Marginal stability of impulsively initiated Couette flow and spin‐decay

A viscous, incompressible fluid is contained within an infinitely long circular cylinder or between a pair of infinitely long concentric cylinders. In both cases, the entire system is in a state of rigid‐body rotation. At time t = 0 the outer flow boundary is impulsively brought to rest, giving rise to a potentially unstable, unsteady swirl flow. The stability of these flows is examined by employing energy theory with a marginal stability criterion to obtain lower bounds on the onset times for instability. In some cases, the asymptotic steady‐state flow will be stable, with any instability merely a transient, while in other cases, stability of the asymptotic state is not guaranteed.