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On the kinetics of internal gravity waves beyond the hydrostatic regime

Published online by Cambridge University Press:  25 October 2024

Vincent Labarre Open the ORCID record for Vincent Labarre [Opens in a new window] ,
Nicolas Lanchon Open the ORCID record for Nicolas Lanchon [Opens in a new window] ,
Pierre-Philippe Cortet Open the ORCID record for Pierre-Philippe Cortet [Opens in a new window] ,
Giorgio Krstulovic Open the ORCID record for Giorgio Krstulovic [Opens in a new window]  and
Sergey Nazarenko Open the ORCID record for Sergey Nazarenko [Opens in a new window]
Vincent Labarre*
Affiliation:
Université Côte d'Azur, Observatoire de la Côte d'Azur, CNRS, Laboratoire Lagrange, 06304 Nice, France
Nicolas Lanchon*
Affiliation:
Université Paris-Saclay, CNRS, FAST, 91405 Orsay, France
Pierre-Philippe Cortet*
Affiliation:
Université Paris-Saclay, CNRS, FAST, 91405 Orsay, France
Giorgio Krstulovic*
Affiliation:
Université Côte d'Azur, Observatoire de la Côte d'Azur, CNRS, Laboratoire Lagrange, 06304 Nice, France
Sergey Nazarenko*
Affiliation:
Université Côte d'Azur, CNRS, Institut de Physique de Nice – INPHYNI, 06200 Nice, France
*
†Email addresses for correspondence: vincent.labarre@oca.eu, nicolas.lanchon@universite-paris-saclay.fr, pierre-philippe.cortet@universite-paris-saclay.fr, giorgio.krstulovic@oca.eu, sergey.nazarenko@unice.fr
†Email addresses for correspondence: vincent.labarre@oca.eu, nicolas.lanchon@universite-paris-saclay.fr, pierre-philippe.cortet@universite-paris-saclay.fr, giorgio.krstulovic@oca.eu, sergey.nazarenko@unice.fr
†Email addresses for correspondence: vincent.labarre@oca.eu, nicolas.lanchon@universite-paris-saclay.fr, pierre-philippe.cortet@universite-paris-saclay.fr, giorgio.krstulovic@oca.eu, sergey.nazarenko@unice.fr
†Email addresses for correspondence: vincent.labarre@oca.eu, nicolas.lanchon@universite-paris-saclay.fr, pierre-philippe.cortet@universite-paris-saclay.fr, giorgio.krstulovic@oca.eu, sergey.nazarenko@unice.fr
†Email addresses for correspondence: vincent.labarre@oca.eu, nicolas.lanchon@universite-paris-saclay.fr, pierre-philippe.cortet@universite-paris-saclay.fr, giorgio.krstulovic@oca.eu, sergey.nazarenko@unice.fr
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Abstract

We present a new derivation of the kinetic equation for weak, non-hydrostatic internal gravity wave turbulence. The equation is equivalent to the one obtained by Caillol & Zeitlin (Dyn. Atmos. Oceans, vol. 32, issue 2, 2000, pp. 81–112), but it takes a canonical form. We show that it conserves the energy without involving the resonance condition in frequency, and look for the isotropic part of the steady, scale-invariant solutions. We provide a parametrization of the resonant manifold of non-hydrostatic internal gravity wave triadic interactions. This allows us to simplify the collision integral, and to evaluate the transfer coefficients of all triadic interactions. In the hydrostatic limit, our equation is equivalent to the Hamiltonian description of Lvov & Tabak (Phys. Rev. Lett., vol. 87, issue 16, 2001, 168501).

JFM classification

Turbulent Flows: Stratified turbulence Turbulent Flows: Turbulence theory

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JFM Papers
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Journal of Fluid Mechanics , Volume 998 , 10 November 2024 , A17
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© The Author(s), 2024. Published by Cambridge University Press

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