<b>Abstract</b>— <p>A modern approach to thermodynamic modeling of developed turbulent flows of micropolar compressible fluid is considered, based on the application of the formalism of extended irreversible thermodynamics. The description of turbulent motion of turbulent fluid is carried out within the framework of the generalized continuum model consisting of two interconnected open subsystems—the averaged motion subsystem and the turbulent chaos subsystem (associated with small-scale vortex motion of the fluid). This made it possible to construct an evolutionary hyperbolic second-order closure model based on nonlinear constitutive equations of turbulent flow transfer using the generalized Gibbs equation and the general form of the entropy flux. The proposed methodology is in good agreement with the idea of A.N. Kolmogorov on the possibility of representing the pseudovector of angular velocity as an internal parameter for a thermodynamically open turbulent system if the scale of the differential grid exceeds the size of the mesovortices. It is this consideration that made it possible to develop continuous equations of turbulence that reflect the effect of internal rotation of turbulent mesovortices, as well as the case of a turbulent fluid with anisotropy of a vortex nature, which is related to the nonzero antisymmetric part of the Reynolds tensor. The results obtained can be used in studying the turbulent motions of micropolar fluids in the depths of stars, giant planets, as well as in the atmosphere of the Sun and other cosmic bodies.</p>