with isolated topography, for example, Zhang &Boyer (1993) and Codiga (1993). These studies of unsteady background flowsused, as did their uniform-approach-flow predecessors, laminar conditionsthroughout the flow field.
To relate laboratory flows to their environmental counterparts, arguments weremade that the appropriate viscosity coefficients in the environmental cases wereconstant-eddy-viscosity coefficients whose values were much larger than themolecular viscosity of the laboratory experiments. This allowed reconcilable esti-mates to be obtained of such parameters as the Ekman and Re numbers betweenthe two systems. It is well known, however, that the transport properties of laminarand turbulent flows differ fundamentally, and these eddy viscosity arguments havelimited value for predictive purposes. Should there be no possibility of examiningturbulent flows in the laboratory, little further progress in laboratory studies ontopographic effects could be anticipated for this class of problems.
Because of the overarching importance of turbulence in large-scale environ-mental flows and the fact that large turntables such as the Coriolis facility can, atleast in principle, accommodate facilities of the size required to realize turbulentflows of stratified and rotating fluids, we suggest that a concerted effort be madeto develop appropriate facilities to study this important problem. These studiesshould also be closely tied to numerical-model developments, owing to the dif-ficulty of obtaining good synoptic field data to test the models and to the fact thatnumerical models must eventually be the key for predicting environmental flows.
It is clear that the Re number obtainable in any laboratory experiment for whichbackground stratification and rotation are important can never be as large as inthe natural system being simulated. Nevertheless, the argument of Re numbersimilarity can be used, leading to the hypothesis that for sufficiently large Renumbers and for flows for which the approach flow is turbulent, the resultingflows are independent of the Re number.
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The development of a facility to investigate the effect of topography on strat-ified, rotating, turbulent background flows would, of course, be significantly morecomplex than for the counterpart laminar flow. To obtain large Re numbers whileat the same time retaining small Ro numbers, such a facility would necessarilyrequire a larger turntable of the size, for example, of the Coriolis platform inGrenoble.
Recalling the physical system given schematically in Figure 1 and now con-sidering a turbulent approach or background flow having a unidirectional mean-shear flow , whereU(z, t)
U(z, t) 4 U (z) ` U (z) sin (x t), (6)0 1 0
, and x0 are taken as characteristic mean values of the approach speed andU , U0 1
the amplitude and frequency of the fluctuating component, respectively. Theapproach flow is also taken to be characterized by the rms velocity scale r, theintegral-length scale L1, and the mean-characteristic-buoyancy frequency . TheNexternal parameter set also includes the Coriolis parameter f and the geometricparameters H, D, W, and h, which are the fluid depth and topography length,width, and height, respectively. Thus, assuming that the profiles of the mean- andfluctuating-velocity components and the buoyancy frequency are similar in thelaboratory and nature, the system, although a simplified one, is nevertheless char-acterized by 11 parameters. Each flow phenomenon to be associated with thecurrent topography interaction, for example, a, can thus be written in the form
a 4 F(U , U , x , r, L , N, f, H, D, W, L). (7)0 1 0 1
There are at least five characteristics of the resulting system that should be param-eterized in terms of the external parameters delineated in Equation 7. These are(a) the mean flow structure in the vicinity of the topographic feature and in thefar field, (b) the structure of the turbulence above and downstream of the topog-raphy, (c) the wave field and the associated dynamics (e.g. lee waves, topograph-ically trapped waves, internal waves, and internal tides), (d) buoyancy fluxesassociated with topographic mixing, and (e) the lift and drag on the topography.
