The Spectrum of the turbulence based on theory of stochastic equations and equivalenceof measures

Abstract

Abstract The formation of the spectrum of turbulence in the inertial interval on the basis of the new theory of stochastic hydrodynamics is presented. This theory is based on the theory of stochastic equations of continuum laws and equivalence of measures between random and deterministic movements. The purpose of the article is to present a solution based on these stochastic equations for the formation of the turbulence spectrum in the inertial interval in the form of the spectral function E(k)j depending on wave numbers k in form E(k)j∼kn. The results of analytical solutions showed a satisfactory correspondence of the obtained dependence with the classical Kolmogorov’s dependence in the form of E(k)j∼k5/3.