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Two-dimensional isotropic inertia–gravity wave turbulence

Published online by Cambridge University Press:  14 June 2019

Jin-Han Xie Open the ORCID record for Jin-Han Xie [Opens in a new window]  and
Oliver Bühler Open the ORCID record for Oliver Bühler [Opens in a new window]
Jin-Han Xie*
Affiliation:
Courant Institute of Mathematical Sciences, New York University, New York, NY 10012, USA
Oliver Bühler
Affiliation:
Courant Institute of Mathematical Sciences, New York University, New York, NY 10012, USA
*
†Email address for correspondence: jhxie@cims.nyu.edu
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Abstract

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.

JFM classification

Turbulent Flows: Isotropic turbulence Turbulent Flows: Rotating turbulence Turbulent Flows: Stratified turbulence
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 872 , 10 August 2019 , pp. 752 - 783
Copyright
© 2019 Cambridge University Press 

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