Critical Velocity and Flow Instability Induced by Kinetic Anisotropy

The onset of flow instability and transition to turbulence in fluids is traditionally characterized using macroscopic parameters such as the Reynolds number. In this work, we propose a complementary microscopic mechanism based on kinetic-theory considerations. Building on a velocity-dependent anisotropic distribution of particle velocities introduced in a recent preprint (Gonuguntla, Zenodo DOI: 10.5281/zenodo.19386768), we show that transverse momentum fluctuations decrease with increasing flow speed, leading to a reduction in transverse pressure and a corresponding loss of restoring forces against perturbations. A critical velocity scale is derived at which transverse fluctuations vanish, and the approach to this regime naturally induces instability. The framework provides a physically transparent connection between microscopic velocity distribution anisotropy and macroscopic flow instability, complementing classical approaches.