Stability of stationary solutions in Acoustic wave turbulence

2025/08/13 by Costa, Guillaume, Krstulovic, Giorgio, Nazarenko, Sergey
#Chaotic Dynamics (nlin.CD) #FOS: Physical sciences #Other Condensed Matter (cond-mat.other)

paper · doi:10.48550/arxiv.2508.09799

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.

Citations

• WavKinS.jl : an efficient and modular Julia software for solving wave kinetic equations
• Turbulence and far-from-equilibrium equation of state of Bogoliubov waves in Bose-Einstein Condensates
• Wave-kinetic dynamics of forced-dissipated turbulent internal gravity waves
• Instability of singular equilibria of a wave kinetic equation
• Stability and cascades for the Kolmogorov-Zakharov spectrum of wave turbulence
• Freely decaying turbulence and Bose-Einstein condensation in Gross-Pitaevski model

Related

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• A reaction network approach to the theory of acoustic wave turbulence