The transient development of the flow in an impulsively rotated annular container

When a fluid-filled container is spun up from rest to a constant angular velocity the fluid responds in such a way that the fluid–container system is ultimately in a state of rigid-body rotation. The fluid can then be said to have traversed a trajectory in phase space from a simple stable equilibrium state of no motion to another stable equilibrium representing full rigid-body rotation. This simple statement belies the fact that during this process the fluid can undergo a series of transitions, from a laminar through a transient turbulent state, before attaining the stable motion that is rigid-body rotation. Using a combination of analytical and computational methods, we focus on the dynamics resulting from an impulsive change in the rotation rate of a fluid-filled annulus, specifically, the impulsive spin-up of a stationary annulus, or the impulsive spin-down of an annulus already in a state of rigid-body rotation. We explore the initial development of the impulsively generated axisymmetric boundary layer, its subsequent instability, and the larger-scale transient features within this class of flows, allowing us to look at the effect these features have on the time it takes for the system to spin up to a steady state, or spin down to rest.