Viscous corrections for the stability of a two-fluid rotating column

A temporal instability analysis of a two-fluid rotating viscous column enclosed in a rigid cylinder is performed by numerically discretizing the equations for the evolution of disturbances in each phase in the rotating frame of reference. Normal mode analysis applied to such equations leads to two eigenvalue problems, each valid in the region occupied by the single phase fluid and mutually related to each other by the interface conditions. The eigenvalue problem has been solved numerically by suitably discretizing the differential operators by means of a Chebyschev collocation spectral method. A complete investigation of the preferred modes of instability has been carried out over a wide range of the parameter space for the case of the higer density fluid located in the annulus. The behavior of the system in some asymptotic limits of the parameters has been determined and compared to the solutions of simplified corresponding formulations.