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 ∝ 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.
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Kochurin et al. (2024) studied this question.
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