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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 Open the ORCID record for Giovanni Dematteis [Opens in a new window]  and
Yuri V. Lvov Open the ORCID record for Yuri V. Lvov [Opens in a new window]
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
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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).

JFM classification

Geophysical and Geological Flows: Internal waves Geophysical and Geological Flows: Ocean processes Turbulent Flows: Wave-turbulence interactions
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 915 , 25 May 2021 , A129
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

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