Exact solution to the main turbulence problem for a compressible medium and the universal -8/3 turbulence spectrum of breaking waves

TL;DR

This paper provides an exact analytical solution to compressible turbulence, resolving the Onsager anomaly, and establishes a universal -8/3 energy spectrum relevant to acoustic and space turbulence observations.

Contribution

It introduces an exact solution to compressible turbulence equations and derives a universal energy spectrum, advancing understanding of turbulence collapse and acoustic turbulence.

Findings

Exact analytical solution for compressible turbulence

Resolution of Onsager dissipative anomaly

Universal -8/3 energy spectrum for turbulence collapse

Abstract

An explicit analitical description of the compressible turbulence, based on the exact solution of the one-dimensional Euler equations in the unbounded case is obtained. The Onsager dissipative anomaly is resolved. The exact universal -8/3 energy spectrum corresponding to the finite time collapse of Euler's solution is stated. That spectrum is relevant to strong acoustic turbulence and observation in the space turbulence.