Proceedings of the HYDRALAB IV Joint User …Proceedings of the HYDRALAB IV Joint User Meeting, Lisbon, July 2014 1 INFLUENCE OF SECONDARY OROGRAPHY ON BOUNDARY LAYER SEPARATION AND

Proceedings of the HYDRALAB IV Joint User Meeting, Lisbon, July 2014

1

INFLUENCE OF SECONDARY OROGRAPHY ON

BOUNDARY LAYER SEPARATION AND ROTORS

Ivana Stiperski (1), Brigitta Goger (1), Stefano Serafin (2), Vanda Grubišić (2,3)

(1) University of Innsbruck, Austria, [email protected], [email protected]

(2) University of Vienna, Austria, [email protected], [email protected]

(3) National Centre of Atmospheric Research, United States

Boundary layer separation and attendant rotors are sources of severe turbulence and mixing in the

atmosphere and ocean. In this study we examine the influence of secondary mountain ridges on rotor

characteristics by means of laboratory experiments and numerical models. Modeling results have

suggested the existence of lee wave interference that modulates rotor strength and also point to the

sources of rotor non-stationarity. Laboratory experiments are going to be carried out at the CNRM-

GAME (METEO-FRANCE and CNRS) Toulouse large stratified water flume in order to examine and

extend the regime diagram determining rotor characteristics over double ridge terrain as well as the

internal structure of rotor flow itself with the aim of improved understanding and possible forecasting of

rotor intensity.

1. INTRODUCTION

Complex topographic features cover most of the Earth’s surface both on land and within the oceans

and influence all scales of motions that permeate the oceans and the atmosphere. Flow of stably

stratified fluid over complex topography can lead to the formation of internal gravity waves and in

cases of significant wave amplitudes, to the development of rotors. Rotors, turbulent horizontal eddies

found in the lee of topography, form as the boundary layer separates from the surface due to adverse

pressure gradients caused by topographically induced gravity waves (Hertenstein & Kuettner, 2005).

They can extend to considerable heights, exceeding the height of topography which caused them, and

are a source of significant turbulence, mixing, dissipation and drag important for both atmospheric and

oceanic flows (e.g. Hertenstein & Kuettner, 2005; Chan et al., 2007; Legg & Klymak, 2008; Grubišić

& Stiperski, 2009; Texeira et al., 2013).

Boundary layer separation (BLS) and rotor formation in the lee of a single ridge have received

renewed interest over the past decade (e.g. Doyle and Durran 2002, 2004, 2007; Vosper, 2004; Jiang

et al., 2007; Cohn et al., 2010; Knigge et al., 2010; Sheridan & Vosper, 2012) especially in connection

with the recent Terrain-Induced Rotor Experiment (T-REX; Grubišić et al., 2008) that took place in

Owens Valley, in the lee of the Sierra Nevada in California. Rotor observations during T-REX have

also drawn attention to the influence of secondary ridges on the amplification of BLS and rotors, a

topic that has been the subject of only a limited number of studies. Laboratory experiments and

numerical simulations of flows over and within valleys, performed in the 1980s (e.g. Tamperi & Hunt,

1985; Kimura & Manins, 1988; Lee et al., 1987) have focused on flow stagnation vs. ventilation and

did not address the influence of secondary orography on rotor strength over the valley. They did,

however, identify important non-dimensional governing parameters for valley flows: Froude number

(Fr), ridge separation distance (V) and horizontal wavelength of the terrain-generated waves ().

Rotors can generally be classified into two types: non-hydrostatic trapped lee wave rotors and

hydrostatic hydraulic jump rotors (Hertenstein & Kuettner, 2005: Jiang et al., 2007). Trapped lee

waves forming over double ridges experience lee wave interference (Scorer, 1997 ; Gyüre & Jánosi,

2003; Chan et al., 2007; Grubišić & Stiperski, 2009; Buijsman et al., 2010; Stiperski & Grubišić,

2011). According to linear theory this interference is governed by the ratio of lee wave horizontal

wavelength () to the ridge separation distance (V) (Scorer, 1997; Stiperski & Grubišić, 2011) that

discriminates between the constructive (wave amplitude increases compared to a single ridge case;

Fig. 1a) and destructive (decreased wave amplitude; Fig. 1b) interference. The idealized 2D linear and

