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R otating tanks have been in use for many years(e.g., Siemens 1866; Mallock 1896; Taylor 1921;Hide 1958; Fultz et al. 1959; Cenedese and White-

head 2000) because of their ability to simulate geo-physical fluid dynamical (GFD) phenomena, sheddinginsight on the sometimes complicated mathematicsused to describe such processes. The devices come ina wide variety of sizes, from small record-player-typeturntables with 10-cm-diameter tanks to the world’slargest turntable with its 13-m-diameter tank atGrenoble, France (Sommeria 2001). Rotating tabledemonstrations and experiments have been and con-tinue to be carried out at specialized GFD laborato-ries around the world, such as those at Woods Hole

Oceanographic Institution, University of California atSan Diego, Cambridge University, and several others.Useful results depend, of course, on the ability to es-tablish dynamical similarity of the laboratory experi-ment with the geophysical phenomenon of interest.

Since there can be many dimensionless parameters(Rossby number, Richardson number, Ekman num-ber, Reynolds number, Prandtl number, Froude num-ber, etc.), precise dynamical similarity is not possible,and one must be satisfied with concentrating on justa few dominant parts of the total dynamics. Becausethey allow us to focus on the basic physics, laboratoryexperiments with rotating fluids can be very usefuland can form an important part of our research tools,which also include observations, theory, and numeri-cal modeling. Laboratory experiments with rotatingfluids can also be an important part of educationalprograms in meteorology and oceanography.

HISTORY OF THE CSU SPIN TANK. In thefall of 2000, the Colorado State University (CSU) De-partment of Atmospheric Science decided to offer agroup of graduate students the opportunity to designand construct a rotating table for classroom use. Thedevice (the terms “rotating table” and “spin tank” willbe used interchangeably) was funded by student tech-

Design and Construction of an AffordableRotating Table for Classroom Demonstrations

of Geophysical Fluid Dynamics Principles

BY BRIAN D. MCNOLDY, ANNING CHENG, ZACHARY A. EITZEN, RICHARD W. MOORE,JOHN PERSING, KEVIN SCHAEFER, AND WAYNE H. SCHUBERT

AFFILIATIONS: MCNOLDY, CHENG, EITZEN, MOORE, PERSING, SCHAEFER,AND SCHUBERT—Department of Atmospheric Science, Colorado StateUniversity, Fort Collins, ColoradoCORRESPONDING AUTHOR: Brian D. McNoldy, Dept. ofAtmospheric Science, Colorado State University, Fort Collins, CO80523-1371E-mail: mcnoldy@atmos.colostate.eduDOI: 10.1175/BAMS-84-12-1827

In final form 11 April 2003© 2003 American Meteorological Society

A rotating table was constructed on a limited budget. Demonstrations of fundamental concepts

supplement graduate coursework in atmospheric dynamics, giving students the opportunity to

experiment with parameters and gain insight into the phenomena being explored.

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nology fees, which are collected and used each semes-ter for general improvement of the department’s class-room facilities. Although a commercially available, re-search-quality rotating table can cost up to $100,000(Australian Scientific Instruments 2000), that amountis not available to most universities’ classroom budgets.However, many of the same experiments can be per-formed using a less sophisticated apparatus, significantlyreducing cost. The project was formally identified as apracticum course to be held during the spring 2001 se-mester. It attracted the interest of five Ph.D. studentsand one M.S. student from various research groupswithin the department; W. Schubert, professor, volun-teered to supervise the course and offered suggestionsand direction at critical intervals during the project.

After 8 months of thought and work, the spin tankwas completed and began classroom use to illustratesome selected principles in geophysical fluid dynamics.We wish to encourage other departments to build suchan affordable device. In today’s environment of numeri-cal models, we are pleased to introduce a new additionto the often-forgotten realm of rotating tables.

