Abstract
The influence of buoyancy on the length-scales for the dissipation rate of kinetic energy, and for momentum, heat, and other scalar transport has to be known for subgrid-scale (SGS) models in a large-eddy simulation (LES). For the inertial subrange, Lilly (1967) has shown that grid spacing is the relevant length-scale for SGS effects. Deardorff (1980) proposed to reduce all the length-scales for stable stratification. Numerical and experimental data show, however, that the dissipation length-scale may strongly increase in stable layers with little shear. Lumley's (1964) theory for the energy spectrum in a stratified fluid also suggests such an increase. In this paper we apply the analysis of previous algebraic second-order closure SGS models, parameter studies with different length-scale models in LES, and the analysis of direct simulations of sheared and unsheared stably stratified homogeneous turbulence. These analyses show advantages of first-order closures for LES and suggest that the limiting effect of stratification should only be applied to the length-scales of vertical eddy-diffusivities of heat and scalars but not to those of momentum and dissipation.
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References
Bougeault, P., and Lacarrère, P. (1989). Parameterization of orography-induced turbulence in a mesobeta-scale model. Monthly Weather Rev., 117, 1872–1890.
Brost, R.A., and Wyngaard, J.C. (1978). A model study of the stably stratified planetary boundary layer. J. Atmos. Sci., 35, 1427–1440.
Deardorff, J.W. (1973). The use of subgrid transport equations in a three-dimensional model of atmospheric turbulence. J. Fluids Engrg., 95, 429–438.
Deardorff, J.W. (1980). Stratocumulus-capped mixed layers derived from a three-dimensional model. Boundary-Layer Meteorol., 18, 495–527.
Druilhet, A, Frangi, J.P., Guedalia, D., and Fontan, J. (1983). Experimental studies of the turbulence structure parameters of the convective boundary layer. J. Climatol. Appl. Meteorol., 22, 594–608.
Ebert, E.E., Schumann, U., and Stull, R.B. (1989). Nonlocal turbulent mixing in the convective boundary layer evaluated from large-eddy simulation. J. Atmos. Sci., 46, 2178–2207.
Gerz, T., and Schumann, U. (1991). Direct simulation of homogeneous turbulence and gravity waves in sheared and unsheared stratified flows. In Turbulent Shear Flows, Vol. 7 (F. Durst et al., eds.), pp. 27–45, Springer-Verlag, Berlin.
Gerz, T., Schumann, U., and Elghobashi, S.E. (1989). Direct numerical simulation of stratified homogeneous turbulent shear flows. J. Fluid Mech., 200, 563–594.
Guillemet, B., Isaka, H., and Mascart, P. (1983). Molecular dissipation of turbulent fluctuations in the convective mixed layer. I: Height variations of dissipation rates. Boundary-Layer Meteorol., 27, 141–162.
Hunt, J.C.R., Kaimal, J.C., and Gaynor, J.E. (1985). Some observations of turbulence structure in stable layers. Quart. J. Roy. Meteorol. Soc., 111, 793–815.
Hunt, J.C.R., Stretch, D.D., and Britter, R.E. (1988). Length scales in stably stratified turbulent flows and their use in turbulence models. In Stably Stratified Flows and Dense Gas Dispersion (J.S. Puttock, ed.), pp. 285–321. Clarendon Press, Oxford.
Hunt, J.C.R., Moin, P., Moser, R.D., Spalart, P., Mansour, N.N., Kaimal, J.C., and Gaynor, E. (1989). Cross correlation and length scales in turbulent flows near surface. In Advances in Turbulence, Vol. 2 (H.-H. Fernholz and H.E. Fielder, ed.), pp. 128–134, Springer-Verlag, Berlin.
Isaka, H., and Guillemet, B. (1983). Molecular dissipation of turbulent fluctuations in the convective mixed layer. II: Height variations of characteristic time scales and experimental test of molecular dissipation models. Boundary-Layer Meteorol., 27, 257–279.
Krettenauer, K. (1991). Numerische Simulation turbulenter Konvektion. über gewellten Flächen. Dissertation, Report DLR-FB-91-12, DLR Oberpfaffenhofen.
