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On the Generalized Kinetic Equation for Surface Gravity Waves, Blow-Up and Its Restraint

Faculty of Civil and Environmental Engineering, Technion–Israel Institute of Technology, Haifa 32000, Israel
Centre for Mathematical Sciences, University of Plymouth, Plymouth PL4 8AA, UK
Author to whom correspondence should be addressed.
Received: 29 November 2018 / Revised: 19 December 2018 / Accepted: 24 December 2018 / Published: 30 December 2018
(This article belongs to the Special Issue Nonlinear Wave Hydrodynamics)
PDF [1817 KB, uploaded 30 December 2018]


This article is concerned with the non-linear interaction of homogeneous random ocean surface waves. Under this umbrella, numerous kinetic equations have been derived to study the evolution of the spectral action density, each employing slightly different assumptions. Using analytical and numerical tools, and providing exact formulas, we demonstrate that the recently derived generalized kinetic equation exhibits blow up in finite time for certain degenerate quartets of waves. This is discussed in light of the assumptions made in the derivation, and this equation is contrasted with other kinetic equations for the spectral action density. View Full-Text
Keywords: ocean-waves; non-linear interactions; kinetic equation ocean-waves; non-linear interactions; kinetic equation

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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).

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Andrade, D.; Stuhlmeier, R.; Stiassnie, M. On the Generalized Kinetic Equation for Surface Gravity Waves, Blow-Up and Its Restraint. Fluids 2019, 4, 2.

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