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nonlinear numerical results of Stiperski and Grubišić (2011) on trapped lee wave interference over

double bell-shaped mountains show that, although useful for predicting the wave amplitude, the linear

interference theory cannot explain the behavior of rotor strength. The secondary ridge does not

facilitate boundary layer separation and rotor formation (negative horizontal velocity Umin in Fig. 2) for

mountain heights for which it would not occur downstream of a single ridge, nor is the rotor strength

increased under constructive interference. It is, however, decreased under destructive interference. As

mountain height (H) increases, the idealized simulations suggest the existence of a limit to rotor

strength over the valley (U1min is constant for H>1000m in Fig 2). If the secondary ridge is lower than

the primary one, lee wave interference can lead to almost complete cancellation of waves in the lee of

the secondary ridge (Fig. 1c). In this regime, termed complete destructive interference (CDI), waves

and rotors over the valley significantly exceed those further downstream.

Figure 1 An example of constructive (left), destructive (center) and complete destructive

interference (right) for first mountain height equal 600m and second mountain height equal 600m

(left and center) and 400m (right). Horizontal wind speed ([ms-1

], gray scale), potential

temperature ([K], black solid lines) and horizontal pressure perturbations (white lines).

Particularly severe rotors can form in relation to hydraulic jumps (Hertenstein & Kuettner, 2005;

Jiang et al., 2007;Legg & Klymak, 2008). The influence of secondary ridge on hydraulic jump

rotors is expected to be significantly different from that for trapped wave rotors. Real case

numerical simulations of bora-induced rotors along the Croatian coast (Gohm et al., 2008;

Grisogono & Belušić, 2009; Stiperski et al., 2012) show that even significantly smaller-scale

terrain downstream of the primary ridge can, in this regime, significantly alter the rotor strength

and vertical extent and could facilitate boundary layer separation where it would not occur in the

absence of this secondary topography (Stiperski et al. 2012).

Figure 2 Minimum horizontal wind speed (Umin<0 signifies rotors) underneath the first lee wave crest

in the lee of the first (U1min) and second (U2min) mountain as functions of mountain height (H) for a

single ridge (black) and double ridges for different ridge-separation distances (V) leading to

constructive (orange) and destructive (blue) interference (from Stiperski & Grubišić, 2011).

In this study we seek to understand the impact of downstream ridges on BLS and rotor formation

under different flow regimes. Following the experimental work of Knigge et al. (2010) and

numerical simulations of Stiperski and Grubišić (2011) we explore the rotor development over

double ridges in a stratified water flume in connection with both trapped lee waves and undular

hydraulic jumps. Particular stress is given to the investigation of the inner structure of the rotor


3

flow as well as unsteadiness of the boundary layer separation, evidenced in observable shifts of the

location of the BLS point, and to the intensity of turbulence along the separation line and within

the rotor.

2. LARGE EDDY SIMULATIONS

Large Eddy Simulations (LES) of boundary layer separation and rotors were performed prior to the

stratified water flume experiments in order to guide the laboratory set-up and provide the rough

guideline on the correct choice of governing parameters needed to produce the phenomena of interest.

The numerical model used in this study is the Cloud Model 1 (CM1; Bryan, 2009), suitable for

idealized simulations of mesoscale as well as boundary layer phenomena. CM1 is a 3D, time-

dependent and non-hydrostatic numerical model that conserves total energy and mass of a moist

atmosphere. The model was employed at a horizontal resolution of dx = 50m, stretched to dx = 1km at

the lateral boundaries and a variable vertical resolution stretching between 3m to 30 m. The

simulations were run in a two- and three-dimensional configuration. The model was initialized with an

idealized sounding, which contrary to Stiperski and Grubišić (2011) had a temperature inversion and a

constant wind profile to facilitate wave trapping. This idealized upstream sounding is relatively easy to

reproduce in the laboratory experiments.

A series of tests was performed studying the sensitivity of rotor flow to terrain shape and width,

inversion strength and height, wind speed and surface friction. The simulation results show that the

proposed set-up is able to produce both trapped lee wave and hydraulic jump rotors (Fig. 3). The

Froude number reliably predicts different flow regimes and the shift between them (trapped lee wave

vs. hydraulic jump) is most easily achieved by changes in wind speed (towing speed for the flume

experiments) rather than changes in inversion strength or height. Surface friction facilitates boundary

layer separation and together with terrain shape and inversion strength has a profound impact on wave

amplitude. Gaussian shaped terrain, as opposed to bell-shaped mountain or cosine mountain, was

shown to produce largest amplitude waves and strongest rotors.

Placing a secondary ridge downstream of the first one causes the emergence of an interference pattern.