DESIGN. At the onset of the practicum course, wewere familiar with research papers that made use of ro-

tating tables, but we lackedpractical experience in con-struction and operation of anysuch device. Thus, we firstcontacted some experiencedpeople—namely, P. Rhines atthe University of Washingtonand R. Krishnamurti at theFlorida State University, whobrought some key issues toour attention. We needed todecide on the size of the tank,construction materials, rangeof desired rotation rates, mo-tor type, etc., not to mentionsuppliers for all of the partswe would be buying or mak-ing during the project. In ad-dition to those unknownswere several “knowns.” Weneeded to build the entire ap-paratus for under $3,000 (classbudget) and it had to be some-what portable (it will be trans-ported a few times each year).

A fundamental questionto address was, “What prin-ciples of fluid dynamics do

we wish to demonstrate?” The answer to that ques-tion would dictate tank size, tank shape, and demandson the motor. Those parameters had to fit within thebudget. This practicum course focused on design andconstruction, leaving the more complicated demonstra-tions for future classes. We spent more than 1 monthlaboring over how we would build this device, what theallotted time should be for each phase, how sturdy orprecise the components must be, and other details.

CONSTRUCTION. In mid-February 2001, we vis-ited J. Hart and S. Kittelman at the University ofColorado’s Geophysical Fluid Dynamics Laboratory(GFDL; see Hart 2000; Rhines 2002; Marshall 2003,for several examples of using a spin tank for classroomdemonstrations). They not only had some great ad-vice on tank construction and visualization, but theykindly donated to us a 1960-vintage Genesco turn-table, which they had obtained through governmentsurplus. The motor and electronics that once ran theturntable no longer functioned. The old componentswere antiquated and included giant variable resistors,transformers, and vacuum tubes, surrounded by ameticulously engineered maze of what seemed to bekilometers of thin red wire, intimidating even to an

FIG. 1. (a) A closeup of the sliprings used. There are a total of 16separates. Each separate com-prises a brush and a rotor. Therotors are stacked vertically onthe drum. Seven of the lowereight separates were used for ACpower transmission. Two of the upper eight separates were used for analogvideo signal transmission. (b) The motor (and pulley wheel), controller, dial, andAC power plug. (c) Construction of the acrylic tank. The wooden jig can be seenat the base of the tank. A circle of adhesive was first applied to the circularbase, then the tube was immediately, but carefully, placed on top of the plate.

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electrician. However, the mechanical parts of theturntable were very sturdy, well-machined, and ingood working order. Thus, the apparatus was guttedand the remaining core (steel shell, structural sup-ports, drive shaft, slip rings, turntable, and turntablebearings) proved to be a valuable starting point forthe remainder of the project.

At this stage, the problem was essentially to selecta new motor for the turntable. We chose a motorbased on the range of torque it was able to supply, thedimensions, and cost. With the use of gear ratios, themotor (Fig. 1b) provided us with a maximum angu-lar velocity of 3.0 rad s-1 and a maximum torque of34.0 N m.

Slip rings are used to transmit electrical signalsfrom the nonrotating frame to the rotating frame, andour design requirements were to deliver AC powerand analog video signal. The slip rings used in thisdevice comprise a drum with two stacks of eight sepa-rates (rotor/brush pairs), one above the other on thedrive axle below the turntable (Fig. 1a). Two of theupper eight separates were designated for video sig-nal transmission (positive and negative connectionsfor analog video), and seven of the lower eight sepa-rates were designed for standard 120 V AC powertransmission (three positive and three negative toaccommodate household current, and one ground).Care was taken to leave enough physical distance be-tween the “live” separates to reduce cross talk, electro-magnetic interference, or electrical arcing. An alterna-tive to slip rings would be to use battery-powered lightsand camera, and a radio transmitter/receiver for the

video signal. Although slip rings are fairly expensiveand somewhat tedious to wire, they are a worthwhileinvestment because the power and signal passes throughthem with little noise or loss. The slip rings, drive cord,motor, and controller are clearly visible in Fig. 2.

