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Diffusion in stably stratified turbulence

Published online by Cambridge University Press:  26 April 2006

Y. Kimura  and
J. R. Herring
Y. Kimura
Affiliation:
National Center for Atmospheric Research, PO Box 3000, Boulder, CO 80307, USA Present address: Graduate School of Polymathematics, Nagoya University. Nagoya 464-01, Japan.
J. R. Herring
Affiliation:
Program in Applied Mathematics. University of Colorado, Campus Box 526, Boulder, CO 80309–0526, USA
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Abstract

We examine results of direct numerical simulations (DNS) of homogeneous turbulence in the presence of stable stratification. We focus on the effects of stratification on eddy diffusion, and the distribution of pairs of particles released in the flow. DNS results are presented over a range of stratification, and at Reynolds numbers compatible with aliased free spectral results for a resolution of 128 mesh points. We compare results for particle dispersion to simple analytic theories such as that proposed by Csanady (1964) and Pearson et al. (1983) by adapting the basic Langevin model to decaying turbulence at low Reynolds numbers. Stable stratification is found to arrest both single particle displacements and pair separation in the direction of stratification, but it leaves these quantities nearly unaltered in the transverse direction. With respect to the dynamics of stratified flows, we find that regions of strong viscous dissipation are intermittently spaced, and are associated with large horizontal vorticity, consistent with recent experimental results by Fincham et al. (1994).

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 328 , 10 December 1996 , pp. 253 - 269
Copyright
© 1996 Cambridge University Press

