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Nonlinear inertia-gravity wave-mode interactions in three dimensional rotating stratified flows

Remmel, M and Sukhatme, J and Smith, LM (2010) Nonlinear inertia-gravity wave-mode interactions in three dimensional rotating stratified flows. Communications in Mathematical Sciences, 8 (2). pp. 357-376.

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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 ≤ Fr ≤ 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: Article
Additional Information: Copyright of this article belongs to Springer
Subjects: Meteorology and Climatology
Depositing User: IITM Library
Date Deposited: 22 May 2015 11:40
Last Modified: 22 May 2015 11:40
URI: http://moeseprints.incois.gov.in/id/eprint/793

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