Journal
JOURNAL OF FLUID MECHANICS
Volume 840, Issue -, Pages 498-529Publisher
CAMBRIDGE UNIV PRESS
DOI: 10.1017/jfm.2018.18
Keywords
geophysical and geological flows; internal waves; stratified flows
Categories
Funding
- European Research Council (ERC) under the European Union's Horizon 2020 research and innovation program [681835-FLUDYCO-ERC-2015-CoG]
- IDRIS (Institut du Developpement et des Ressources en Informatique Scientifique) [100508, 100614]
- HPC resources of Aix-Marseille Universite - project Equip@Meso of the program Investissements d'Avenir [15b011, 16b020, ANR-10-EQPX-29-01]
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We investigate the stability of stratified fluid layers undergoing homogeneous and periodic tidal deformation. We first introduce a local model which allows us to study velocity and buoyancy fluctuations in a Lagrangian domain periodically stretched and sheared by the tidal base flow. While keeping the key physical ingredients only, such a model is efficient in simulating planetary regimes where tidal amplitudes and dissipation are small. With this model, we prove that tidal flows are able to drive parametric subharmonic resonances of internal waves, in a way reminiscent of the elliptical instability in rotating fluids. The growth rates computed via direct numerical simulations (DNSs) are in very good agreement with Wentzel-Kramers-Brillouin analysis and Floquet theory. We also investigate the turbulence driven by this instability mechanism. With spatio-temporal analysis, we show that it is weak internal wave turbulence occurring at small Froude and buoyancy Reynolds numbers. When the gap between the excitation and the Brunt-Vaisiilii frequencies is increased, the frequency spectrum of this wave turbulence displays a -2 power law reminiscent of the high-frequency branch of the Garett and Munk spectrum (Geophys. Fluid Dyn., vol. 3 (1), 1972, pp. 225-264) which has been measured in the oceans. In addition, we find that the mixing efficiency is altered compared to what is computed in the context of DNS of stratified turbulence excited at small Froude and large buoyancy Reynolds numbers and is consistent with a superposition of waves.
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