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Spectral eddy viscosity of stratified turbulence

Published online by Cambridge University Press:  18 August 2014

Sebastian Remmler  and
Stefan Hickel Open the ORCID record for Stefan Hickel [Opens in a new window]
Sebastian Remmler*
Affiliation:
Institute of Aerodynamics and Fluid Mechanics, Technische Universität München, 85747 Garching bei München, Germany
Stefan Hickel
Affiliation:
Institute of Aerodynamics and Fluid Mechanics, Technische Universität München, 85747 Garching bei München, Germany
*
†Email address for correspondence: remmler@tum.de
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Abstract

The spectral eddy viscosity (SEV) concept is a handy tool for the derivation of large-eddy simulation (LES) turbulence models and for the evaluation of their performance in predicting the spectral energy transfer. We compute this quantity by filtering and truncating fully resolved turbulence data from direct numerical simulations (DNS) of neutrally and stably stratified homogeneous turbulence. The results qualitatively confirm the plateau–cusp shape, which is often assumed to be universal, but show a strong dependence on the test filter size. Increasing stable stratification not only breaks the isotropy of the SEV but also modifies its basic shape, which poses a great challenge for implicit and explicit LES methods. We find indications that for stably stratified turbulence it is necessary to use different subgrid-scale (SGS) models for the horizontal and vertical velocity components. Our data disprove models that assume a constant positive effective turbulent Prandtl number.

JFM classification

Turbulent Flows: Homogeneous turbulence Turbulent Flows: Stratified turbulence Turbulent Flows: Turbulence modelling
Type
Rapids
Information
Journal of Fluid Mechanics , Volume 755 , 25 September 2014 , R6
Copyright
© 2014 Cambridge University Press 

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References

Aspden, A. J., Nikiforakis, N., Dalziel, S. B. & Bell, J. B. 2008 Analysis of implicit LES methods. Commun. Appl. Math. Comput. Sci. 3 (1), 103–126.CrossRefGoogle Scholar
Brethouwer, G., Billant, P., Lindborg, E. & Chomaz, J.-M. 2007 Scaling analysis and simulation of strongly stratified turbulent flows. J. Fluid Mech. 585, 343–368.CrossRefGoogle Scholar
Chollet, J.-P.1984 Two-point closures as a subgrid scale modeling for large eddy simulations. In 4th Symposium on Turbulent Shear Flows (ed. H. Viets, R. J. Bethke & D. Bougine), p. 9.Google Scholar
Domaradzki, J. A., Metcalfe, R. W., Rogallo, R. S. & Riley, J. J. 1987 Analysis of subgrid-scale eddy viscosity with use of results from direct numerical simulations. Phys. Rev. Lett. 58 (6), 547–550.CrossRefGoogle ScholarPubMed
Dougherty, J. P. 1961 The anisotropy of turbulence at the meteor level. J. Atmos. Sol.-Terr. Phys. 21, 210–213.Google Scholar
Galperin, B. & Sukoriansky, S. 2010 Geophysical flows with anisotropic turbulence and dispersive waves: flows with stable stratification. Ocean Dyn. 60, 1319–1337.Google Scholar
Germano, M., Piomelli, U., Moin, P. & Cabot, W. H. 1991 A dynamic subgrid-scale eddy viscosity model. Phys. Fluids A 3 (7), 1760–1765.CrossRefGoogle Scholar
Godeferd, F. S. & Cambon, C. 1994 Detailed investigation of energy transfers in homogeneous stratified turbulence. Phys. Fluids 6 (6), 2084–2100.CrossRefGoogle Scholar
Godeferd, F. S. & Staquet, C. 2003 Statistical modelling and direct numerical simulations of decaying stably stratified turbulence. Part 2. Large-scale and small-scale anisotropy. J. Fluid Mech. 486, 115–159.Google Scholar
Heisenberg, W. 1948 Zur statistischen Theorie der Turbulenz. Z. Phys. A 124, 628–657.CrossRefGoogle Scholar
Hickel, S., Adams, N. A. & Domaradzki, J. A. 2006 An adaptive local deconvolution method for implicit LES. J. Comput. Phys. 213, 413–436.CrossRefGoogle Scholar
Hickel, S., Adams, N. A. & Mansour, N. N. 2007 Implicit subgrid-scale modeling for large-eddy simulation of passive scalar mixing. Phys. Fluids 19, 095102.Google Scholar
Khani, S. & Waite, M. L. 2013 Effective eddy viscosity in stratified turbulence. J. Turbul. 14 (7), 49–70.CrossRefGoogle Scholar
Kitsios, V., Frederiksen, J. S. & Zidikheri, M. J. 2012 Subgrid model with scaling laws for atmospheric simulations. J. Atmos. Sci. 69 (4), 1427–1445.CrossRefGoogle Scholar
Kitsios, V., Frederiksen, J. S. & Zidikheri, M. J. 2013 Scaling laws for parameterisations of subgrid eddy–eddy interactions in simulations of oceanic circulations. Ocean Model. 68, 88–105.Google Scholar
Kraichnan, R. H. 1976 Eddy viscosity in two and three dimensions. J. Atmos. Sci. 33, 1521–1536.Google Scholar
Lilly, D. K. 1992 A proposed modification of the German subgrid-scale closure method. Phys. Fluids A 4 (3), 633–635.CrossRefGoogle Scholar
Orszag, S. A. 1970 Analytical theories of turbulence. J. Fluid Mech. 41 (02), 363–386.Google Scholar
Ozmidov, R. V. 1965 On the turbulent exchange in a stably stratified ocean. Izv., Atmos. Ocean. Phys. 1, 493–497.Google Scholar
Pope, S. B. 2000 Turbulent Flows. Cambridge University Press.CrossRefGoogle Scholar
Remmler, S. & Hickel, S. 2012 Direct and large eddy simulation of stratified turbulence. Intl J. Heat Fluid Flow 35, 13–24.CrossRefGoogle Scholar
Remmler, S. & Hickel, S. 2013 Spectral structure of stratified turbulence: direct numerical simulations and predictions by large eddy simulation. Theor. Comput. Fluid Dyn. 27, 319–336.Google Scholar
Shu, C.-W. 1988 Total-variation-diminishing time discretizations. SIAM J. Sci. Stat. Comput. 9 (6), 1073–1084.Google Scholar
Smagorinsky, J. 1963 General circulation experiments with the primitive equations. I: The basic experiment. Mon. Weath. Rev. 91, 99–164.2.3.CO;2>CrossRefGoogle Scholar
Staquet, C. & Godeferd, F. S. 1998 Statistical modelling and direct numerical simulations of decaying stably stratified turbulence. Part 1. Flow energetics. J. Fluid Mech. 360, 295–340.CrossRefGoogle Scholar
Sukoriansky, S., Galperin, B. & Staroselsky, I. 2005 A quasinormal scale elimination model of turbulent flows with stable stratification. Phys. Fluids 17 (8), 085107.CrossRefGoogle Scholar