On the instability of rapidly rotating shear flows to non-axisymmetric disturbances

Abstract

The stability is considered of the flow with velocity components \[ \{0,\Omega r[1+O(\epsilon^2)],\;2\epsilon\Omega r_0f(r/r_0)\} \] (where f(x) is a function of order one) in cylindrical polar co-ordinates (r, ϕ, z), bounded by the rigid cylinders r/r₀ = x₁ and r/r₀ = 1 (0 [les ] x₁ < 1). When ε [Lt ] 1, the flow is shown to be unstable to non-axisymmetric inviscid disturbances of sufficiently large axial wavelength. The case of Poiseuille flow in a rotating pipe is considered in more detail, and the growth rate of the most rapidly growing disturbance is found to be 2εΩ.