Subgrid lengthscales for largeeddy simulation of stratified turbulence
 Ulrich Schumann
 … show all 1 hide
Rent the article at a discount
Rent now* Final gross prices may vary according to local VAT.
Get AccessAbstract
The influence of buoyancy on the lengthscales for the dissipation rate of kinetic energy, and for momentum, heat, and other scalar transport has to be known for subgridscale (SGS) models in a largeeddy simulation (LES). For the inertial subrange, Lilly (1967) has shown that grid spacing is the relevant lengthscale for SGS effects. Deardorff (1980) proposed to reduce all the lengthscales for stable stratification. Numerical and experimental data show, however, that the dissipation lengthscale 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 secondorder closure SGS models, parameter studies with different lengthscale models in LES, and the analysis of direct simulations of sheared and unsheared stably stratified homogeneous turbulence. These analyses show advantages of firstorder closures for LES and suggest that the limiting effect of stratification should only be applied to the lengthscales of vertical eddydiffusivities of heat and scalars but not to those of momentum and dissipation.
 Bougeault, P., and Lacarrère, P. (1989). Parameterization of orographyinduced turbulence in a mesobetascale 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 threedimensional model of atmospheric turbulence. J. Fluids Engrg., 95, 429–438.
 Deardorff, J.W. (1980). Stratocumuluscapped mixed layers derived from a threedimensional model. BoundaryLayer 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 largeeddy 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, SpringerVerlag, 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. BoundaryLayer 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, SpringerVerlag, 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. BoundaryLayer Meteorol., 27, 257–279.
 Krettenauer, K. (1991). Numerische Simulation turbulenter Konvektion. über gewellten Flächen. Dissertation, Report DLRFB9112, 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 secondmoment closure. In Advances in Turbulence, vol. 2 (H.H. Fernholz, and H.E. Fiedler, eds.), pp. 338–358. SpringerVerlag, Berlin.
 Lilly, D.K. (1967). The representation of smallscale 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 highaltitude 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). Largeeddy simulation of the stablystratified atmospheric boundary layer. BoundaryLayer 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 secondorder modeling. J. Atmos. Sci., 46, 2311–2330.
 Nieuwstadt, F.T.M. (1990). Direct and largeeddy 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 threedimensional 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 largeeddy simulations. J. Fluid Mech., 200, 511–562.
 Schumann, U. (1977). Realizability of Reynolds stress turbulence models. Phys. Fluids, 20, 721–725.
 Schumann, U. (1990). Largeeddy 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 scaledependent 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.
 Title
 Subgrid lengthscales for largeeddy simulation of stratified turbulence
 Journal

Theoretical and Computational Fluid Dynamics
Volume 2, Issue 56 , pp 279290
 Cover Date
 19910801
 DOI
 10.1007/BF00271468
 Print ISSN
 09354964
 Online ISSN
 14322250
 Publisher
 SpringerVerlag
 Additional Links
 Topics
 Industry Sectors
 Authors

 Ulrich Schumann ^{(1)}
 Author Affiliations

 1. DLR, Institute of Atmospheric Physics, W8031, Oberpfaffenhofen, Federal Republic of Germany