Hydrodynamic perturbations in a rotating viscous fluid and their stability (Q2754769)

The Navier-Stokes equations, continuity equation, and equation of state \(p=f(\rho)\) are linearized about a reference state. For the linearized system of equations, the author seeks solutions for pressure, density and velocity in a form containing multipliers \(\exp(i{\mathbf k}\cdot{\mathbf r}-i\omega t)\). To this end, the author derives in cylindrical coordinates an algebraical system of equations for the perturbations of pressure, density and components of velocity. Different simplified versions of this general system, corresponding to particular symmetries, are considered, and conditions for stability are established for these cases.