Acoustic scattering by turbulent fluctuations of pressure and entropy

Detailed analysis is presented of the well-known Tatarskii’s formula, which describes sound wave scattering in a turbulent atmosphere. The adiabaticity of the acoustic fluctuations and incompressibility of the turbulent fluctuations are assumed only. This yields to additional 1 terms in the classical formula (probably, small in the inertial range of turbulence). We show the change of Obukhov’s formula, which describes the connection between turbulent fluctuations of pressure and velocities in a compressible atmosphere, and also demonstrate the effect of the independence of fluctuations of the potential and thermodynamic temperatures. By analogy with the formula for small-scale isotropic temperature fluctuations, which was also obtained by Obukhov, we derive a formula for the fluctuations of entropy and potential density as function of entropy, which describes spatial distribution of the probability density of identical “fluid particles” in the turbulent media.