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Large-eddy simulation of homogeneous turbulence and diffusion in stably stratified shear flow

Published online by Cambridge University Press:  26 April 2006

H.-J. Kaltenbach ,
T. Gerz  and
U. Schumann
H.-J. Kaltenbach
Affiliation:
DLR, Institute of Atmospheric Physics, D-82230 Oberpfaffenhofen, Germany
T. Gerz
Affiliation:
DLR, Institute of Atmospheric Physics, D-82230 Oberpfaffenhofen, Germany
U. Schumann
Affiliation:
DLR, Institute of Atmospheric Physics, D-82230 Oberpfaffenhofen, Germany
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Abstract

By means of large-eddy simulation, homogeneous turbulence is simulated for neutrally and stably stratified shear flow at gradient-Richardson numbers between zero and one. We investigate the turbulent transport of three passive species which have uniform gradients in either the vertical, downstream or cross-stream direction. The results are compared with previous measurements in the laboratory and in the stable atmospheric boundary layer, as well as with results from direct numerical simulations. The computed and measured flow properties agree with each other generally within the scatter of the measurements. At strong stratification, the Froude number becomes the relevant flow-controlling parameter. Stable stratification suppresses vertical overturning and mixing when the inverse Froude number based on a turn-over timescale exceeds a critical value of about 3. The turbulent diffusivity tensor is strongly anisotropic and asymmetric. However, only the vertical and the cross-stream diagonal components are of practical importance in shear flows. The vertical diffusion coefficient is much smaller than the cross-stream one at strong stratification. This anisotropy is stronger than predicted by second-order closure models. Turbulence fluxes in downstream and cross-stream directions follow classical mixing-length models.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 280 , 10 December 1994 , pp. 1 - 40
Copyright
© 1994 Cambridge University Press