We anticipate that the mean flow structure will bear many qualitative similar-ities to its laminar counterpart, that is, anticyclonic motions atop the feature forsteady background flows and rectified anticyclonic flow around the topographyfor the oscillatory flows. However, we expect substantial quantitative differencesin the mean flow field, owing to the different momentum transport mechanismsof the two systems. After the acquisition of good data sets for the mean flow andan objective measure of the errors involved, the challenge is to parameterize theeddy coefficients based on Equation 7 and then to use suitable numerical modelsto predict the mean-flow field. These comparisons will give a good check on theparameterizations used in the numerical model and thus provide a validation ofthe model against a turbulent-flow field akin to the oceanic case. Particular atten-tion should be given to the distortions of the mean flow caused by the topographicfeature and to large-scale features of the flow that may be introduced. One inter-
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esting aspect is a determination of the critical Re number at which eddies beginto attach to the topography and then the condition for eddy shedding from thetopography.
The turbulence field will, of course, be distorted by the topography. Duringthe distortion the smaller scales are expected to be relatively undisturbed whereasnew scales might be formed and the larger scales strongly distorted. Knowledgeof this distortion field might be tied to an improved parameterization of the eddycoefficients in the vicinity of the topography in the numerical model. By carefullaboratory–numerical-model comparisons, improved parameterization of the eddycoefficients in complex terrain might be attained.
ACKNOWLEDGMENTS
The authors thank the U.S. National Science Foundation and the Office of NavalResearch, NATO Scientific Affairs Division, The Carnegie Trust for the Univer-sities of Scotland, and the UK Natural Environment Research Council for thesupport provided to the authors for their individual and collaborative researchover the past several decades. We also acknowledge the helpful discussions wehave had with Harindra J. S. Fernando regarding aspects of the review. Thanksare also given to Nicholas Perenne and Dale Haidvogel for providing data ontheir submarine-canyon studies in advance of their publication. Finally, theauthors dedicate this review to the late David Tritton, a longtime friend andmentor whose keen insight into the mechanics of fluids and warm and pleasantdemeanor are the envy of us all.
Visit the Annual Reviews home page at www.AnnualReviews.org.
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Annual Review of Fluid Mechanics Volume 32, 2000
CONTENTS
Scale-Invariance and Turbulence Models for Large-Eddy Simulation, Charles Meneveau, Joseph Katz 1
Hydrodynamics of Fishlike Swimming, M. S. Triantafyllou, G. S. Triantafyllou, D. K. P. Yue 33
Mixing and Segregation of Granular Materials, J. M. Ottino, D. V. Khakhar 55
Fluid Mechanics in the Driven Cavity, P. N. Shankar, M. D. Deshpande 93
Active Control of Sound, N. Peake, D. G. Crighton 137
Laboratory Studies of Orographic Effects in Rotating and Stratified Flows, Don L. Boyer, Peter A. Davies 165
Passive Scalars in Turbulent Flows, Z. Warhaft 203
Capillary Effects on Surface Waves, Marc Perlin, William W. Schultz 241Liquid Jet Instability and Atomization in a Coaxial Gas Stream, J. C. Lasheras, E. J. Hopfinger 275
Shock Wave and Turbulence Interactions, Yiannis Andreopoulos, Juan H. Agui, George Briassulis 309
Flows in Stenotic Vessels, S. A. Berger, L-D. Jou 347
Homogeneous Dynamos in Planetary Cores and in the Laboratory, F. H. Busse 383
Magnetohydrodynamics in Rapidly Rotating spherical Systems, Keke Zhang, Gerald Schubert 409
Sonoluminescence: How Bubbles Turn Sound into Light, S. J. Putterman, K. R. Weninger 445
The Dynamics of Lava Flows, R. W. Griffiths 477
Turbulence in Plant Canopies, John Finnigan 519
Vapor Explosions, Georges Berthoud 573
Fluid Motions in the Presence of Strong Stable Stratification, James J. Riley, Marie-Pascale Lelong 613
The Motion of High-Reynolds-Number Bubbles in Inhomogeneous Flows,J. Magnaudet, I. Eames 659
Recent Developments in Rayleigh-Benard Convection, Eberhard Bodenschatz, Werner Pesch, Guenter Ahlers 709
Flows Induced by Temperature Fields in a Rarefied Gas and their Ghost Effect on the Behavior of a Gas in the Continuum Limit, Yoshio Sone 779
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