Anisotropic spectra of acoustic type turbulence

TL;DR

This paper investigates the spectra of acoustic turbulence generated by shocks, revealing that weak anisotropy results in a $k^{-2}$ spectrum similar to KP, with a universal $requency^{-2}$ frequency fall-off, and strong anisotropy leads to jet-like spectra.

Contribution

It provides a theoretical analysis of anisotropic spectra in shock-generated acoustic turbulence, extending understanding of spectral behaviors under different anisotropy conditions.

Findings

Weak anisotropy yields a $k^{-2}$ spectrum similar to KP.

Frequency spectrum consistently falls off as $requency^{-2}$ regardless of anisotropy.

Strong anisotropy causes the formation of jet-like spectra in large $k$ regions.

Abstract

We consider the problem of spectra for acoustic type of turbulence generated by shocks being randomly distributed in space. We show that for turbulence with a weak anisotropy such spectra have the same dependence in $k$-space as the Kadomtsev-Petviashvili (KP) spectrum: $E(k)\sim k^{-2}$. However, the frequency spectrum has always the falling $\sim \omega^{-2}$, independently on anisotropy. In the strong anisotropic case the energy distribution relative to wave vectors takes anisotropic dependence forming in the large $% k $ region the spectra of the jet type.