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References

Britter, R. E., Hunt, J. C. R., Marsh, G. L. & Snyder, W. H. 1993 The effects of stable stratification on the turbulent diffusion and the decay of grid turbulence J. Fluid Mech. 127, 27–44.Google Scholar
Cox, C. Y., Nagata, Y. & Osborn, T. 1969 Oceanic fine structure and internal waves. Papers in dedication to Prof. Michitaka Uda. Bull. Japan Soc. Fish. Oceanogr. Tokyo 1, 67–71.Google Scholar
Csanady, G. T. 1964 Turbulent diffusion in a stratified fluid. J. Atmos. Sci. 21, 439–447.Google Scholar
Fernando, H. J. S. 1988 On the oscillations of harbors of arbitrary shape. The growth of a turbulent patch in a stratified flow. J. Fluid Mech. 190, 55–70.Google Scholar
Fincham, A., Maxworthy, M. T. & Spedding, G. R. 1994 The horizontal and vertical structure of the vorticity field in freely—decaying, stratified grid—turbulence. In Preprints, 4th Symp. on Stratified Flows, vol. 2, A4.
Fung, J. C. F., Hunt, J. C. R., Malik, N. A. & Perkins, R. J. 1991 Kinematic simulation of homogeneous turbulence by unsteady random Fourier modes. J. Fluid Mech. 236, 281–318.Google Scholar
Godeferd, F. S. & Cambon, C. 1994 Detailed investigation of energy transfer in homogeneous stratified turbulence. Phys. Fluids A 6, 2084–2100.Google Scholar
Herring, J. R. 1988 The inverse cascade range of quasigeostrophic turbulence Met. Atmos Phys. 38, 106–115.Google Scholar
Herring, J. R. & Métais, O. 1989 Numerical experiments in forced stably stratified turbulence. J. Fluid Mech. 202, 97–115.Google Scholar
Herring, J. R. & Métais, O. 1992 Spectral transfer and bispectra for turbulence with passive scalars. J. Fluid Mech. 235, 103–121.Google Scholar
Herring, J. R., Schertzer, D., Lesieur, M., Newman, G. R., Chollet, J.–P. & Larcheveque, M. 1982 A comparative assessment of spectral closure as applied to passive scalar diffusion. J. Fluid Mech. 124, 411–437.Google Scholar
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.Google Scholar
Kimura, Y. 1992 Intermittency growth in 3D turbulence. In Proc. of NATO Advanced Research Workshop on Topological Fluid Dynamics (ed. H. K Moffatt, R. M Zaslavsky, M Tabor & P Comte). pp. 401–413. Kluwer.
Kimura, Y. & Herring, J. R. 1995 Stratified Turbulence: Structural Issues, and Turbulent Diffusion (ed. M Meneguzzi, A Pouquet & P. L Sulem). Lecture Notes in Physics, vol. 462, pp. 195–204. Springer.
Kolmogorov, A. N. 1942 On degeneration of isotropic turbulence in an incompressible viscous liquid. Dokl. Akad. Nauk. SSSR 31, 538–541.Google Scholar
Kraichnan, R. H. 1971 An almost markovian Galilean invariant turbulence model J. Fluid Mech. 47, 513–524.Google Scholar
Kraichnan, R. H. 1976 Eddy viscosity in two- and three-dimensional turbulence. J. Atmos. Sci. 33, 1521–1536.Google Scholar
Leith, C. E. 1967 Diffusion approximation to the inertial energy transfer in isotropic turbulence. Phys. Fluids 10, 1409–1416.Google Scholar
Lesieur, M. 1990 Turbulence in Fluids, 2nd edn. Kluwer.
Lesieur, M. & Schertzer, D. 1978 Amortissement auto similarité d'une turbulence à grand nombre de Reynolds. J. Méc. 17, 609–646.Google Scholar
Lilly, D. K., Walko, D. E. & Adelfang, S. I. 1974 Stratospheric Mixing estimated from high-altitude turbulence measurements. J. Appl Met. 13, 488–493.Google Scholar
McWilliams, J. C., Weiss, J. B. & Yavneh, I. 1994 Anisotropy and coherent vortex structures in planetary turbulence Science 264, 410–413.Google Scholar
Metais, O., Bartello, P., Garnier, E., Riley, J. J. & Lesieur, M. 1996 Inverse cascade in stably stratified rotating turbulence. Dyn. Atmos. Oceans 23, 193–203.Google Scholar
Metais, O. & Herring, J. R. 1989 Numerical studies of freely decaying homogeneous stratified turbulence. J. Fluid Mech. 202, 117–148.Google Scholar
Rszag, S. A. & Patterson, G. S. 1972 Numerical simulation of turbulence. In Statistical Models of Turbulence (ed. M Rosenblatt & C Van Atta), pp 127–147. Springer.
Earson, H. J., Puttock, J. S. & Hunt, J. C. R. 1983 A Statistical model of fluid—element motions and vertical diffusion in a homogeneous stratified turbulent flow. J. Fluid Mech. 129, 219–249.Google Scholar
Riley, J. J. & Metcalfe, R. W. 1990 Direct numerical simulations of turbulent patches in stable—stratified fluids. In Stratified Flows (ed. E. J List & G. H Jirka), pp. 541–549. ASME.
Riley, J. J., Metcalfe, R. W. & Weissman, M. A. 1982 Direct numerical simulations of homogeneous turbulence in density stratified fluids. In Proc. AIP Conf. on Nonlinear Properties of Internal Waves, pp. 679–712.
She, Z.-S., Jackson, E. & Orszag, S. A. 1991 Structure and dynamics of homogeneous turbulence: models and simulation. Proc R. Soc. Lond. A 434, 101–124.Google Scholar
Siggia, E. D. & Patterson, G. S. 1978 Intermittency effects in a numerical simulation of stationary turbulence. J. Fluid Mech. 86, 567–592.Google Scholar
Taylor, G. I. 1921 Diffusion by continuous motion. Proc. Lond. Math Soc. 20, 10–25.Google Scholar
Weinstock, J. 1978 Vertical turbulent diffusion in a stably stratified fluid. J. Atmos. Sci. 35, 1022–1027.Google Scholar
Yeung, P. K. & Pope, S. B. 1989 Lagrangian statistics from direct numerical simulations of isotropic turbulence. J. Fluid Mech. 207, 531–586.Google Scholar
Yeung, P. K. & Zhou, Y. 1995 Two dimensionalization and spectral transfer in rotating turbulence Bull. Am. Phys. Soc. 40.Google Scholar
Zhou, Y. 1995 A phenomenlogical treatment of rotating turbulence Phys. Fluids 7, 2092–2094.Google Scholar