Formation of a Turbulence Spectrum in the Inertial Interval on the Basis of the Theory of Stochastic Equations and Equivalence of Measures

An analytical representation of a turbulence spectrum in the inertial interval is given based on stochastic equations for the continual laws of continuous medium and the laws of the equivalence of measures between random and deterministic motions in the theory of stochastic hydrodynamics. The analytical solution of these equations is presented in the form of spectral function E(k) similar to k(n) corresponding to the classical dependence E(k) similar to k(-5/3) obtained earlier by A. N. Kolmogorov in the statistical theory on the basis of dimensional considerations. The presented solution confirms the possibility of determining partial solutions for the spectral function depending on the wave number on the base of single implications of the theory of stochastic hydrodynamics within the framework of which the solutions in the fi eld of wave numbers of turbulence generation were obtained.