Asymmetric dual cascade in gravitational wave turbulence

TL;DR

This paper numerically investigates gravitational wave turbulence, revealing a dual cascade phenomenon with a novel inertial range where wave action extends beyond initial excitation scales, supported by theoretical insights.

Contribution

It introduces a fourth-order nonlinear diffusion model for gravitational wave turbulence and uncovers a unique dual cascade with an extended inertial range in decay regimes.

Findings

Dual cascade of energy and wave action observed.

Wave action spectrum extends beyond initial excitation wavenumber.

Wave action decays as t^{-1/3} while energy front advances as t^{1/3}.

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.