Two-dimensional acoustic turbulence

Two-dimensional turbulence of the waves with linear dispersion law is analyzed numerically at small Mach numbers and large Reynolds numbers. It is shown that the energy-flux relation is close to E∝${\mathit{P}}^{2/3}$ as for a one-dimensional system. The analysis of the wave distribution in k space shows that the anisotropic large-scale pumping produces turbulence as a set of narrow jets that do not smear as the cascade proceeds towards high wave numbers. The energy spectrum along the direction of a jet is close to E(${\mathbf{k}}_{\mathbf{\parallel }}$ ${)\mathbf{\propto }\mathbf{k}}_{\mathbf{\parallel }}^{\mathbf{-}2}$ due to shock waves, while the spectrum per unit interval of wave numbers is E(k)∝${\mathit{P}}^{2/3}$ ${\mathit{k}}^{\mathrm{-}1}$ contrary to all previous predictions. Probability density functions of the velocity and velocity differences are found and compared with recent theoretical predictions. © 1996 The American Physical Society.