Instability criterion for oblique modes in stratified circular Couette flow

An analytical approach is carried out that provides an inviscid stability criterion for the strato-rotational instability (in short SRI) occurring in a Taylor-Couette system. The control parameters of the problem are the rotation ratio μ and the radius ratio η. The study is motivated by recent experimental [1] and numerical [2, 3] results reporting the existence of unstable modes beyond the Rayleigh line for centrifugal instability (μ = η2). The modified Rayleigh criterion for stably stratified flows provides the instability condition, μ < 1, while in experiments unstable modes were never found beyond the line μ = η. Taking into account finite gap effects, we consider non axisymmetric perturbations with azimuthal wavenumber l in the limit lFr << 1, where Fr is the Froude number. We derive a necessary condition for instability : μ < μ∗ where μ∗, a function of η, takes the asymptotic values, μ∗ → 1 in the narrow gap limit, and μ∗ → 2η2(1 + η) in the wide gap limit, in agreement with recent numerical findings. A stronger condition, μ < η, is found when η > 0.38, in agreement with experimental results obtained for η = 0.8. Whatever the gap size, instability is predicted for values of μ larger than the critical one, μc = η 2, corresponding to centrifugal instability.