A one-dimensional model for dispersive wave turbulence
type: Item
instance of: scholarly article
title: A one-dimensional model for dispersive wave turbulence
zbMATH Open document ID: 0882.76035
DOI: 10.1007/BF02679124
author: David W. McLaughlin
author: Esteban G. Tabak
author: Andrew J. Majda
published in: Journal of Nonlinear Science
publication date: 1998-03-11T00:00:00Z
review text: A family of one-dimensional nonlinear dispersive wave equations is introduced as a model for assessing the validity of weak turbulence theory for random waves in an unambiguous and transparent fashion. Special form of solution (sum of dispersive waves plus one unknown function) is assumed, and the family of equations is transformed into a system of four nonlinear ordinary differential equations. These equations can be integrated explicitly in terms of elliptic functions. Instead of the analytical solution, the authors present a numerical one for several values of parameters. The equation considered in Fourier space is generalized to the case when forcing and dissipation are present. For this case, the direct and inverse turbulent cascades are obtained and reduced to the Kolmogorov solution. The numerical simulation based on this model is a subject for detailed discussion. To bring the obtained results nearer to the theoretical ones, a critical review of the assumption of weak turbulence theory is made. The authors discuss the possibilities for improvement to the theory.
Mathematics Subject Classification ID: 76F99
Mathematics Subject Classification ID: 60G10
Mathematics Subject Classification ID: 60H15
zbMATH DE Number: 994021
zbMATH Keywords: weak turbulence theory
zbMATH Keywords: random waves
zbMATH Keywords: system of four nonlinear ordinary differential equations
zbMATH Keywords: elliptic functions
zbMATH Keywords: Fourier space
zbMATH Keywords: forcing
zbMATH Keywords: dissipation
zbMATH Keywords: inverse turbulent cascades
zbMATH Keywords: Kolmogorov solution
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 994021