HYDRODYNAMIC STABILITY OF A FLUID LAYER FLOWING DOWN A ROTATING INCLINED PLANE

Abstract

The linear stability of a fluid layer flowing down a rotating inclined plant is investigated. The analysis leads to a system of two coupled ordinary differential equations that generalizes the well-known Orr-Sommerfeld equation. These coupled equations are solved by means of two approximations: the small wave-number approximation and the small Reynolds number approximation. For the small wave-number approximation, it is shown that the Coriolis force not only may decrease the growth rate of the instability, but it may stabilize the flow for all angles of propagation of the perturbation. For the small Reynolds and Taylor numbers and small angle of inclination, it is shown that an increase in Taylor number may destabilize the fluid layer.