Turbulence of capillary waves - theory and numerical simulation

A. N. Pushkarev, V. E. Zakharov

Research output: Contribution to journalArticlepeer-review

93 Scopus citations

Abstract

An ensemble of weakly interacting capillary waves on a free surface of deep ideal fluid is described statistically by methods of weak turbulence. The stationary kinetic equations for capillary waves have an exact Kolmogorov solution which gives for the spatial spectrum of elevations asymptotics Ik = C(P1/23/4)k-19/4. The Kolmogorov constant C is found analytically together with the interval of locality in K-space. Direct numerical simulation of the dynamical equations in the approximation of small surface angles confirms the presence of almost isotropic Kolmogorov spectrum in the large k region. Besides, at small amplitudes of the pumping, an essentially new phenomenon is found: 'frozen' turbulence, in which, despite the big number of interacting waves (of the order of 100) there is no energy flux toward high k. This phenomenon is connected with the finiteness of the region (or, in other words, discreteness of the spectrum in Fourier space). This is believed to be universal for different sorts of nonlinear systems.

Original languageEnglish (US)
Pages (from-to)98-116
Number of pages19
JournalPhysica D: Nonlinear Phenomena
Volume135
Issue number1
DOIs
StatePublished - Jan 1 2000

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Condensed Matter Physics
  • Applied Mathematics

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