Direct Numerical Simulation of Acoustic Turbulence: Zakharov–Sagdeev Spectrum

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 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.

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