Finite gap effects on the instability of stratified circular Couette flow

Abstract

We investigate, in the inviscid limit, the conditions for the occurrence of the strato-rotational instability (in short SRI) in a Taylor–Couette system controlled by a rotation ratio μ and a radius ratio η . In the small gap limit, the modified Rayleigh criterion provides the instability condition, μ < 1 . However, unstable modes were only observed in experiments when μ < η . Taking into account finite gap effects, we derive the dispersion relation for non-axisymmetric perturbations and compute the exact value of the growth rate. Besides, an analytical approach is carried out providing approximate values of the selected axial wavenumbers. For three representative values of the gap size, it is found that as μ increases, the narrowing of the band of axial wavenumbers is enhanced and accompanied by a shift towards higher wavenumber values. Wavenumbers observed in experiments and computations fall inside the bounded interval predicted by the finite gap approach provided μ is less than a value μ s close to the stability limit found in these available data.