Non-equilibrium Statistical Thermohydrodynamics of Turbulence

A new approach to the theory of the small-scale dissipative turbulence based on non-equilibrium thermodynamics, continuum-mechanics and the statistical physics is developed in the monograph. The classical expression for the macroscopic kinetic energy of a small fluid particle in classical non-equilibrium thermodynamics is generalized by taking into account the local velocity shear related with the rate of strain tensor. The closure relation for the three-dimensional isotropic homogeneous small-scale dissipative turbulence (in an incompressible viscous Newtonian fluid) is founded by combining the classical statistical approaches, the conception of the statistical ensemble and the classical formulation of the law of large numbers. The significance of the new approach is evaluated for laboratory and oceanic stratified turbulence. The practical application of the new approach is shown in physical oceanography.