Geometrical Optics Stability Analysis of Rotating Visco-Diffusive Flows

Geometrical optics stability analysis has proven effective in addressing stability problems in ideal hydrodynamics and magnetohydrodynamics for 3D flows of both compressible and incompressible fluids. The method models perturbations as high frequency wavelets, evolving along fluid trajectories. Detecting local instabilities reduces to solving ODEs for the wave vector and amplitude of the wavelet envelope along streamlines, with coefficients derived from the background flow. While viscosity and diffusivity were historically considered stabilizing, recent studies incorporating both in the geometrical optics framework revealed their destabilizing potential in visco-diffusive and multi-diffusive flows. This extension has enabled analysis across a broad range of Prandtl, Schmidt, and magnetic Prandtl numbers, uncovering new instability citeria. This paper reviews these advancements and explores future applications and directions for the method.