Three-Dimensional Acoustic Turbulence: Weak Versus Strong

Direct numerical simulation of three-dimensional acoustic turbulence has been performed for both weak and strong regimes. Within the weak turbulence, we demonstrate the existence of the Zakharov-Sagdeev spectrum $\propto k^{-3/2}$ not only for weak dispersion but in the non-dispersion (ND) case as well. Such spectra in the $k$-space are accompanied by jets in the form of narrow cones. These distributions are realized due to small nonlinearity compared with both dispersion/diffraction. Increasing pumping in the ND case due to dominant nonlinear effects leads to the formation of shocks. As a result, the acoustic turbulence turns into an ensemble of random shocks with the Kadomtsev-Petviashvili spectrum.