Three-Dimensional Acoustic Turbulence: Weak Versus Strong

TL;DR

This paper investigates three-dimensional acoustic turbulence through direct numerical simulations, revealing distinct spectral behaviors in weak and strong regimes, including the Zakharov-Sagdeev spectrum and shock formation.

Contribution

It demonstrates the existence of the Zakharov-Sagdeev spectrum in weak acoustic turbulence and explores the transition to shock-dominated turbulence in the strong regime.

Findings

Zakharov-Sagdeev spectrum $ ightarrow k^{-3/2}$ in weak turbulence

Jets in $k$-space form narrow cones

Shocks form in strong turbulence with KP spectrum

Abstract

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.