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arXiv · 2501.17023

Asymmetric dual cascade in gravitational wave turbulence

Benoît Gay·Sébastien Galtier
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Abstract

We numerically simulate, in both the forced and decay regimes, a fourth-order nonlinear diffusion equation derived from the kinetic equation of gravitational wave turbulence in the limit of strongly local quartic interactions. When a forcing is applied to an intermediate wavenumber $k_i$, we observe a dual cascade of energy and wave action. In the stationary state, the associated flux ratio is proportional to $k_i$, and the Kolmogorov-Zakharov spectra are recovered. In decaying turbulence, the study reveals that the wave action spectrum can extend to wavenumbers greater than the initial excitation $k_i$ with constant negative flux, while the energy flux is positive with a power law dependence in $k$. This leads to an unexpected result: a single inertial range with a Kolmogorov-Zakharov wave action spectrum extending progressively to wavenumbers larger than $k_i$. We also observe a wave action decay in time in $t^{-1/3}$ while the front of the energy spectrum progresses according to a $t^{1/3}$ law. These properties can be understood with simple theoretical arguments.

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BibTeXRIS

Benoît Gay, Sébastien Galtier. 2025-01-28. Asymmetric dual cascade in gravitational wave turbulence. https://arxiv.org/abs/2501.17023

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