Nonlinear diffusion models for gravitational wave turbulence

PHYSICA D-NONLINEAR PHENOMENA

卷:390

Article

Galtier, Sebastien^1,2  Nazarenko, Sergey, V³  Buchlin, Eric⁴  Thaiabard, Simon⁵ 

[1] Univ Paris Saclay, Lab Phys Plasmas, Univ Paris Sud, Ecole Polytech, F-91128 Palaiseau, France

[2] Inst Univ France, Paris, France

[3] Univ Cote dAzur, INPHYNI, CNRS, Nice, France

[4] Univ Paris Saclay, Inst Astrophys Spatiale, CNRS, Univ Paris Sud, Bat 121, F-91405 Orsay, France

[5] IMPA, Inst Nacl Matemat Pura & Aplicada, BR-22460320 Rio De Janeiro, Brazil

关键词: Wave turbulence;    Diffusion model;    Inverse cascade;    Cosmology;   

DOI  :  10.1016/j.physd.2019.01.007

来源: Elsevier

【 摘 要 】

A fourth-order and a second-order nonlinear diffusion model in spectral space are proposed to describe gravitational wave turbulence in the approximation of strongly local interactions. We show analytically that the model equations satisfy the conservation of energy and wave action, and reproduce the power law solutions previously derived from the kinetic equations with a direct cascade of energy and an explosive inverse cascade of wave action. In the latter case, we show numerically by computing the second-order diffusion model that the non-stationary regime exhibits an anomalous scaling which is understood as a self-similar solution of the second kind with a front propagation following the law k(f) similar to (t(*) - t)(3.296) with t < t(*). These results are relevant to better understand the dynamics of the primordial universe where potent sources of gravitational waves may produce space-time turbulence. (C) 2019 Elsevier B.V. All rights reserved.

【 授权许可】

Free