Two-fluid Taylor-Couette flow with countercurrent axial flow: Linear theory for immiscible liquids between corotating cylinders

We computationally investigate the stability of a pair of radially stratified immiscible liquids undergoing countercurrent axial flow in the annular gap between rapidly corotating coaxial cylinders: two-fluid Taylor-Couette flow with counterflow. A simple analysis determines conditions under which a nearly cylindrical interface is maintained in the presence of counterflow (i.e., axial pressure gradients). Stability analysis reveals that for small axial Reynolds numbers, the flow is slightly stabilized against Taylor-Couette instability, consistent with results for a single phase. At axial Reynolds numbers greater than about ten, however, the flow is susceptible to a (generally nonaxisymmetric) Kelvin-Helmholtz instability, which precedes the Taylor-Couette mode. Furthermore, new results are presented for the case without axial flow. A bifurcation to vortices that corotate with their counterparts in the other phase is found. Finally, limitations of the generalized Rayleigh criterion developed in our earlier work are elucidated. In particular, we show how it fails if one of the fluid layers is very thin. (C) 2000 American Institute of Physics. [S1070-6631(00)00602-4].