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Properties and asymptotics of water waves nonlinear interaction coefficient

Published online by Cambridge University Press:  21 April 2025

Vladimir Geogjaev Open the ORCID record for Vladimir Geogjaev [Opens in a new window]
Vladimir Geogjaev*
Affiliation:
Shirshov Institute of Oceanology of Russian Academy of Sciences, Nakhimovsky pr. 36, Moscow 117997, Russia Skolkovo Institute of Science and Technology, Bolshoy Boulevard 30, bld.1, Moscow 121205, Russia
*
Corresponding author: Vladimir Geogjaev, [email protected]
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Abstract

The Hasselmann equation for the nonlinear interactions of deep-water gravity waves differs from other four-wave kinetic equations by the interaction coefficient. The explicit formula for this coefficient (e.g. Krasitskii, J. Fluid. Mech., vol. 272, 1994, pp. 1–20; Zakharov, Eur. J. Mech. B/Fluids, vol. 18. issue 3, 1999, pp. 327–344) is of great complexity and leaves its properties obscured. We provide analytical results for the behaviour of the coefficient in different domains. The Phillips curve and discrete interaction approximation-like quadruplets are studied in detail. The coupling coefficient for the long–short wave interactions is calculated and found to be surprisingly small. This smallness greatly reduces the non-locality of the interactions.

JFM classification

Turbulent Flows: Turbulence theory Waves/Free-surface Flows: Surface gravity waves Waves/Free-surface Flows: Wave-structure interactions
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 1009 , 25 April 2025 , A54
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Copyright
© The Author(s), 2025. Published by Cambridge University Press

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