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Turbulence and waves in numerically simulated slope flows

Published online by Cambridge University Press:  05 August 2009

Evgeni Fedorovich  and
Alan Shapiro
Evgeni Fedorovich
Affiliation:
School of Meteorology, Universtiy of Oklahoma, 120 David L. Boren Blvd., 73072 Norman, USA
Alan Shapiro
Affiliation:
School of Meteorology, Universtiy of Oklahoma, 120 David L. Boren Blvd., 73072 Norman, USA
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Abstract

Direct numerical simulation (DNS) is applied to investigate properties of katabatic and anabatic flows along thermally perturbed (in terms of surface buoyancy flux) sloping surfaces in the absence of rotation. Numerical experiments are conducted for homogeneous surface forcings over infinite planar slopes. The simulated flows are the turbulent analogs of the Prandtl (1942) one-dimensional laminar slope flow. The simulated flows achieve quasi-steady periodic regimes at large times, with turbulent fluctuations being modified by persistent low-frequency oscillatory motions with frequency equal to the product of the ambient buoyancy frequency and the sine of the slope angle. These oscillatory wave-type motions result from interactions between turbulence and ambient stable stratification despite the temporal constancy of the surface buoyant forcing. The structure of the mean-flow fields and turbulence statistics in simulated slope flows is analyzed. An integral dynamic similarity constraint for steady slope/wall flows forced by surface buoyancy flux is proposed and quantitatively verified against the DNS data.

Keywords

Katabaticanabaticnumerical simulationboundary layerturbulenceCatabatiqueanabatiquesimulation numériquecouche limiteturbulence
Type
Research Article
Information
Mechanics & Industry , Volume 10 , Issue 3-4: 19e Congrès français de mécanique (CFM 2009) , May 2009 , pp. 175 - 179
Copyright
© AFM, EDP Sciences, 2009

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References

E. Fedorovich, A. Shapiro, Turbulent natural convection along a vertical plate immersed in a stably stratified fluid, J. Fluid Mech. (2009) to be published
L. Prandtl, Führer durch die Strömungslehre, Vieweg und Sohn, Braunschweig 1942, pp. 382
Shapiro, A., Fedorovich, E., Prandtl-number dependence of unsteady natural convection along a vertical plate in a stably stratified fluid. Int. J. Heat and Mass Transfer 47 (2004) 4911–4927
Shapiro, A., Fedorovich, E., Natural convection in a stably stratified fluid along vertical plates and cylinders with temporally-periodic surface temperature variations, J. Fluid Mech. 546 (2006) 295–311 CrossRef
Shapiro, A., Fedorovich, E., Coriolis effects in homogeneous and inhomogeneous katabatic flows, Q. J. R. Meteorol. Soc. 134 (2008) 353–370 CrossRef