Figure 1c shows the construction of the tank. Thetube is a cylinder 50.8 cm in inner diameter and is 61.0cm tall (capable of holding 124 kg of water). To con-struct the tank, we used a jigsaw to cut a circular pieceof acrylic (55.9 cm in diameter) from a square sheetand the prefabricated tube was then glued to the sheetusing an acrylic adhesive. All acrylic pieces were cho-sen to be 1.3 cm thick, which is amply rigid under thestrains of handling the tank or filling it with water. Be-fore gluing, we constructed a wooden support jig toassure proper placement during gluing and to securethe tank during the drying/curing stage. The assembledtank stood for 2 days beneath 20 kg of evenly distrib-uted mass (cinder blocks on top of a piece of plywood)before disturbing it to en-sure a complete and firmbond was made.

To the platter was at-tached a modular, re-movable superstructuremade of aluminum rodsand clamps to whichlights and a small videocamera were attached.Two rods were tappedand connected perpen-dicular to the turntable,and connected at the topby a rod of the same di-ameter. Clamp holdersare used to assemble thesuperstructure and tohold the electric accesso-ries. A standard ACpower strip is secured tothe turntable. The pur-pose for such a versatilesuperstructure is to allowflexible lighting and visu-alization options in therotating frame. Onesetup is shown in Fig. 3,where the lights areplaced on the side nearthe top of the fluid, andthe camera is placed suchthat it can be pointedstraight down into the

FIG. 2. A photograph of the inside of the apparatus. Keycomponents are (a) the slip rings, (b) motor, (c) drivecord, and (d) motor controller. The dimensions of thebase are 92 cm long, 40 cm tall, and 61 cm wide. Thethick aluminum platter (partially shown at the top ofthe photograph) is 61 cm in diameter and extends 15cm beyond the top of the base.

FIG. 3. A full view of the en-tire spin tank. The base (de-tailed in Fig. 2) supports the(a) platter, (b) tank, and (c)superstructure. Attached tothe superstructure are (d)two small lights and (e) avideo camera. (f) The stan-dard AC power strip at-tached to the platter is alsovisible. The acrylic tank is 61cm tall and 53 cm in diam-eter. The full apparatus, in-cluding the superstructure, is177 cm tall and rests on asturdy wooden cart withlocking wheels.

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fluid. We needed to solder standard RC audio/videojacks to the wires coming from the slip rings. Lightingis also tricky when dealing with a tube of acrylic filledwith water, as finding an acceptable arrangement tominimize reflections takes a lot of patience.

For further details about construction materials,time line, specifications, and still and video files of theexperiments, see McNoldy (2003). Without the inher-ited mechanical parts, the task would have been moredifficult and would have involved a lot of time in themachine shop, but would still have been accomplishedwithin the budget.

DEMONSTRATIONS. Here we present threegeophysical fluid dynamics principles that are easilydemonstrated with the apparatus described in the pre-vious section: Ekman boundary layers, the Taylor–Proudman theorem, and barotropic instability. All arecovered in the first-year graduate-level atmosphericdynamics courses at CSU. The experiments utilize aconstant volume of a rotating, incompressible, homo-geneous fluid (water) with a free upper surface.

Ekman boundary layers, Ekman pumping/suction, andspinup/spindown. Suppose our cylindrical tank hasbeen rotating counterclockwise at a constant angularvelocity for such a long time that the fluid within ithas adjusted to a state of solid-body rotation. In otherwords, when viewed through the video camera in therotating frame, the fluid is motionless. Now supposethe rotation rate of the container is suddenly, but onlyslightly, increased. Except very near the containerfloor and walls, the fluid is now in clockwise motionrelative to the new rotation rate, which is denoted byW. How long will it take for the clockwise motion todisappear, that is, for the fluid to spin up to the newrotation rate? One might argue (erroneously) thatspinup is a pure viscous diffusion process whose timescale can be estimated from the vertical diffusion ofvorticity via the diffusion equation dz/dt = v(d2z/dz2),where z is the initial relative vorticity and v is the ki-nematic viscosity. We can estimate the magnitude ofthe left-hand side of this equation as |z |/td and theright-hand side as v|z |/H2, where td is the diffusiontimescale, and H is the mean fluid depth. Equating themagnitudes of the two sides, we conclude that thediffusion timescale is given by td = H2/v. For the typi-cal values v = 1.0 ¥ 10-6 m2 s-1 and H = 0.15 m, we ob-tain td = 6.25 h. Compared to the actually observedspinup time, td is much too long. The actual spinuptime of the fluid in the tank can be roughly deter-mined by adding some dye just after the containerrotation rate is suddenly increased. As seen from the

video camera rotating with the container, the dyemoves clockwise and eventually comes to a stop afterapproximately 5 min. Thus, td is approximately 75times larger than the observed spinup time.