This pattern, however, is not identical to the one obtained by Stiperski and Grubišić (2011), due to the

strong inversion that causes stronger flow non-linearity. A lower downstream ridge (ratio of second to

first ridge = 2/3) does produce complete destructive interference and almost total cancellation of wave

field in the lee of the second ridge for certain ridge separation distances in agreement with Stiperski

and Grubišić (2011).

The strength and height of the inversion has a strong impact on the intensity of the flow, the location

of the BLS point and on the steadiness of the simulation through controlling nonlinear wave-breaking

events, but the main flow regime remains mostly governed by the Froude number. The results thus

conform to the flow regime diagram proposed by Vosper (2004) with some modifications.

The flow regime is not affected by the change from two-dimensional to three-dimensional simulations.

The amplitude of the phenomena, however, is affected so that 3D trapped lee waves induce weaker

rotors than in the respective 2D simulations. Unlike 2D, the 3D simulations on the other hand

reproduce the inner rotor structure and development of intense sub-rotors that are responsible for most

severe turbulence. Trapped lee waves are also shown to be steadier than the hydraulic jump rotors.


4

Figure 3 Trapped lee wave rotor (upper panel) with Fr = 0.38, and hydraulic jump rotor (lower panel)

with Fr = 0.7. Terrain height to inversion height ratio = 0.6 is the same for both simulations. Left: X-Z

cross section of horizontal vorticity ([s-1

], color) and potential temperature ([K], black lines). Right: X-

Z cross section of across-mountain wind speed ([ms-1

] color) and potential temperature ([K], black

lines) (from Goger, 2014, unpublished master thesis)

3. LABORATORY EXPERIMENTS

Laboratory experiments take place in the CNRM-GAME (METEO-FRANCE and CNRS) large

stratified water flume, which allows generation of stratified flow at high Reynolds number with low

confinement effect.

The numerical simulations have shown that regime diagram of Vosper (2004) can be reliably used to

predict the occurrence of trapped lee wave rotors or hydraulic jump rotors. Whereas Knigge et al.

(2010) were already able to reproduce the trapped lee wave rotors in the stratified water flume using

this regime diagram as a guide, it wasn’t clear whether the unsteady hydraulic jump rotors can be

reproduced as well, since they did not occur in the simulations of Vosper (2004).

The following guidelines for the laboratory experiments were obtained from the numerical

simulations. The optimal mountain shape was shown to be Gaussian. The size of the ridges similar to

Knigge et al. (2010) was tested and is used in the experiments (Table 1).

Fig. 4 shows two sketches of the laboratory setup. In panel a, two equally high ridges are placed at a

certain ridge separation distance, which is varied in order to examine lee wave interference. Single

mountain tests have to be conducted first though, in order to determine the horizontal lee wave

wavelength that governs the interference pattern. For the experiments on the influence of a lower

downstream mountain and the associated rotors (Fig. 4b), a strong inversion is important in order to

induce large-amplitude lee waves that lead to rotor formation. In this latter setup, lower-lying

inversions may be useful for testing the reverse flow strength behind both obstacles. The suggested

non-dimensional parameters for the simulations are given in Table 2.

4 Numerical Simulat ions 4.4 3D Simulat ions

Lee wave rotor (T ype 1)

Type 1 rotors are known to form under large-amplitude lee wave crests when BLS occurs.

Fig. 4.33 shows a lee wave rotor after 4.2h of simulat ion t ime of a 2D and 3D simulat ion.

In both cases, a thin sheet of posit ive horizontal vort icity is present on the mountain

slope due to BL shear effects. At the BLS point , the vort icity sheet is lifted into the lee

wave and breaks into smaller vort ices (subrotors). However, due to twist ing and t ilt ing

effects (Doyle and Durran, 2007), the subrotors in the 3D simulat ion are smaller yet more

intense. In both simulat ions, someperturbat ionscan beseen along the inversion, although

the perturbat ions in the 2D simulat ion are larger, especially close to the second lee wave

crest . In the 3D case, however, the perturbat ions remain small-scale and are eventually

dissipated, which is possibly the reason for thickening of the inversion at later simulat ion

t imes.

− 10 − 5 0 5Distance [km]

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Figure 4.33: Lee waves. h/ zi = 0.6, F r = 0.7. Lower panels: X-Z cross-sect ions (Colors: u [m s≠ 1],

contours: ◊ [K ] (intervals2K)); Upper panels: Corresponding X-Z cross-sect ionsof thehorizontal vort icity

(Colors: ÷ [s≠ 1], contours: ◊ [K ] (intervals 2K)).

