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Downscale energy fluxes in scale-invariant oceanic internal wave turbulence

Published online by Cambridge University Press:  31 March 2021

Giovanni Dematteis*
Affiliation:
Department of Mathematical Sciences, Rensselaer Polytechnic Institute, 110 8th St, Troy, NY12180, USA
Yuri V. Lvov
Affiliation:
Department of Mathematical Sciences, Rensselaer Polytechnic Institute, 110 8th St, Troy, NY12180, USA
*
Email address for correspondence: dematg@rpi.edu

Abstract

We analyse analytically and numerically the scale-invariant stationary solution to the internal-wave kinetic equation. Our analysis of the resonant energy transfers shows that the leading-order contributions are given (i) by triads with extreme scale separation and (ii) by triads of waves that are quasi-collinear in the horizontal plane. The contributions from other types of triads is found to be subleading. We use the modified scale-invariant limit of the Garrett and Munk spectrum of internal waves to calculate the magnitude of the energy flux towards high wavenumbers in both the vertical and the horizontal directions. Our results compare favourably with the finescale parametrization of ocean mixing that was proposed in Polzin et al. (J. Phys. Oceanogr., vol. 25, issue 3, 1995, pp. 306–328).

Type
JFM Papers
Copyright
© The Author(s), 2021. Published by Cambridge University Press

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