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Sensitivity of stratified turbulence to the buoyancy Reynolds number

Published online by Cambridge University Press:  14 May 2013

P. Bartello  and
S. M. Tobias
P. Bartello*
Affiliation:
Departments of Mathematics & Statistics and Atmospheric & Oceanic Sciences, McGill University, 805 rue Sherbrooke ouest, Montréal, Québec, H3A 0B9 Canada
S. M. Tobias
Affiliation:
Department of Mathematics, University of Leeds, Woodhouse Lane, Leeds, LS2 9JT, UK
*
†Email address for correspondence: bartello@math.mcgill.ca
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Abstract

In this article we present direct numerical simulations of stratified flow at resolutions of up to $204{8}^{2} \times 513$, to explore scalings for the dynamics of stably stratified turbulence. Recent work suggests that for strong enough stratification, the vertical integral scale of the turbulence adjusts to yield a vertical Froude number, ${F}_{v} $, of order unity at high enough Reynolds number, whilst the horizontal Froude number, ${F}_{h} $, decreases as stratification is increased. Our numerical simulations are consistent with predictions by Lindborg (J. Fluid Mech., vol. 550, 2006, pp, 207–242), and with numerical simulations at lower resolution, in that the horizontal kinetic energy spectrum follows a Kolmogorov spectrum (after replacing the wavenumber with the horizontal wavenumber) and that the horizontal potential energy spectrum similarly follows the Corrsin–Obukhov spectrum for a passive scalar. Most importantly, we build upon these previous results by thoroughly exploring the dependence of the horizontal spectrum of horizontal kinetic energy on both the stratification and the relative size of the vertical dissipation terms, as quantified by the buoyancy Reynolds number. Our most important result is that variations in the power-law exponent scale entirely with the buoyancy Reynolds number and not with the stratification itself, lending considerable support to the Lindborg (2006) hypothesis that horizontal spectra are independent of stratification at large Reynolds numbers. We further demonstrate that even at the large numerical resolution of this study, the spectrum and hence the dynamics are affected by the buoyancy Reynolds number unless it is larger than $O(10)$, indicating that extreme care must be taken when assessing claims made from previous numerical simulations of stratified flow at low or moderate resolution and extrapolating the results to geophysical or astrophysical Reynolds numbers.

JFM classification

Geophysical and Geological Flows: Stratified flows Turbulent Flows: Stratified turbulence Turbulent Flows: Turbulent Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 725 , 25 June 2013 , pp. 1 - 22
Copyright
©2013 Cambridge University Press 

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