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4 Numerical Simulat ions 4.4 3D Simulat ions

Lee wave rotor (T ype 1)

Type 1 rotors are known to form under large-amplitude lee wave crests when BLS occurs.

Fig. 4.33 shows a lee wave rotor after 4.2h of simulat ion t ime of a 2D and 3D simulat ion.

In both cases, a thin sheet of posit ive horizontal vort icity is present on the mountain

slope due to BL shear effects. At the BLS point , the vort icity sheet is lifted into the lee

wave and breaks into smaller vort ices (subrotors). However, due to twist ing and t ilt ing

effects (Doyle and Durran, 2007), the subrotors in the 3D simulat ion are smaller yet more

intense. In both simulat ions, someperturbat ionscan beseen along the inversion, although

the perturbat ions in the 2D simulat ion are larger, especially close to the second lee wave

crest . In the 3D case, however, the perturbat ions remain small-scale and are eventually

dissipated, which is possibly the reason for thickening of the inversion at later simulat ion

t imes.


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Figure 4.33: Lee waves. h/ zi = 0.6, F r = 0.7. Lower panels: X-Z cross-sect ions (Colors: u [m s≠ 1],

contours: ◊ [K ] (intervals2K)); Upper panels: Corresponding X-Z cross-sect ionsof thehorizontal vort icity

(Colors: ÷ [s≠ 1], contours: ◊ [K] (intervals 2K)).

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4.4 3D Simulat ions 4 Numerical Simulat ions

H ydraulic Jump Rotor (T ype 2)

The hydraulic jump rotor shows a completely different picture than the lee wave induced

rotor. While the mot ions in the Type 1 rotor is quite organized under the lee wave crest ,

the Type 2 rotor is characterized by completely turbulent flow within the hydraulic jump.

No reverse flow is present at the ground, but rather appears in the turbulent flow within

the hydraulic jump. The temporal and spat ial variability of the eddies is high. As already

noted for Type 1 rotors, the perturbat ions in the 2D simulat ions are stronger than in the

3D case. Some further differences include the locat ion of BLS not being clearly defined

for Type 2 rotors and no reverse flow at the ground but rather appearing in the turbulent

flow behind the hydraulic jump. The values of the horizontal vort icity ÷ are larger in the

3D than in the 2D simulat ions, which is also a sign of the contribut ion of twist ing and

t ilt ing effects in the 3D simulat ions. The upper-level wave breaking contributes to the

split t ing of the inversion, while the reverse flow wind speeds are generally smaller than

in the 2D case. However, in both 2D and 3D, the hydraulic jump rotor flow in the lee

is characterized by rapid changes over t ime in the horizontal vort icity ÷ and u on small

scales, while the port ion of the jump itself mainly remains constant .


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Figure 4.34: H ydraulic jump. h/ zi = 0.6, F r = 0.38. Lower panels: X-Z cross-sect ions (Colors: u

[m s≠ 1], contours: ◊ [K ] (intervals 2K)); Upper panels: Corresponding X-Z cross-sect ions of the horizontal

vort icity (Colors: ÷ [s≠ 1], contours: ◊ [K ] (intervals 2K)).

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4.4 3D Simulat ions 4 Numerical Simulat ions

H ydraulic Jump Rotor (Type 2)

The hydraulic jump rotor shows a completely different picture than the lee wave induced

rotor. While the mot ions in the Type 1 rotor is quite organized under the lee wave crest ,

the Type 2 rotor is characterized by completely turbulent flow within the hydraulic jump.

No reverse flow is present at the ground, but rather appears in the turbulent flow within

the hydraulic jump. The temporal and spat ial variability of the eddies is high. As already

noted for Type 1 rotors, the perturbat ions in the 2D simulat ions are stronger than in the

3D case. Some further differences include the locat ion of BLS not being clearly defined

for Type 2 rotors and no reverse flow at the ground but rather appearing in the turbulent

flow behind the hydraulic jump. The values of the horizontal vort icity ÷ are larger in the

3D than in the 2D simulat ions, which is also a sign of the contribut ion of twist ing and

t ilt ing effects in the 3D simulat ions. The upper-level wave breaking contributes to the

split t ing of the inversion, while the reverse flow wind speeds are generally smaller than

in the 2D case. However, in both 2D and 3D, the hydraulic jump rotor flow in the lee

is characterized by rapid changes over t ime in the horizontal vort icity ÷ and u on small

scales, while the port ion of the jump itself mainly remains constant .


