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The structure of energy fluxes in wave turbulence

Published online by Cambridge University Press:  06 January 2023

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, NY 12180, USA
Yuri V. Lvov
Affiliation:
Department of Mathematical Sciences, Rensselaer Polytechnic Institute, 110 8th St, Troy, NY 12180, USA
*
†Email address for correspondence: dematg@rpi.edu
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Abstract

We calculate the net energy per unit time exchanged between two sets of modes in a generic system governed by a three-wave kinetic equation. Our calculation is based on the property of detailed energy conservation of the triadic resonant interactions. In a first application to isotropic systems, we re-derive the previously used formula for the energy flux as a particular case for adjacent sets. We then exploit the new formalism to quantify the level of locality of the energy transfers in the example of surface capillary waves. A second application to anisotropic wave systems expands the currently available set of tools to investigate magnitude and direction of the energy fluxes in these systems. We illustrate the use of the formalism by characterizing the energy pathways in the oceanic internal wavefield. Our proposed approach, unlike traditional approaches, is not limited to stationarity, scale invariance and strict locality. In addition, we define a number $w$ that quantifies the scale separation necessary for two sets of modes to having negligible mutual energy exchange, with potential consequences in the interpretation of wave turbulence experiments. The methodology presented here provides a general, simple and systematic approach to energy fluxes in wave turbulence.

JFM classification

Geophysical and Geological Flows: Internal waves Turbulent Flows: Wave-turbulence interactions Waves/Free-surface Flows: Capillary waves
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 954 , 10 January 2023 , A30
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Copyright
© The Author(s), 2023. Published by Cambridge University Press

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References

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