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On non-perturbative formulation of hydrodynamics using kinetic theory

We show that some hydrodynamics problems can be analyzed by extracting the rich non-equilibrium information available in kinetic theory in a non-perturbative way. Examples include (i) an exactly derived generalized hydrodynamics description of finite Knudsen phenomena and (ii) a description of statistical properties of inhomogeneous turbulent flows. In the first case, for simple flows driven by external force (channel) or moving boundaries (Couette), the exact analytical solutions demonstrate substantial deviation from the classical behavior resulting from the Navier–Stokes equation, due to the presence of strong non-equilibrium effects. In the case of turbulence, the kinetic theoretic approach advocated here represents a coarse-grained statistical description of turbulent eddies with a specified non-constant interaction time. We argue that this approach is advantageous and more general for modeling turbulent flows including strongly non-equilibrium non-homogeneous turbulence phenomena, such as rapid distortion effects and secondary turbulent structures.