Direct numerical simulation of acoustic turbulence: Zakharov-Sagdeev spectrum

TL;DR

This study uses direct numerical simulation to analyze three-dimensional acoustic turbulence, revealing jet formation, spectrum broadening, and a power-law energy distribution consistent with Zakharov-Sagdeev theory.

Contribution

It provides the first detailed numerical evidence of the Zakharov-Sagdeev spectrum in acoustic turbulence with weak positive dispersion.

Findings

Jets form in the initial energy distribution at long wavelengths.

The turbulence spectrum follows a power-law with an exponent near 3/2.

Spectrum becomes isotropic at higher wavenumbers.

Abstract

We present the results of direct numerical simulation of three-dimensional acoustic turbulence in medium with weak positive dispersion. It is shown that at the beginning of the long-wavelength region in the turbulence energy distribution in the $k$-space, there are formed jets in the form of narrow cones. At larger wavenumbers, the cones broaden, and the distribution accordingly tends to isotropic. In this region of wavenumbers, the angle-averaged turbulence spectrum acquires a power-law character, $E(k)\propto k^{-\alpha}$, with the exponent close to $3/2$, which corresponds to the Zakharov-Sagdeev weak acoustic turbulence spectrum.