The stability of shearing motion in a rotating fluid

This paper is concerned with the stability of a parallel shear flow in an inviscid homogeneous unbounded rotating fluid. A sufficient condition for stability is obtained in terms of the dimensionless parameter N = (cosϕ)/S, where ϕ is the angle between the wave-number K of the disturbance and the axis of rotation, and S is the Rossby number based on the thickness of the shear layer and the change in velocity across the layer. The condition is that infinitesimal disturbances are stable if either N ≥ 1/2(1-sin\; θ)\; \; or\; \; N ≤ -1/2(1+sin\; θ) Where θ is the angle between k and the direction of streaming. For a shear layer profile of the type U = tanh z, the neutral curves are calculated for various Rossby numbers. These are compared to the stability of a shear layer in a stratified non-rotating fluid. The stability criterion for the large wave-numbers in a cylindrical shear layer is inferred from these results.