The resolution of this discrepancy involves consid-eration of the Ekman layer and the associated second-ary circulation. What actually happens during spinupis as follows. Within a few rotation periods after thesudden change of rotation rate, viscous layers are es-tablished along the floor (Ekman layer) and the walls(Stewartson layer) of the tank. The thickness of theEkman layer is O{(v/W)1/2}. For W = 1.0 s-1 and thevalue of v given above, we obtain (v/W)1/2 = 1 mm, sothe Ekman layer is essentially confined to the lowestfew millimeters of the container. In this shallow layer,after a few rotation periods, there is an approximatebalance between the frictional, Coriolis, and pressuregradient forces, with a mass transport outward nearthe floor of the tank and upward along the walls (seeFig. 4). Due to mass continuity, the outward motionalong the floor of the tank induces inward and down-ward motion through most of the fluid interior (i.e.,boundary-layer suction). The suction at the top of theEkman layer causes stretching of vortex tubes in thefluid interior. This stretching increases the relativevorticity and therefore returns the anticyclonic rela-tive vorticity to zero—that is, it returns the fluid to anew state of solid-body rotation. The time requiredto reestablish a state of solid-body rotation via thisprocess can be estimated by considering the vorticitydynamics or the absolute angular momentum dynam-ics of the interior fluid. The spinup time turns out tobe O{E-1/2(2W)-1}, where E = v(2WH2)-1 is the Ekmannumber. For the values of v, W, and H given above,

FIG. 4. Ekman pumping shown schematically through avertical cross section. Relative motion is clockwise asviewed from above the tank. Thick arrows show theEkman layer along the floor of the tank and theStewartson layer along the wall.

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we obtain E ª 2.2 ¥ 10-5, so that the spinup time dueto the secondary circulation is ts ª 212(2W)-1 ª 5 min.

In summary, there are three timescales: 1) the time-scale to set up the Ekman layer, on the order of 10 s inour case; 2) the timescale to spinup the interior via Ek-man suction at the topof the boundary layerand vortex stretching inthe fluid interior, about5 min in our case; 3) thetimescale for diffusionthrough the total depth,about 6 h in our case. Itis the first two time-scales that are most rel-evant to understandingthe actual behavior ofthe fluid in the tank.

Figure 5 illustratesthe Ekman pumpingand resulting second-ary circulation. Thefluid is initially atsolid-body rotation.Several drops of redfood coloring areadded to the fluid atthe surface near thecenter of the tank. Toproduce a strong rela-tive flow, the tank’sangular velocity is sud-denly accelerated. Im-mediately, the dye isdrawn to the bottom ofthe tank, rapidly out-ward along the bot-tom, upward along thesides, and finally thedye moves inwardthrough the bulk of thefluid. In our setup, the fluid achieves solid-body ro-tation again in approximately 5 min.

Greenspan and Howard (1963) presented an elegantmathematical analysis of the spinup problem. The threetimescales discussed above are explicit features of theiranalysis. Very readable summaries of their work can befound in Greenspan (1968, 34–38) and Salmon (1998,146–150). A review of spinup, including the stratifiedcase, can be found in Benton and Clark (1974).

Taylor–Proudman theorem. The Taylor–Proudmantheorem illustrates the powerful constraint that rotation

can place on geophysical flows. The theorem states that,if the Rossby number is small, if friction can be ne-glected, and if there is no baroclinicity, then du/dz =dv/dz = dw/dz = 0, where z is the coordinate parallelto the axis of rotation (i.e., the vertical coordinate). The

small Rossby numberand neglect of frictionmeans that the horizon-tal flow components(u,v) tend to begeostrophic and hori-zontally nondivergent,and therefore that thethermal wind equationsapply. The thermalwind equations relatedu/dz and dv/dz todensity variations alongthe pressure surface(i.e., baroclinicity).Since there are no suchdensity variations in ahomogeneous fluid,then du/dz = dv/dz = 0.With no vertical varia-tion of the horizontalcomponents u and v, itfollows that a materialline initially parallel tothe rotation axis re-mains parallel to thataxis as it moves aroundlike a rigid column.This raises the followingquestion: If we place ashallow obstacle at thebottom of the tank sothat low-level flow isforced around it, willthe fluid at all levelsabove the obstacle flow

in an identical manner, as if there were a phantom ob-stacle extending through the whole depth of the tank(see Fig. 6)?