Launder, B.E. (1975). On the effects of a gravitational field on the turbulent transport of heat and momentum. J. Fluid Mech., 67, 569–581.
Launder, B.E. (1989). The prediction of force field effects on turbulent shear flows via second-moment closure. In Advances in Turbulence, vol. 2 (H.-H. Fernholz, and H.E. Fiedler, eds.), pp. 338–358. Springer-Verlag, Berlin.
Lilly, D.K. (1967). The representation of small-scale turbulence in numerical simulation experiments. In Proc. IBM Sci. Comput. Symp. on Environmental Science, pp. 195–210. Thomas J. Watson Research Center, Yorktown Heights, N.Y., 14–16 November 1966. IBM Form 320–1951.
Lilly, D.K., Waco, D.E., and Adelfang, S.I. (1974). Stratospheric mixing estimated from high-altitude turbulence measurements. J. Appl. Meteorol, 13, 488–493.
Lumley, J.L. (1964). The spectrum of nearly inertial turbulence in a stably stratified fluid. J. Atmos. Sci., 21, 99–102.
Mason, P.J. (1989). Large eddy simulation of the convective atmospheric boundary layer. J. Atmos. Sci., 46, 1492–1516.
Mason, P.J., and Derbyshire, S.H. (1990). Large-eddy simulation of the stably-stratified atmospheric boundary layer. Boundary-Layer Meteorol., 53, 117–162.
Mellor, G.L., and Yamada, T. (1982). Development of a turbulence closure model for geophysical fluid problems. Rev. Geophys. Space Phys., 20, 851–875.
Moeng, C.-H., and Wyngaard, J.C. (1989). Evaluation of turbulent transport and dissipation closures in second-order modeling. J. Atmos. Sci., 46, 2311–2330.
Nieuwstadt, F.T.M. (1990). Direct and large-eddy simulation of free convection. In Proc. 9th Internat. Heat Transfer Conf., Vol. I, pp. 37–47. Jerusalem, 19–24 August 1990.
Ozmidov, R.V. (1965). On the turbulent exchange in a stably stratified ocean. Bull. Acad. Sci. U.S.S.R. Atmos. Ocean. Phys., 1, 493–497.
Schemm, C.E., and Lipps, F.B. (1976). Some results of a simplified three-dimensional numerical model of atmospheric turbulence. J. Atmos. Sci., 33, 1021–1041.
Schmidt, H., and Schumann, U. (1989). Coherent structure of the convective boundary layer derived from large-eddy simulations. J. Fluid Mech., 200, 511–562.
Schumann, U. (1977). Realizability of Reynolds stress turbulence models. Phys. Fluids, 20, 721–725.
Schumann, U. (1990). Large-eddy simulation of the upslope boundary layer. Quart. J. Roy Meteorol. Soc., 116, 637–670.
Thorpe, S.A. (1978). On the shape and breaking of finite amplitude internal gravity waves in a shear flow. J. Fluid Mech., 85, 7–31.
Vinnichenko, N.K., Pinus, N.Z., Shmeter, S.M., and Shur, G.N. (1973). Turbulence in the Free Atmosphere, pp. 120–127. Consultants Bureau, New York.
Webster, C.A.G. (1964). An experimental study of turbulence in a density stratified shear flow. J. Fluid Mech., 19, 221–245.
Weinstock, J. (1978). Vertical diffusion in a stably stratified fluid. J. Atmos. Sci., 35, 1022–1027.
Weinstock, J. (1990). Saturated and unsaturated spectra of gravity waves and scale-dependent diffusion. J. Atmos. Sci., 47, 2211–2225.
Zeman, O., and Lumley, J.L. (1976). Modeling buoyancy driven mixed layers. J. Atmos. Sci., 33, 1974–1988.
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Dedicated to Professor J.L. Lumley on the occasion of his 60th birthday.
This work was supported by the Deutsche Forschungsgemeinschaft.
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Schumann, U. Subgrid length-scales for large-eddy simulation of stratified turbulence. Theoret. Comput. Fluid Dynamics 2, 279–290 (1991). https://doi.org/10.1007/BF00271468
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DOI: https://doi.org/10.1007/BF00271468