Two-dimensional isotropic inertia–gravity wave turbulence

We present an idealized study of rotating stratified wave turbulence in a two-dimensional vertical slice model of the Boussinesq equations, focusing on the peculiar case of equal Coriolis and buoyancy frequencies. In this case the fully nonlinear fluid dynamics can be shown to be isotropic in the ve...

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Bibliographic Details
Published inJournal of fluid mechanics Vol. 872; pp. 752 - 783
Main Authors Xie, Jin-Han, Bühler, Oliver
Format Journal Article
LanguageEnglish
Published Cambridge Cambridge University Press 10.08.2019
Subjects
Boussinesq approximation
Boussinesq equations
Computational fluid dynamics
Computer simulation
Coriolis force
Energy
Energy transfer
Fluctuations
Fluid dynamics
Fluid flow
Fluxes
Gravitational waves
Gravity waves
Hydrodynamics
Inertia
Isotropic turbulence
Mathematical models
Nonlinear dynamics
Parameters
Robustness (mathematics)
Simulation
Theory
Turbulence
Two dimensional models
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Summary:We present an idealized study of rotating stratified wave turbulence in a two-dimensional vertical slice model of the Boussinesq equations, focusing on the peculiar case of equal Coriolis and buoyancy frequencies. In this case the fully nonlinear fluid dynamics can be shown to be isotropic in the vertical plane, which allows the classical methods of isotropic turbulence to be applied. Contrary to ordinary two-dimensional turbulence, here a robust downscale flux of total energy is observed in numerical simulations that span the full parameter regime between Ozmidov and forcing scales. Notably, this robust downscale flux of the total energy does not hold separately for its various kinetic and potential components, which can exhibit both upscale and downscale fluxes, depending on the parameter regime. Using a suitable extension of the classical Kármán–Howarth–Monin equation, exact expressions that link third-order structure functions and the spectral energy flux are derived and tested against numerical results. These expressions make obvious that even though the total energy is robustly transferred downscale, the third-order structure functions are sign indefinite, which illustrates that the sign and the form of measured third-order structure functions are both crucially important in determining the direction of the spectral energy transfer.
ISSN:0022-1120
1469-7645
DOI:10.1017/jfm.2019.406