Renormalized Resonance Quartets in Dispersive Wave Turbulence

Wonjung Lee, Gregor Kovačič, and David Cai
Phys. Rev. Lett. 103, 024502 – Published 7 July 2009

Abstract

Using the (1+1)D Majda-McLaughlin-Tabak model as an example, we present an extension of the wave turbulence (WT) theory to systems with strong nonlinearities. We demonstrate that nonlinear wave interactions renormalize the dynamics, leading to (i) a possible destruction of scaling structures in the bare wave systems and a drastic deformation of the resonant manifold even at weak nonlinearities, and (ii) creation of nonlinear resonance quartets in wave systems for which there would be no resonances as predicted by the linear dispersion relation. Finally, we derive an effective WT kinetic equation and show that our prediction of the renormalized Rayleigh-Jeans distribution is in excellent agreement with the simulation of the full wave system in equilibrium.

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  • Received 15 December 2008

DOI:https://doi.org/10.1103/PhysRevLett.103.024502

©2009 American Physical Society

Authors & Affiliations

Wonjung Lee1, Gregor Kovačič2, and David Cai1,3,*

  • 1Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, New York 10012, USA
  • 2Mathematical Sciences Department, Rensselaer Polytechnic Institute, 110 8th Street, Troy, New York 12180, USA
  • 3Mathematics Department, Shanghai Jiao Tong University, Shanghai 200240, China

  • *cai@cims.nyu.edu.

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Vol. 103, Iss. 2 — 10 July 2009

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