Energy spectrum of two-dimensional acoustic turbulence

Abstract

We report an exact unique constant-flux power-law analytical solution of the wave kinetic equation for the turbulent energy spectrum, $E(k)=C_1\sqrt{\epsilon a{c}_{\mathrm{s}}}/k$, of acoustic waves in 2D with almost linear dispersion law, ${\omega }_k=c_{\mathrm{s}}k[1+(ak{)}^2]$, $ak\ll 1$. Here $\epsilon$ is the energy flux over scales, and $C_1$ is the universal constant which was found analytically. Our theory describes, for example, acoustic turbulence in 2D Bose-Einstein condensates (BECs). The corresponding 3D counterpart of turbulent acoustic spectrum was found over half a century ago, however, due to the singularity in 2D, no solution has been obtained until now. We show the spectrum $E(k)$ is realizable in direct numerical simulations of forced-dissipated Gross-Pitaevskii equation in the presence of strong condensate.

References in corpus (2)

• Emergence of a Turbulent Cascade in a Quantum Gas
• Experiments in Surface Gravity-Capillary Wave Turbulence

Cited by in corpus (14)

• Direct and inverse cascades in turbulent Bose-Einstein condensate
• Turbulent dynamics in two-dimensional paraxial fluid of light
• Spectral analysis for compressible quantum fluids
• Direct numerical simulation of acoustic turbulence: Zakharov-Sagdeev spectrum
• Inverse cascade of gravity waves in the presence of condensate: numerical simulation
• Feynman rules for forced wave turbulence
• Self-similar evolution of wave turbulence in Gross-Pitaevskii system
• Transition from wave turbulence to acousticlike shock-wave regime
• Nonlocal gravity wave turbulence in presence of condensate
• Numerical Study of Free-Surface Electrohydrodynamic Wave Turbulence
• Simulation of the Wave Turbulence of a Liquid Surface Using the Dynamic Conformal Transformation Method
• Internal gravity waves in stratified flows with and without vortical modes
• Observation of Jones-Roberts solitons in a paraxial quantum fluid of light
• Stability of stationary solutions in Acoustic wave turbulence