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References

Brost, R. A. & Wyngaard, J. C. 1978 A model study of the stably-stratified planetary boundary layer. J. Atmos. Sci. 35, 1427–1440.Google Scholar
Corrsin, S. 1974 Limitations of gradient transport models in random walks and in turbulence. Adv. Geophys. 18A, 25–60.Google Scholar
Dörnbrack, A. 1991 Tensor der turbulenten Diffusion - Eigenschaften und Anwendungen. Met. Rdsch. 44, 73–79.Google Scholar
Ellison, T. H. 1957 Turbulent transport of heat and momentum from an infinite rough plane. J. Fluid Mech. 2, 456–466.Google Scholar
Freeman, B. E. 1977 Tensor diffusivity of a trace constituent in a stratified boundary layer. J. Atmos. Sci. 34, 124–136.Google Scholar
Galperin, B. 1986 A modified turbulent energy model for diffusion from elevated and ground point sources in neutral boundary layers. Boundary-Layer Met. 37, 245–262.Google Scholar
Germano, M., Piomelli, U., Moin, P. & Cabot, W. 1991 A dynamic subgrid-scale eddy viscosity model. Phys. Fluids A 3, 1760–1765.Google Scholar
Gerz, T. 1991 Coherent structures in stratified turbulent shear flows deduced from direct simulations. In Turbulence and Coherent Structures (ed. O. Métais & M. Lesieur), pp. 449–468. Kluwer.
Gerz, T. 1993 Vortex structure and persistent counter-gradient fluxes. In Dynamics and Geometry of Vortical Structures, EUROMECH 305, Cortona, 28–30 June 1993, pp. 13–14.
Gerz, T. & Schumann, U. 1989 Influence of initial conditions on the development of stratified homogeneous turbulent shear flow. In Finite Approximations in Fluid Mechanics II, Notes on Numerical Fluid Dynamics (ed. E. H. Hirschel), vol. 25, pp. 142–156. Vieweg.
Gerz, T. & Schumann, U. 1991 Direct simulation of homogeneous turbulence and gravity waves in sheared and unsheared stratified flows. In Turbulent Shear Flow 7 (ed. F. Durst, B. E. Launder, W. C. Reynolds, F. W. Schmidt & J. H. Whitelaw), pp. 27–45. Springer.
Gerz, T., Schumann, U. & Elghobashi, S. E. 1989 Direct numerical simulation of stratified homogeneous turbulent shear flows. J. Fluid Mech. 200, 563–594.Google Scholar
Holloway, G. 1988 The buoyancy flux from internal gravity wave breaking. Dyn. Atmos. Oceans 12, 107–125.Google Scholar
Holt, S. E. 1990 The evolution and structure of homogeneous stably stratified sheared turbulence. PhD dissertation, Dept of Civil Engng, Stanford University, Stanford CA.
Holt, S. E., Koseff, J. R. & Ferziger, J. H. 1992 A numerical study of the evolution and structure of homogeneous stably stratified sheared turbulence. J. Fluid Mech. 237, 499–539.Google Scholar
Hopfinger, E. J. 1987 Turbulence in stratified fluids: A review. J. Geophys. Res. 92, 5287–5303.Google Scholar
Hunt, J. C. R. & Carruthers, D. J. 1990 Rapid distortion theory and the ‘problems’ of turbulence. J. Fluid Mech. 212, 497–532.Google Scholar
Hunt, J. C. R., Kaimal, J. C. & Gaynor, J. E. 1985 Some observations of turbulence structure in stable layers. Q. J. R. Met. Soc. 111, 793–815.Google Scholar
Hunt, J. C. R., Stretch, D. D. & 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 (ed. J. S. Puttock), pp. 285–321. Clarendon.
Itsweire, E. C., Helland, K. N. & Van Atta, C. W. 1986 The evolution of grid-generated turbulence in a stably stratified fluid. J. Fluid Mech. 162, 299–338.Google Scholar
Itsweire, E. C., Koseff, J. R., Briggs, D. A. & Ferziger, J. H. 1993 Turbulence in stratified shear flows: implications for interpreting shear-induced mixing in the ocean. J. Phys. Ocean. 23, 1508–1522.Google Scholar
Ivey, G. N. & Imberger, J. 1991 On the nature of turbulence in a stratified fluid. Part I: The energetics of mixing. J. Phys. Ocean. 21, 650–658.Google Scholar
Kaltenbach, H.-J. 1992 Turlbulente Diffusion in einer homogenen Scherströmung mit stabiler Dichteschichtung. Diss. TU München, report DLR-FB 92–26, 142 pp.
Kaltenbach, H.-J., Gerz, T. & Schumann, U. 1991 Transport of passive scalars in neutrally and stably stratified homogeneous turbulent shear flows. In Advances in Turbulence 3 (eds. A. Johansson & H. Alfredsson), pp. 327–334. Springer.
Komori, S., Ueda, H., Ogino, F. & Mizushina, T. 1983 Turbulence structure in stably stratified open-channel flow. J. Fluid Mech. 130, 13–26.Google Scholar
Launder, B. E. 1978 Heat and mass transport. In Turbulence (ed. P. Bradshaw), pp. 231–287. Springer.
Lienhard, J. H. & Van Atta, C. W. 1990 The decay of turbulence in thermally stratified flow. J. Fluid Mech. 210, 57–112.Google Scholar
Lilly, D. K. 1967 The representation of small-scale turbulence in numerical simulation experiments. Proc. IBM Sci. Comput. Symp. on Environmental Sci., Nov. 14–16, 1966, Thomas J. Watson Res. Center, Yorktown Heights, NY, IBM Form no. 320–1951, pp. 195–210.
Lilly, D. K., Waco, D. E. & Adelfang, S. I. 1974 Stratospheric mixing estimated from high-altitude turbulence measurements. J. Appl. Met. 13, 488–493.Google Scholar
