Inverse cascade anomalies in fourth-order Leith models

Abstract We analyze a family of fourth-order non-linear diffusion models corresponding to local approximations of four-wave kinetic equations of weak wave turbulence. We focus on a class of parameters for which a dual cascade behavior is expected with an infrared finite-time singularity associated t...

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Bibliographic Details
Published inJournal of physics. A, Mathematical and theoretical Vol. 55; no. 1
Main Authors Thalabard, Simon, Medvedev, Sergey, Grebenev, Vladimir, Nazarenko, Sergey
Format Journal Article
LanguageEnglish
Published IOP Publishing 15.12.2021
Subjects
Physics
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Summary:Abstract We analyze a family of fourth-order non-linear diffusion models corresponding to local approximations of four-wave kinetic equations of weak wave turbulence. We focus on a class of parameters for which a dual cascade behavior is expected with an infrared finite-time singularity associated to inverse transfer of waveaction. This case is relevant for wave turbulence arising in the nonlinear Schrödinger model and for the gravitational waves in the Einstein’s vacuum field model. We show that inverse transfer is not described by a scaling of the constant-flux solution but has an anomalous scaling. We compute the anomalous exponents and analyze their origin using the theory of dynamical systems.
ISSN:1751-8113
1751-8121
DOI:10.1088/1751-8121/ac3858