Effect of rotation on stability of advective flow in horizontal liquid layer with a free upper boundary

A horizontal liquid film of infinite extent is bounded below by a rigid plane and above by free surface, rotating about a vertical axis. Advective flow is set by imposing a constant temperature gradient on both boundaries. In the framework of Boussinesq approximation, we obtain an exact stationary solution of Navier–Stokes equations. The linear theory of stability for such flow is numerically investigated by reducing the initial system to the boundary problem for linear one-dimensional partial differential equations. The neutral stability flow states for normal perturbations are carried out; then the critical flow parameters allow us to get the dependence between the critical Grashof number and the wave number for various Taylor ones at a fixed Prandtl number, Pr=6.7.