Nonlinear gravity-wave interactions in stratified turbulence

Remmel, Mark and Sukhatme, Jai and Smith, Leslie M (2014) Nonlinear gravity-wave interactions in stratified turbulence. In: THEORETICAL AND COMPUTATIONAL FLUID DYNAMICS, 28 (2). pp. 131-145.

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Abstract

To investigate the dynamics of gravity waves in stratified Boussinesq flows, a model is derived that consists of all three-gravity-wave-mode interactions (the GGG model), excluding interactions involving the vortical mode. The GGG model is a natural extension of weak turbulence theory that accounts for exact three-gravity-wave resonances. The model is examined numerically by means of random, large-scale, high-frequency forcing. An immediate observation is a robust growth of the so-called vertically sheared horizontal flow (VSHF). In addition, there is a forward transfer of energy and equilibration of the nonzero-frequency (sometimes called ``fast'') gravity-wave modes. These results show that gravity-wave-mode interactions by themselves are capable of systematic interscale energy transfer in a stratified fluid. Comparing numerical simulations of the GGG model and the full Boussinesq system, for the range of Froude numbers (Fr) considered (0.05 a parts per thousand currency sign Fr a parts per thousand currency sign 1), in both systems the VSHF is hardest to resolve. When adequately resolved, VSHF growth is more vigorous in the GGG model. Furthermore, a VSHF is observed to form in milder stratification scenarios in the GGG model than the full Boussinesq system. Finally, fully three-dimensional nonzero-frequency gravity-wave modes equilibrate in both systems and their scaling with vertical wavenumber follows similar power-laws. The slopes of the power-laws obtained depend on Fr and approach -2 (from above) at Fr = 0.05, which is the strongest stratification that can be properly resolved with our computational resources.

Item Type:	Journal Article
Publication:	THEORETICAL AND COMPUTATIONAL FLUID DYNAMICS
Publisher:	SPRINGER
Additional Information:	Copyright for this article belongs to the SPRINGER, USA
Keywords:	Gravity waves; Stratified turbulence; Geophysical flows
Department/Centre:	Division of Mechanical Sciences > Centre for Atmospheric & Oceanic Sciences
Date Deposited:	21 May 2014 11:02
Last Modified:	21 May 2014 11:02
URI:	http://eprints.iisc.ac.in/id/eprint/48976

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