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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[ϵac_{s}]/k, of acoustic waves in 2D with almost linear dispersion law, ω_{k}=c_{s}k[1+(ak)^{2}], ak≪1. Here, ϵ 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. 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.
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