Stability of stationary solutions in Acoustic wave turbulence
Guillaume Costa, Giorgio Krstulovic, Sergey Nazarenko
TL;DR
This paper investigates the stability of steady-state solutions in acoustic wave turbulence, using theoretical and numerical methods to analyze how small perturbations evolve in 2D and 3D cases.
Contribution
It provides a combined theoretical and numerical analysis of the stability mechanisms for equilibrium and non-equilibrium solutions in acoustic wave turbulence.
Findings
Stability mechanisms differ between Rayleigh-Jeans and Kolmogorov-Zakharov solutions.
Small isotropic perturbations evolve differently in 2D and 3D.
The study characterizes the time evolution of perturbations in both equilibrium and non-equilibrium states.
Abstract
We study the stability of steady-state solutions of the Wave-Kinetic Equations for acoustic waves. Combining theoretical analysis and numerical simulations, we characterise the time evolution of small isotropic perturbations for both 2D and 3D equilibrium Rayleigh-Jeans and non-equilibrium Kolmogorov-Zakharov solutions. In particular, we show that the stability of these solutions is ensured by different mechanisms.
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