To the theory of turbulent micropolar fluid with an internal vortex structure
Abstract:
A modern approach to thermodynamic modelling of developed turbulent flows of micropolar compressible fluid based on the formalism of extended irreversible thermodynamics is considered. The description of the turbulent motion of a micropolar fluid is carried out in the framework of a generalised continuum model consisting of two interconnected open subsystems - the subsystem of averaged motion and the subsystem of turbulent chaos (associated with small-scale vortex motion of the fluid). This allowed us to construct a second-order evolutionary hyperbolic closure model based on nonlinear constitutive equations of turbulent flow transport using the generalised Gibbs equation and a general form of entropy flux. The proposed approach agrees well with the idea of A.N. Kolmogorov about the possibility of representing the angular velocity pseudovector as an internal parameter for a thermodynamically open turbulent system if the scale of the differential grid exceeds the size of mesovortices. It is this consideration that allowed us to develop continuum turbulence equations that reflect the effect of internal rotation of turbulent mesovortices, as well as the case of a turbulent micropolar fluid with aniso-tropy of vortex character, which correlates with the nonzero antisymmetric part of the Reynolds tensor. The results obtained can be used in the study of turbulent motions of micropolar fluids in the interior of stars, giant planets, as well as in the atmosphere of the Sun and other cosmic bodies.
