Longitudinal Instability in Start-Stop Taylor-Couette Flow

Studies of flows in a differentially rotating annulus with time-varying boundary rotation have included sinusoidal modulations, impulsive starts, and impulsive stops. Here, a combined start-stop motion applied to the outer cylinder (with the inner cylinder held at rest) has revealed a novel instability to Taylor--Couette flow, namely a longitudinal mode approximately aligned with the axis of rotation that appears in the deceleration phase for a sufficiently narrow gap and rapidly breaks down to turbulence. In earlier work similar `tangential waves' were

observed, although mentioned only in passing; their appearance was surmised to be due to Tollmein instability, but our initial calculations have suggested this to be unlikely. Here we report on additional simulations and data on this instability and also show that it is closely related to the instability of Stokes oscillating boundary layer.