TY - JOUR

T1 - Inverse cascade anomalies in fourth-order Leith models

AU - Thalabard, Simon

AU - Medvedev, Sergey

AU - Grebenev, Vladimir

AU - Nazarenko, Sergey

N1 - The authors thank A Mailybaev for useful discussions. ST acknowledges support from the Programa de CapacitacAo Institucional of CNPq and the French-Brazilian network in mathematics. The work of VG was partially supported by the 'chercheurs invites' awards of the Federation Doeblin FR 2800, Universite de la Cote d'Azur, France. The work of SN was supported by the Chaire D'Excellence IDEX (Initiative of Excellence) awarded by Universite de la Cote d'Azur, France, Simons Foundation Collaboration grant Wave Turbulence (Award ID 651471), the European Unions Horizon 2020 research and innovation programme in the framework of Marie Skodowska-Curie HALT project (Grant Agreement No. 823937) and the FET Flagships PhoQuS project (Grant Agreement No. 820392). The work of SM was supported by state funding program FSUS-2020-0034. Publisher Copyright: © 2021 IOP Publishing Ltd.

PY - 2022/1/7

Y1 - 2022/1/7

N2 - 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.

AB - 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.

KW - anomalous scaling

KW - differential models

KW - inverse cascade

KW - kinetic theory

KW - wave turbulence

UR - http://www.scopus.com/inward/record.url?scp=85122863263&partnerID=8YFLogxK

U2 - 10.1088/1751-8121/ac3858

DO - 10.1088/1751-8121/ac3858

M3 - Article

AN - SCOPUS:85122863263

VL - 55

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

IS - 1

M1 - 015702

ER -