Mason, P. J. & Derbyshire, H. 1990 Large-eddy simulations of the stably-stratified atmospheric boundary layer. Boundary-Layer Met. 53, 117–162.Google Scholar
Métais, O. & Herring, J. R. 1989 Numerical simulation of freely evolving turbulence in stably stratified fluids. J. Fluid Mech. 202, 117–148.Google Scholar
Métais, O. & Lesieur, M. 1992 Spectral large-eddy simulation of isotropic and stably stratified turbulence. J. Fluid Mech. 239, 157–194.Google Scholar
Moin, P., Squires, K., Cabot, W. & Lee, S. 1991 A dynamic subgrid-scale model for compressible turbulence and scalar transport. Phys. Fluids A 3, 2746–2757.Google Scholar
Monin, A. S. & Ozmidov, R. V. 1985 Turbulence in the Ocean. Dordrecht: Reidel. 247 pp.
Morel, R., Alcaraz, E., Ayrault, M., Zegadi, R. & Mejean, P. 1991 Effects of thermal stable stratification on turbulent boundary layer characteristics. Atmos. Environ. 25A, 1263–1269.Google Scholar
Nieuwstadt, F. T. M. 1984 The turbulent structure of the stable, nocturnal boundary layer. J. Atmos. Sci. 41, 2202–2216.Google Scholar
Richardson, L. F. 1920 The supply of energy from and to the atmospheric eddies. Proc. R. Soc. Lond. A 97, 354–373.Google Scholar
Rogallo, R. S. & Moin, P. 1984 Numerical simulation of turbulent flows. Ann. Rev. Fluid Mech. 16, 99–137.Google Scholar
Rogers, M. M., Mansour, N. N. & Reynolds, W. C. 1989 An algebraic model for the turbulent flux of a passive scalar. J. Fluid Mech. 203, 77–101.Google Scholar
Rogers, M. M., Moin, P. & Reynolds, W. C. 1986 The structure and modeling of the hydrodynamic and passive scalar fields in homogeneous turbulent shear flow. NASA Rep. TF-25, Dept Mech. Engng, Stanford University.
Rohr, J. J. 1985 An experimental study of evolving turbulence in uniform mean shear flows with and without stable stratification. PhD dissertation, University of California, San Diego.
Rohr, J. J., Itsweire, E. C., Helland, K. N. & Van Atta, C. W. 1988a An investigation of the growth of turbulence in a uniform-mean-shear flow. J. Fluid Mech. 187, 1–33.Google Scholar
Rohr, J. J., Itsweire, E. C., Helland, K. N. & Van Atta, C. W. 1988b Growth and decay of turbulence in a stably stratified shear flow. J. Fluid Mech. 195, 77–111.Google Scholar
Rubinstein, R. & Barton, J. M. 1991 Renormalization group analysis of anisotropic diffusion in turbulent shear flows. Phys. Fluids A 3, 415–421.Google Scholar
Schmidt, H. & Schumann, U. 1989 Coherent structure of the convective boundary layer derived from large eddy simulations. J. Fluid Mech. 200, 511–562.Google Scholar
Schumann, U. 1975 Subgrid scale model for finite difference simulations of turbulent flows in plane channels and annuli. J. Comput. Phys. 18, 376–404.Google Scholar
Schumann, U. 1987 The counter-gradient heat-flux in turbulent stratified flows. Nucl. Engng Des. 100, 255–262.Google Scholar
Schumann, U. 1991 Subgrid length-scales for large-eddy simulation of stratified turbulence. Theoret. Comput. Fluid Dyn. 2, 279–290.Google Scholar
Schumann, U. & Gerz, T. 1994 Turbulent mixing in stably stratified homogeneous turbulence. J. Appl. Met. (in press).Google Scholar
Shirani, E., Ferziger, J. H. & Reynolds, W. C. 1981 Mixing of a passive scalar in isotropic and sheared homogeneous turbulence. Rep. no. TF-15, Thermosciences Division, Dept of Mech. Engng, Stanford University, Stanford, CA.
Stillinger, D. C., Helland, K. H. & Van Atta, C. W. 1983 Experiments on the transition of homogeneous turbulence to internal waves in a stratified fluid. J. Fluid Mech. 131, 91–122.Google Scholar
Tavoularis, S. & Corrsin, S. 1981 Experiments in nearly homogeneous turbulent shear flow with a uniform mean temperature gradient, Part 1. J. Fluid Mech. 104, 311–347.Google Scholar
Tavoularis, S. & Corrsin, S. 1985 Effects of shear on the turbulent diffusivity tensor. Intl. J. Heat Mass Transfer 28, 265–276.Google Scholar
Tavoularis, S. & Karnik, U. 1989 Further experiments on the evolution of turbulent stresses and scales in uniformly sheared turbulence. J. Fluid Mech. 204, 457–478.Google Scholar
Tsarenko, V. M. 1989 Determination of the turbulent diffusion tensor in a stratified atmospheric surface layer. Izv. Atmos. Oceanic Phys. 25, 189–194.Google Scholar
Tsarenko, V. M. & Yaglom, A. M. 1991 Semiempirical theories for turbulent diffusion in a neutrally stratified atmospheric surface layer. Phys. Fluids A 3, 2199–2206.Google Scholar
Webster, C. A. G. 1964 An experimental study of turbulence in a density-stratified shear flow. J. Fluid Mech. 19, 221–245.Google Scholar
Yamada, T. 1977 A numerical experiment on pollutant dispersion in a horizontally-homogeneous atmospheric boundary layer. Atmos. Environ. 11, 1015–1024.Google Scholar
Yoon, K. & Warhaft, Z. 1990 The evolution of grid generated turbulence under conditions of stable thermal stratification. J. Fluid Mech. 215, 601–638.Google Scholar