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Discrete and mesoscopic regimes of finite-size wave turbulence

V. S. L’vov1 and S. Nazarenko2

  • 1Department of Chemical Physics, The Weizmann Institute of Science, Rehovot 76100, Israel
  • 2Mathematics Institute, University of Warwick, Coventry CV4 7AL, United Kingdom

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Phys. Rev. E 82, 056322 – Published 19 November, 2010

DOI: https://doi.org/10.1103/PhysRevE.82.056322

Abstract

Bounding volume results in discreteness of eigenmodes in wave systems. This leads to a depletion or complete loss of wave resonances (three-wave, four-wave, etc.), which has a strong effect on wave turbulence (WT) i.e., on the statistical behavior of broadband sets of weakly nonlinear waves. This paper describes three different regimes of WT realizable for different levels of the wave excitations: discrete, mesoscopic and kinetic WT. Discrete WT comprises chaotic dynamics of interacting wave “clusters” consisting of discrete (often finite) number of connected resonant wave triads (or quarters). Kinetic WT refers to the infinite-box theory, described by well-known wave-kinetic equations. Mesoscopic WT is a regime in which either the discrete and the kinetic evolutions alternate or when none of these two types is purely realized. We argue that in mesoscopic systems the wave spectrum experiences a sandpile behavior. Importantly, the mesoscopic regime is realized for a broad range of wave amplitudes which typically spans over several orders on magnitude, and not just for a particular intermediate level.

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Phys. Rev. E 82, 056322– Published 19 November, 2010
  • Received 18 June 2010

© 2010 American Physical Society

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