Theory of turbulent transport on the basis of nonequilibrium statistical thermodynamics

A study is made of the transport of energy and momentum in systems with strong fluctuations when the description of the nonequitibrium state requires knowledge of not only the mean values of the densities of the energy and the momentum but also the distribution function of small-scale fluctuations. The nonequilibrium statistical operator method is used to obtain a coupled system of hydrodynamic equations for the mean densities of the energy and the momentum and a Fokker–Planck equation for the distribution function of the short-wavelength fluctuations. In the hydrodynamic equations for the large-scale motions, the transport coefficients are linear functionals of the distribution function of the short-wavelength fluctuations. It follows from the obtained system of equations that the hydrodynamic motions excite fluctuations, transferring to them energy and momentum, while the fluctuations damp the hydrodynamic motion, realizing thereby a feedback mechanism.