A One-Dimensional Model for Dispersive Wave Turbulence

Research output: Contribution to journalArticle

Abstract

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. These models have an explicitly solvable weak turbulence theory which is developed here, with Kolmogorov-type wave number spectra exhibiting interesting dependence on parameters in the equations. These predictions of weak turbulence theory are compared with numerical solutions with damping and driving that exhibit a statistical inertial scaling range over as much as two decades in wave number. It is established that the quasi-Gaussian random phase hypothesis of weak turbulence theory is an excellent approximation in the numerical statistical steady state. Nevertheless, the predictions of weak turbulence theory fail and yield as much flatter (|k|-1/3) spectrum compared with the steeper (|k|-3/4) spectrum observed in the numerical statistical steady state. The reasons for the failure of weak turbulence theory in this context are elucidated here. Finally, an inertial range closure and scaling theory is developed which successfully predicts the inertial range exponents observed in the numerical statistical steady states.

Original languageEnglish (US)
Pages (from-to)9-44
Number of pages36
JournalJournal of Nonlinear Science
Volume7
Issue number1
StatePublished - Jan 1997

Fingerprint

One-dimensional Model
Turbulence
turbulence
Range of data
scaling
Dispersive Equations
Scaling Theory
Prediction
Wave equations
predictions
closures
wave equations
Wave equation
Damping
Closure
damping
Exponent
Numerical Solution
exponents
Scaling

Keywords

  • Cascades
  • Inertial range
  • Turbulence

ASJC Scopus subject areas

  • Computational Mechanics
  • Mechanics of Materials
  • Mathematics(all)
  • Applied Mathematics
  • Mathematical Physics
  • Statistical and Nonlinear Physics

Cite this

A One-Dimensional Model for Dispersive Wave Turbulence. / Majda, A. J.; McLaughlin, D. W.; Tabak, E. G.

In: Journal of Nonlinear Science, Vol. 7, No. 1, 01.1997, p. 9-44.

Research output: Contribution to journalArticle

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