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Figure 4.34: H ydraulic jump. h/ zi = 0.6, F r = 0.38. Lower panels: X-Z cross-sect ions (Colors: u

[m s≠ 1], contours: ◊ [K ] (intervals 2K)); Upper panels: Corresponding X-Z cross-sect ions of the horizontal

vort icity (Colors: ÷ [s≠ 1], contours: ◊ [K] (intervals 2K)).

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5

Table 1. The choice of topography for the laboratory experiments

Figure 4 Possible laboratory setups for the rotor measurements. Both setups include an idealized

vertical profile with a neutral lower layer and a stable upper layer, but in setup 2, the inversion is

stronger. Setups also differ in mountain height ratio, the mountain heights (i.e. inversion height) and

the horizontal wind speed (from Goger, 2014, unpublished master thesis)

The unique characteristics of the large stratified water flume combined with the CNRM-GAME fluid

mechanics laboratory team expertise on measurements in high Reynolds number stratified flows

allows not only the study of rotor development within the valley and downstream of the two ridges,

but also an unprecedented insight into the inner rotor structure, such as sub-rotors, breakup into

turbulence, characteristics of the boundary layer at the separation point etc.

Table 2. Non-dimensional parameters for the laboratory experiments

Parameter Setup 1 Setup 2

Density 1121 kg m-3

1121 kg m-3

Inversion strength 13 kg m-3

31 kg m-3

Brunt-Väisälä frequency 1 s-1

1 s-1

Valley width 50-150 cm 200 cm

Inversion height 26 cm 16.3 cm

Mountain height/

inversion height

0.5 0.8

Wind speed 26 cm s-1

26 cm s-1

(Lee waves)

13 cm s-1

(Hydraulic jump)

4. DISCUSSION

Laboratory experiments are going to be performed in the summer of 2014 in the CNRM-GAME

(METEO-FRANCE and CNRS) large stratified water flume. They will allow us to investigate, for

Mountain

height [cm]

Horizontal scale

(2L2) [cm

2]

Total mountain

width (L0) [cm]

First ridge 13.2 1060 66.3

Second ridge 13.2 1060 66.3




6

the first time in the laboratory, the influence of secondary obstacles on the rotor flow. The

relevance of laboratory experiments carried out in this tank on atmospheric lee waves and rotors

has been demonstrated by Knigge et al. (2010). It relies on the unique characteristics of this tank,

combining large dimensions to the ability to generate high Reynolds number and stratified flows.

These experiments will extend the results from Knigge et al. (2010) carried out with a single

obstacle, and therefore extend the regime diagram of Vosper (2004) adding valley width and

second mountain height as additional parameters. They will also allow a closer look at the

turbulence and inner structure of the rotor flow. It will give a unique opportunity to compare an

extensive dataset on a perfectly controlled high Reynolds number stratified real flow to prediction

of numerical simulations, in which turbulence properties may be affected among other things by

small scales parameterizations.

ACKNOWLEDGEMENTS

This work has been supported by European Community's Seventh Framework Program through

the grant to the budget of the Integrating Activity HYDRALAB IV within the Transnational

Access Activities, Contract no. 261520. Work of Brigitta Goger and Stefano Serafin was financed

through the STABLEST - Stable boundary-layer separation and turbulence grant to FWF.

This document reflects only the authors’ views and not those of the European Community. This

work may rely on data from sources external to the HYDRALAB IV project Consortium.

Members of the Consortium do not accept liability for loss or damage suffered by any third party

as a result of errors or inaccuracies in such data. The information in this document is provided ‘‘as

is’’, and no guarantee or warranty is given that the information is fit for any particular purpose.

The user thereof uses the information at its sole risk and neither the European Community nor any

member of the HYDRALAB IV Consortium is liable for any use that may be made of the

information. We thank A. Belleudy, R. Calmer, J.-C. Canonici, F. Murguet, A. Paci and V. Valette

of the CNRM-GAME (UMR3589, METEO-FRANCE and CNRS) fluid mechanics laboratory for

their work preparing the experiments.

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Proceedings of the HYDRALAB IV Joint User …Proceedings of the HYDRALAB IV Joint User Meeting, Lisbon, July 2014 1 INFLUENCE OF SECONDARY OROGRAPHY ON BOUNDARY LAYER SEPARATION AND