Small Reynolds number instabilities in two-layer Couette flow
The authors investigate instabilities in a two-layer Couette flow by using a small-Reynolds-number expansion of the eigenvalue problem governing the linear stability. The wave velocity and growth rate are given explicitly, and previous results for long waves and short waves are retrieved as special cases. In addition to the inertial instability due to viscosity stratification, the flow can also be subject to Rayleigh-Taylor instability. As a result of the competition between these two instabilities, inertia may completely stabilize a gravity-unstable flow above some critical Froude number, or conversely, for a gravity-stable flow, inertia may give rise to finite wave number instability above some finite critical Weber number. Here, the authors give general conditions for these phenomena, as well as calculate exact or approximate the values of critical numbers. The validity of asymptotic solutions is then investigated through comparison with numerical solutions.
scientific article; zbMATH DE number 1462578