Hostname: page-component-76fb5796d-qxdb6 Total loading time: 0 Render date: 2024-04-25T16:31:00.760Z Has data issue: false hasContentIssue false
  • English
  • Français

Direct numerical simulation of turbulence in a salt-stratified fluid

Published online by Cambridge University Press:  23 March 2020

Shinya Okino Open the ORCID record for Shinya Okino [Opens in a new window]  and
Hideshi Hanazaki Open the ORCID record for Hideshi Hanazaki [Opens in a new window]
Shinya Okino*
Affiliation:
Department of Mechanical Engineering and Science, Kyoto University, Kyoto615-8540, Japan
Hideshi Hanazaki
Affiliation:
Department of Mechanical Engineering and Science, Kyoto University, Kyoto615-8540, Japan
*
†Email address for correspondence: okino.shinya.8n@kyoto-u.ac.jp
Get access Rights & Permissions [Opens in a new window]

Abstract

Decaying turbulence in salt-stratified fluid with Schmidt number $700$ is investigated by direct numerical simulation. In the final period of decay, and after the Ozmidov scale becomes smaller than the Kolmogorov scale, potential-energy distribution due to salinity fluctuations shows large-scale clouds composed of structures smaller than the Kolmogorov scale. When these clouds appear, potential energy has a flat spectrum in the viscous-convective subrange, rather than a $k^{-1}$ spectrum observed initially before the stratification effect becomes significant. This transition occurs since the potential energy near the Kolmogorov scale or the primitive scale of stratified turbulence defined by $\sqrt{\unicode[STIX]{x1D708}^{\ast }/N^{\ast }}$, where $\unicode[STIX]{x1D708}^{\ast }$ is the kinematic viscosity and $N^{\ast }$ the Brunt–Väisälä frequency, decreases significantly due to the persistent conversion of potential energy into kinetic energy by the counter-gradient density flux.

JFM classification

Turbulent Flows: Stratified turbulence Turbulent Flows: Turbulence simulation Geophysical and Geological Flows: Internal waves
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 891 , 25 May 2020 , A19
Copyright
© The Author(s), 2020. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Bartello, P. & Tobias, S. M. 2013 Sensitivity of stratified turbulence to the buoyancy Reynolds number. J. Fluid Mech. 725, 1–22.CrossRefGoogle Scholar
Batchelor, G. K. 1959 Small-scale variation of convected quantities like temperature in turbulent fluid. Part 1. General discussion and the case of small conductivity. J. Fluid Mech. 5, 113–133.CrossRefGoogle Scholar
Bradshaw, P. 1971 An Introduction to Turbulence and its Measurement. Pergamon Press.Google Scholar
Brethouwer, G., Billant, P., Lindborg, E. & Chomaz, J. M. 2007 Scaling analysis and simulation of strongly stratified turbulent flows. J. Fluid Mech. 585, 343–368.CrossRefGoogle Scholar
Brethouwer, G., Hunt, J. C. R. & Nieuwstadt, F. T. M. 2003 Micro-structure and Lagrangian statistics of the scalar filed with a mean gradient in isotropic turbulence. J. Fluid Mech. 474, 193–225.CrossRefGoogle Scholar
Gargett, A. E. 1985 Evolution of scalar spectra with the decay of turbulence in a stratified fluid. J. Fluid Mech. 159, 379–407.CrossRefGoogle Scholar
Gargett, A. E., Merryfield, W. J. & Holloway, G. 2003 Direct numerical simulation of differential scalar diffusion in three-dimensional stratified turbulence. J. Phys. Oceanogr. 33, 1758–1782.CrossRefGoogle Scholar
Gerz, T. & Yamazaki, H. 1993 Direct numerical simulation of buoyancy-driven turbulence in stably stratified fluid. J. Fluid Mech. 249, 415–440.CrossRefGoogle Scholar
Gibson, C. H. 1980 Fossil temperature, salinity, and vorticity turbulence in the ocean. In Marine Turbulence (ed. Nihoul, J.), pp. 221–257. Elsevier.Google Scholar
Gibson, C. H. & Schwarz, W. H. 1963 The universal equilibrium spectra of turbulent velocity and scalar fields. J. Fluid Mech. 16, 365–384.CrossRefGoogle Scholar
Hanazaki, H. & Hunt, J. C. R. 1996 Linear processes in unsteady stably stratified turbulence. J. Fluid Mech. 318, 303–337.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
Keller, K. H. & Van Atta, C. W. 2000 An experimental investigation of the vertical temperature structure of homogeneous stratified shear turbulence. J. Fluid Mech. 425, 1–29.CrossRefGoogle Scholar
Komori, S. & Nagata, K. 1996 Effects of molecular diffusivities on counter-gradient scalar and momentum transfer in strongly stable stratification. J. Fluid Mech. 326, 205–237.CrossRefGoogle Scholar
Lienhard, J. H. & Van Atta, C. W. 1990 The decay of turbulence in thermally stratified flow. J. Fluid Mech. 210, 57–112.CrossRefGoogle Scholar
Maffioli, A. & Davidson, P. A. 2016 Dynamics of stratified turbulence decaying from a high buoyancy Reynolds number. J. Fluid Mech. 786, 210–233.CrossRefGoogle Scholar
Métais, O. & Herring, J. R. 1989 Numerical simulations of freely evolving turbulence in stably stratified fluids. J. Fluid Mech. 202, 117–148.CrossRefGoogle Scholar
Okino, S. & Hanazaki, H. 2019 Decaying turbulence in a stratified fluid of high Prandtl number. J. Fluid Mech. 874, 821–855.CrossRefGoogle Scholar
Perry, A. E., Henbest, S. & Chong, M. S. 1986 A theoretical and experimental study of wall turbulence. J. Fluid Mech. 165, 163–199.CrossRefGoogle Scholar
Praud, O., Fincham, A. M. & Sommeria, J. 2005 Decaying grid turbulence in a strongly stratified fluid. J. Fluid Mech. 522, 1–33.CrossRefGoogle Scholar
Riley, J. J., Metcalfe, R. W. & Weissman, M. A. 1981 Direct numerical simulations of homogeneous turbulence in density-stratified fluids. In Proc. AIP Conf. on Nonlinear Properties of Internal Waves (ed. West, B. J.), pp. 79–112. American Institute of Physics.Google Scholar
Smyth, W. D. 1999 Dissipation-range geometry and scalar spectra in sheared stratified turbulence. J. Fluid Mech. 401, 209–242.CrossRefGoogle Scholar
Staquet, C. & Godeferd, F. S. 1998 Statistical modelling and direct numerical simulations of decaying stably stratified turbulence. Part 1. Flow energetics. J. Fluid Mech. 360, 295–340.CrossRefGoogle Scholar
Stillinger, D. C., Helland, K. N. & 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.CrossRefGoogle Scholar
Townsend, A. A. 1976 The Structure of Turbulent Shear Flow. Cambridge University Press.Google Scholar
Yeung, P. K., Xu, S., Donzis, D. A. & Sreenivasan, K. R. 2004 Simulations of three-dimensional turbulent mixing for Schmidt numbers of the order 1000. Flow Turbul. Combust. 72, 333–347.CrossRefGoogle Scholar
Yeung, P. K., Xu, S. & Sreenivasan, K. R. 2002 Schmidt number effects on turbulent transport with uniform mean scalar gradient. Phys. Fluids 14, 4178–4191.CrossRefGoogle Scholar