Abstract
The collapse of homogeneous three-dimensional turbulence submitted to stable stratification is investigated with the help of direct numerical simulations (643 resolution points) and by performing large-eddy simulations (323) with the subgrid scale procedure developed by Chollet and Lesieur for isotropic turbulence.
Comparisons between the direct numerical simulations and the laboratory experiments performed by Itsweire, Heiland and Van Atta show that the numerical techniques have a satisfactory degree of realism. In the computation, the vertical integral scale is frozen by the stratification and some signs of flow two-dimensionalization are exhibited at time of the order of 6N −1 (N Brunt-Väisälä frequency). These results seem to qualitatively reproduce what one observes in the wake of a slender body towed in a stratified channel.
The same signs of “collapse” are exhibited in the large-eddy simulations. Although the subgrid-scale model simulates the dissipation effects of infinitely large Reynolds number turbulence, the collapse time is of the same order as the one given by direct numerical simulations. The model, although isotropic, allows for an anisotropy to grow from large to small scales. Furthermore, the improved large-scale resolution permits a more precise study of the dynamics of these scales with the help of spectral transfer functions.
We then focus on the spatial structure of the stratified flow.
A simple model derived from two-point closure techniques (E.D.Q.N.M.) is presented. This model could be very useful to describe very high Reynolds number stratified flows and to modify the subgrid- scale parameterization.
Institut National Polytechnique et Université Joseph Fourier de Grenoble, Unité associée au CNRS
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References
Chollet, J. P. (1983): “Two-Point Closure Used for a Sub-Grid Scale Model in Large Eddy Simulations,” in 4th Symposium on Turbulent Shear Flows, Karlsruhe, ed. by Bradbury, Launder, Schmidt, Whitelaw (Springer, Berlin, Heidelberg) pp. 62–72
Chollet, J. P. (1984): “Spectral Closures to Derive a Subgrid Scale Modeling for Large Eddy Simulations,” in Macroscopic Modelling of Turbulent Flows Lecture Notes in Physics Vol. 230 (Springer, Berlin, Heidelberg) pp. 161–176
Chollet, J. P., Lesieur, M. (1981): Parameterization of small scales of three-dimensional isotropic turbulence utilizing spectral closures. J. Atmos. Sci. 38, 2747–2757
Chollet, J. P., Lesieur, M. (1982): Modélisation sous maille des flux de quantité de mouvement et de chaleur en turbulence tridimensionnelle isotrope. La Métérologie 29–30, 183–191
Craya, A. (1958): Contribution à l’analyse de la turbulence associée à des vitesses moyennes. P.S.T. Ministère de l’Air 345
Dickey, T. D., Mellor, G. L. (1980): Decaying turbulence in neutral and stratified fluids. J. Fluid Mech. 99, 13–31
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
Gage, K. S. (1979): Evidence for a k −5/3 law inertial range in mesoscale two dimensional turbulence. J. Atm. Sci. 36, 1950–1954
Herring, J. R. (1974): Approach of axisymmetric turbulence to isotropy. Phys. Fluids 17, 859–872
Herring, J. R., Métais, O. (1987): Numerical experiments in forced stably stratified turbulence. (Submitted to J. Fluid Mech.)
Herring, J. R., Orszag, S. A., Kraichnan, R. H., Fox, D. F. (1974): Decay of two-dimensional homogeneous turbulence. J. Fluid Mech. 66, 417–444
Herring, J. R., Schertzer, D., Lesieur, M., Newman, G. R., Chollet, J.-P., Larchevêque, M. (1982): A comparative assessment of spectral closures as applied to passive scalar diffusion. J. Fluid Mech. 124, 411–437
Holloway, G. (1980): Oceanic internal waves are not weak waves. J. Phys. Oceanogr. 10/6, 906–914
Holloway, G., Hendershott, M. C. (1977): Stochastic closure for nonlinear Rossby waves. J. Fluid Mech. 82, 747–765
Hopfinger, E. J. (1987): Turbulence collapse in stratified fluids: a review. J. Geophys. Res. C5, 92, 5287–5303
Itsweire, E. C., Heiland, K. N., Van Atta, C. W. (1986): The evolution of grid-generated turbulence in a stably stratified fluid. J. Fluid Mech. 162, 299–338
Kerr, R. M. (1985): Higher-order derivative correlations and the alignment of small-scale structures in isotropic numerical turbulence. J. Fluid Mech. 153, 31–58
Kraichnan, R. H. (1967): Inertial ranges in two dimensional turbulence. Phys. Fluids 10, 1417–1423
Kraichnan, R. H. (1976): Eddy-viscosity in two and three dimensions. J. Atmos. Sci. 33, 1521–1536
Leith, C. E. (1971): Atmospheric predictability and two dimensional turbulence. J. Atmos. Sci. 28, 145–161
Lesieur, M. (1987): Turbulence in Fluids (Nijhoff Publishers)
Lilly, D. K. (1983): Stratified turbulence and the mesoscale variability of the atmosphere. J. Atmos. Sci. 40, 749–761
Lin, J. T., Pao, H.-H. (1979): Wakes in stratified fluids. Ann. Rev. Fluid Mech. 11, 317–338
Métais, O. (1985): “Evolution of Three Dimensional Turbulence Under Stratification”, Turbulent Shear Flows V, Cornell University, ed. by J. L. Lumley, pp. 22.27–22.32
Métais, O., Herring, J. R. (1988): “Numerical simulations of freely evolving turbulence in stably stratified fluids. (Submitted to J. Fluid Mech.)
Métais, O., Herring, J. R., Lesieur, M., Chollet, J.-P. (1987): “Turbulence in Stably Stratified Fluids: Statistical Theory and Direct Numerical Simulations”, Third International Symposium on Stratified Flows, Pasadena, California, USA, February 3–5
Nastrom, G. D., Gage, K. S. (1984): A brief climatology of vertical wind variability in the troposphere and stratosphere as seen by the Poker Flat, Alaska, MST radar. J. Clin. Appl. Meteor. 23, 453–460
Orszag, S. A. (1970): Analytical theories of turbulence. J. Fluid Mech. 13, 369–382
Ozmidov, R. V. (1975): On the turbulent exchange in a stably stratified ocean. Izv. Acad. Sci. USSR, Atmos. Ocean. Phys. 1, 493–497
Riley, J. J., Metcalfe, R. W., Weissman, M. A. (1981): “Direct Numerical Simulations of Homogeneous Turbulence in Density Stratified Fluids”, in Non linear Properties of Internal Waves, La Jolla Institute, AIP Conference Proceedings 76, ed. by B. J. West, pp. 79–112
Riley, J. J. (1985): A review of turbulence in stably-stratified fluids. Nov. 1985
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Métais, O., Chollet, JP. (1989). Turbulence Submitted to Stable Density Stratification: Large-Eddy Simulations and Statistical Theory. In: André, JC., Cousteix, J., Durst, F., Launder, B.E., Schmidt, F.W., Whitelaw, J.H. (eds) Turbulent Shear Flows 6. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-73948-4_31
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