We tested this in our spin tank as follows. We firstplaced a shallow obstacle (a small unopened can ofFriskies cat food) on the bottom of the tank, abouttwo-thirds of the way out from the center of the tank(see Fig. 7). We then spun up the fluid to a solid body,counterclockwise rotation. After spinup, we slowlyand slightly increased the rotation rate of the con-tainer, thus creating a weak (small Rossby number)clockwise flow relative to the new rotation rate. We

FIG. 5. Photographs from a demonstration of Ekmanpumping. Red dye was added first, followed by greendye, both at the top surface. (top) The rapid outwardmotion along a shallow layer at the bottom of the tank(time scale is a few seconds). (bottom) The broad, dif-fuse return flow through the upper portion of the tank(time scale for the return flow to develop is a few min-utes). Dark area in the middle of the tank is remnantsof dye where it was initially added.

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then dropped red dye on the water surface upstreamof the obstacle, and observed the movement of thedye through the video camera rotating with the table.We used dye that is slightly more dense than waterso that it sank and partially mixed, resulting in a red

color over the entiredepth of the fluid re-gion upstream of theobstacle. The ratheramorphous blob ofred fluid upstream ofthe obstacle is seen inthe top panel of Fig. 7.At a later time (Fig. 7,bottom), the red fluidis seen moving aroundthe phantom obstacle,with no red fluid inthe cylindrical regiondirectly above the trueobstacle. If the flow isobserved from the sideof the tank rather thanfrom the top, one cansee “Proudman pil-

lars” of dye moving around the obstacle like rigid ver-tical rods extending the entire depth of the tank. Thisresult was apparently very surprising even to Taylor(1923), who, as noted by Pedlosky (1987), stated that“the idea appears fantastic, but the experiments . . .show that the true motion does, in fact, approximateto this curious type.”

Although detailed dynamical arguments leading tothe Taylor–Proudman theorem are given in severaltextbooks (e.g., Pedlosky 1987, 42–45), it is our ex-perience that most students do not truly grasp theconcept until they see both the mathematical argu-ment and the laboratory demonstration.

Barotropic instability. While experimenting withspinup and spindown, it is easy to produce flow in-stabilities. For example, near the end of the spinupprocess shown in Fig. 5, water containing red andgreen dye has moved radially outward along the bot-tom, up the side wall, and then radially inward a smalldistance through the remaining depth, stopping itsinward radial displacement when spinup is complete.We end up with a banded pattern near the outer edgeof the tank. Now suppose the rotation rate of the tankis abruptly and significantly decreased. The relativeflow is now counterclockwise, with a large radial shearof the azimuthal velocity near the edge of the tank.In this region of large shear, barotropic instability (il-

lustrated schematically by Fig. 8) begins to set in, asshown by the waviness in Fig. 9 (top). As this insta-bility extracts increasing amounts of kinetic energyfrom the primary circulation, the waves continue toamplify, resembling the cresting and breaking ofocean waves, as shown in Fig. 9 (bottom). These ed-dies can rapidly mix the dye, leaving a featureless col-ored haze. This process can be repeated over and overuntil the water is too murky with dye to see these fea-tures. If the change in rotation rate is not largeenough, the spinup time (see “Ekman boundary lay-ers, Ekman pumping/suction, and spinup/spin-down”) will actually be shorter than the time requiredto set up the barotropic instability, and the aforemen-tioned features will never be seen.

FIG. 6. The Taylor column shownschematically from an angleslightly above the obstacle.The blue arrows represent therelative flow around the ob-stacle and Taylor column.

