Direct numerical simulation of acoustic turbulence: Zakharov–Sagdeev spectrum

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 higher 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.