On the viscous decay rates of inertial waves in a rotating circular cylinder

Abstract

In the literature, there are two different asymptotic results for the viscous decay rates of inertial modes in a rotating circular cylinder. In the absence of a viscous corner solution, either result can only be an estimate of the true decay rate. In this note, we numerically calculate the viscous decay rates for some experimentally excited inertial modes (Malkus 1989; Malkus & Waleffe 1991) in order to (i) assist in the interpretation of these experiments and (ii) to assess the usefulness of the two asymptotic estimates available. Our results indicate that the asymptotic estimate due to Kudlick (1966) is more accurate and that the asymptotic regime in which this estimate is useful (accurate to within 10%) can be smaller than is commonly thought.