FIG. 7. Series of photographs from a demonstration ofthe Taylor–Proudman theorem. The fluid is approxi-mately 5 times the depth of the obstacle. (top) Blue dyewas initially added over the obstacle to check that solid-body rotation had been achieved and that the fluid wasessentially two-dimensional through its depth. The ro-tation rate of the tank was then slightly increased, cre-ating a relative flow around the obstacle. Finally, reddye was added “upstream” and the relative flow ad-vected the red dye toward the Taylor column. (bottom)The blue dye remained over the obstacle and the reddye followed around the phantom column.

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WHAT DOES THE FUTURE HOLD? A rotat-ing table can be viewed as a basic facility on whichmany different types of fluid tanks and experimentscan be mounted. We have given only three examplesof the many experiments that can be performed. Toget a feeling for the enormous possibilities, the readeris referred to J. Hart’s (Hart 2000) and J. Marshall’s(Marshall 2003) GFDL Web pages, where many class-room demonstrations are discussed. For example,Hart has shown that even baroclinic instability in adifferentially heated annulus is within the realm ofportable classroom demonstration.

In the near future for our device, we hope to im-prove visualization techniques, to demonstrate awider range of fluid dynamics principles, and to pre-cisely control the motor speed using a computer. Dif-ferent tanks or additions to the current tank wouldallow Rossby waves, baroclinic instability, vortexmerger, and thermal convection to be demonstrated.To show these principles as well as others, complica-tions such as a wave maker, differential heating, con-centric cylindrical tanks, stratified fluids, and variousobstructions to the flow would be required. Althoughcoming at a higher cost, improved visualization could

be achieved by using small reflective particles andspecialized lighting to trace out the flow (e.g.,Greenspan 1968; Griffiths and Linden 1981;Sommeria 2001; Montgomery et al. 2002) rather thaneasily diluted food coloring. Other practicum courses,similar to the one responsible for the creation of theapparatus, will be held in the future with a goal ofperforming some of the experiments listed above.

DISCUSSION. We have demonstrated that it is notdifficult to design and build an inexpensive rotatingturntable with variable rotation rate and with an at-tached video camera. The completed apparatus fitswithin several constraints: 1) it is capable of demon-strating fluid dynamics principles relevant to gradu-ate-level courses; 2) it was completed for under$3,000; 3) it is portable enough to be moved betweenclassrooms; and 4) there are a variety of visualizationoptions from the rotating frame, including live trans-mission to a television and recorded playback. Theentire project took 8 months to complete, with sixstudents each working an average of 1.5 h per week

FIG. 8. A simplified schematic drawing of barotropic orshear instability. (a) A fluid experiences differentialshear (horizontal shear in the atmosphere, and moreprecisely, radial shear in a tank). Assuming the insta-bility criteria are met, the interface will become un-stable, forming waves that (b) amplify, (c) crest, and (d)eventually break.

FIG. 9. (a) Barotropic instability and (b) wave breakingas a result of radial shear in an actual demonstration.Largest vortices are 5 cm in diameter and persist forseveral minutes. As in Fig. 5, the dark area in the middleof the tank is remnants of dye where it was initially added.

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on it. Although we benefited from the donation ofsome important turntable parts, including slip rings,the entire apparatus could still have been constructedwithin the budget (perhaps by choosing a smallertank and a less powerful motor). A project as de-scribed in this paper would take significantly less timeto complete for other departments using our expe-rience as a guide.

The spin tank has been and will continue to beused in the classroom at CSU, utilizing the apparatusitself, or at least a video recording of the demonstra-tions, to complement and enhance the mathematicaltreatment of atmospheric dynamics. In September2001, we presented the finished project at the weeklydepartment seminar in front of a standing-room-onlyaudience. Just weeks later, it was used in a classroomfor the first time, with volunteer class members asoperators and the tank creators as supervisors; studentfeedback was unanimously positive. It is hoped thatfuture classes will continue to improve and build uponthis work, allowing an increasing variety of fluid dy-namics principles to be demonstrated.

