The linear stability of thermally stratified rotating channel flow

A linear stability analysis has been made of the hydrodynamic stability of viscous flow in a thermally stratified rotating channel. To understand the competition mechanism of the flow stabilization and destabilization, an inviscid stability criterion including effects of the rotation and stratification was first formulated for indicating the stable and unstable regimes of the flow. Then, an eigenvalue problem was derived for the viscous flow and solved using a shooting method. The combined effect of the Coriolis force and centrifugal-type buoyancy force on the longitudinal roll-cell instability was examined. For Prandtl number 7.11, the critical Reynolds number, corresponding critical wave number, and induced cell pattern of the longitudinal vortices are shown for various values of the rotation number and rotational Rayleigh number. Based on the analytical results, we predict the onset of the longitudinal roll-cell instability in this nonisothermal rotating channel flow. As compared to the isothermal rotating channel flow case, not only the critical Reynolds number but also the onset mode of the roll cell are altered significantly by the centrifugal-type buoyancy force. It is found that the flow may be stabilized or destabilized depending on the rotation and stratification of the channel. In the presence of a positive rotational Rayleigh number, the flow becomes more stable as compared with the isothermal rotating channel flow, otherwise, the flow becomes more unstable.