Stratified circular Couette flow: instability and flow regimes

Abstract

The stability conditions of the flow between two concentric cylinders with the inner one rotating (circular Couette flow) have been investigated experimentally and theoretically for a fluid with axial, stable linear density stratification. The behaviour of the flow, therefore, depends on the Froude number Fr = Ω/N (where Ω is the angular velocity of the inner cylinder and N is the buoyancy frequency of the fluid) in addition to the Reynolds number and the non-dimensional gap width ε, here equal to 0.275.Experiments show that stratification has a stabilizing effect on the flow with the critical Reynolds number depending on N, in agreement with linear stability theory. The selected, most amplified, vertical wavelength at onset of instability is reduced by the stratification effect and is for the geometry considered only about half the gap width. Furthermore, the observed instability is non-axisymmetric. The resulting vortex motion causes some mixing and this leads to layer formation, clearly visible on shadowgraph images, with the height of the layer being determined by the vertical vortex size. This regime of vertically reduced vortex size is referred to as the S-regime.For larger Reynolds and Froude numbers the role of stratification decreases and the most amplified vertical wavelength is determined by the gap width, giving rise to the usual Taylor vortices (we call this the T-regime). The layers which emerge are determined by these vortices. For relatively small Reynolds number when Fr ≈ 1 the Taylor vortices are stable and the layers have a height h equal to the gap width; for larger Reynolds number or Fr ≈ 2 the Taylor vortices interact in pairs (compacted Taylor vortices, regime CT) and layers of twice the gap width are predominant. Stratification inhibits the azimuthal wavy vortex flow observed in homogeneous fluid. By further increasing the Reynolds number, turbulent motions appear with Taylor vortices superimposed like in non-stratified fluid.The theoretical analysis is based on a linear stability consideration of the axisymmetric problem. This gives bounds of instability in the parameter space (Ω, N) for given vertical and radial wavenumbers. These bounds are in qualitative agreement with experiments. The possibility of oscillatory-type instability (overstability) observed experimentally is also discussed.