In concluding, we would like to reemphasize theimportance of combining laboratory demonstrationswith mathematical derivations in the study of geo-physical fluid dynamics. This view was clearly statedby Greenspan (1968) who begins a mathematicallyrigorous textbook with the opinion that “these dem-onstrations really give the subject life and their rolein developing intuition cannot be overestimated.”

ACKNOWLEDGMENTS. We thank John Davis andBrian Jesse at CSU for their help throughout the construc-tion and testing phases of the project. We are grateful toJohn Hart and Scott Kittelman at CU for their advice andthe gift of an old turntable that we used as the “backbone”of our table. Peter Rhines at UW and Ruby Krishnamurtiat FSU were extremely helpful during the concept and de-sign phases. We would also like to thank Michael Mont-gomery at CSU for his enthusiastic encouragement and forquickly incorporating the laboratory demonstrations intohis atmospheric dynamics course. Finally, helpful com-ments from Jack Whitehead and an anonymous reviewerimproved the manuscript.

REFERENCESAustralian Scientific Instruments, cited 2000: ANU rotat-

ing table. [Available online at http://rses.anu.edu/au/gfd/Gfd_other_pages/rotating_table/index.html.]

Benton, E. R., and A. Clark, 1974: Spin-up. Annu. Rev.Fluid Mech., 6, 257–280.

Cenedese, C., and J. A. Whitehead, 2000: Eddy-sheddingfrom a boundary current around a cape over a slop-ing bottom. J. Phys. Oceanogr., 30, 1514–1531.

Fultz, D., R. R. Long, G. V. Owens, W. Bohan, R. Kaylor,and J. Weil, 1959: Studies of Thermal Convection in aRotating Cylinder with Some Implications for Large-Scale Atmospheric Motions. Meteor. Monogr., No. 4,Amer. Meteor. Soc., 1–104.

Greenspan, H. P., 1968: The Theory of Rotating Fluids.Cambridge University Press, 328 pp.

——, and L. N. Howard, 1963: On a time-dependent mo-tion of a rotating fluid. J. Fluid Mech., 17, 385–404.

Griffiths, R. W., and P. F. Linden, 1981: The stability ofvortices in a rotating, stratified fluid. J. Fluid Mech.,105, 283–316.

Hart, J. E., cited 2000: Geophysical Fluid DynamicsLaboratory, University of Colorado. [Available onlineat http://nimbus.colorado.edu/hart/science.htm.]

Hide, R., 1958: An experimental study of thermal con-vection in a rotating liquid. Philos. Trans. Roy. Soc.London, 250A, 441–478.

Mallock, A., 1896: Experiments on fluid viscosity. Philos.Trans. Roy. Soc. London, 187A, 41–56.

Marshall, J., cited 2003: MIT PAOC experiments.[Available online at http://www-paoc.mit.edu/labweb/experiments.htm.]

McNoldy, B. D., cited 2003: The CSU spin tank. [Avail-able online at http://einstein.atmos.colostate.edu/~mcnoldy/spintank/.]

Montgomery, M. T., V. A. Vladimorov, and P. V.Denissenko, 2002: An experimental study on hurri-cane mesovortices. J. Fluid Mech., 471, 1–32.

Pedlosky, J., 1987: Geophysical Fluid Dynamics. 2d ed.Springer–Verlag, 710 pp.

Rhines, P. B., cited 2002: Geophysical Fluid DynamicsLaboratory, School of Oceanography, University ofWashington. [Available online at http://www.ocean.washington.edu/research/gfd/gfd.html.]

Salmon, R., 1998: Lectures on Geophysical Fluid Dynam-ics. Oxford University Press, 378 pp.

Siemens, C. W., 1866: On uniform rotation. Philos.Trans. Royal Soc. London, 156, 657–670.

Sommeria, J., cited 2001: Coriolis turntable. [Availableonline at http://www.coriolis-legi.org.]

Taylor, G. I., 1921: Experiments with rotating fluids.Proc. Cambridge Philos. Soc., 20, 326–329.

——, 1923: Experiments on the motion of solid bodies inrotating fluids. Proc. Roy. Soc. London, 104A, 213–218.