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Nonlinear gravity-wave interactions in stratified turbulence

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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.

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Authors and Affiliations

  1. Mathematics Department, University of California-Davis, Davis, CA, 95616, USA

    Mark Remmel

  2. Centre for Atmospheric and Oceanic Sciences, Indian Institute of Science, Bangalore, 560012, India

    Jai Sukhatme

  3. Mathematics Department, University of Wisconsin-Madison, Madison, WI, 53706, USA

    Leslie M. Smith

  4. Engineering Physics Department, University of Wisconsin-Madison, Madison, WI, 53706, USA

    Leslie M. Smith

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  1. Mark Remmel
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  2. Jai Sukhatme
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  3. Leslie M. Smith
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Correspondence to Jai Sukhatme.

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Communicated by R. Klein.

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Remmel, M., Sukhatme, J. & Smith, L.M. Nonlinear gravity-wave interactions in stratified turbulence. Theor. Comput. Fluid Dyn. 28, 131–145 (2014). https://doi.org/10.1007/s00162-013-0305-2

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