Mesoscopic theory of sound wave mechanics in gases: an anisotropic approach

Abstract Background: Classical statistical mechanics and traditional Navier-Stokes gas dynamics describe acoustic perturbation transport in gaseous media through isotropic macroscopic approximations based on the postulate of permanent thermodynamic chaos. This approach assumes instantaneous equipartition of energy across all internal degrees of freedom, which inherently creates systematic deviations when compared to empirical field measurements in the real atmosphere and dense boundary layers. Methods: This paper operates within the deterministic paradigm of Ibragimov-Gert extended anisotropic thermodynamics to present a mesoscopic model of pre-relaxation wave transport. The proposed physical framework rejects Maxwell-Boltzmann velocity distributions, interpreting acoustic perturbations as the result of localized potential Coulomb interactions of particle electron shells forming dynamic, elastic mesostructures termed chains of molecules. Results: Based strictly on the law of conservation of momentum, we demonstrate that the translation of a directed amount of motion along the wave vector enforces a kinematic prohibition on transverse and rotational dissipation. This boundary condition suppresses parasitic degrees of freedom, driving the effective number of degrees of freedom strictly to unity. From this microstructural mechanics, a strict deterministic invariant relationship between the speed of sound and packaging density is derived, eliminating the need for empirical approximations. Furthermore, exact kinetic and thermodynamic thresholds governing the sudden phase breakdown and destruction of the linear mesostructure are mathematically established. Conclusions: The resulting model proves that keeping the medium in an anisotropic state during pre-relaxation collision stages eliminates classical entropy losses. The derived critical degradation temperature provides a rigorous engineering framework for calculating flow stall triggers and the transition of boundary layers from harmonic wave transport into unsteady shock wave modes with an anisotropic density jump. The theoretical model is validated against real-world atmospheric profiles, demonstrating an accuracy exceeding 99 percent. This is an English translation of an article published earlier