Next Article in Journal
Rheological Characterization of Carbopol® Dispersions in Water and in Water/Glycerol Solutions
Next Article in Special Issue
Generation of Wave Groups by Shear Layer Instability
Previous Article in Journal
Minkowski and Galilei/Newton Fluid Dynamics: A Geometric 3 + 1 Spacetime Perspective
Article Menu

Export Article

Open AccessArticle

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

1
Faculty of Civil and Environmental Engineering, Technion–Israel Institute of Technology, Haifa 32000, Israel
2
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]
  |  

Abstract

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
Figures

Figure 1

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).
SciFeed

Share & Cite This Article

MDPI and ACS Style

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

Show more citation formats Show less citations formats

Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Metrics

Article Access Statistics

1

Comments

[Return to top]
Fluids EISSN 2311-5521 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top