Energy Spectrum of Two-Dimensional Acoustic Turbulence

We report an exact unique constant-flux power-law analytical solution of the wave kinetic equation for law, ??k = csk[1 + (ak)2], ak << 1. Here, ?? is the energy flux over scales, and C1 is the universal constant which was found analytically. Our theory describes, for example, acoustic turbulence in 2D Bose-Einstein condensates. 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.

Automated summary

We present an exact unique constant-flux power-law analytical solution for the wave kinetic equation, applicable for ak << 1. Our theory describes acoustic turbulence in 2D Bose-Einstein condensates, and the corresponding spectrum is confirmed through numerical simulations.