Viscous interlayer structure and transport properties in von Kármán swirling flows

Abstract

This paper is a discussion of the thin viscous regions that separate the nearly inviscid cellular domains arising at large Reynolds number in von Kármán swirling flow. A review and extension are given of previous analyses of the inviscid structure and the associated critical-layer structure that occurs in the regime of small positive radial pressure gradients. It is first shown that the inviscid perturbation analysis can be cast into an analytical closed form, from which an explicit expression for the first-order viscous correction at arbitrary pressure gradients is obtained. By then allowing for negative pressure gradients, of the kind associated with weakly stagnating flows, the present analysis serves to describe the transition from the Prandtl-layer structure characteristic of stagnation-dominated flows to a diffuse viscous damping associated with rotation-dominated flows. Finally, it is shown that, in a discretely stratified flow, the hydrodynamic transition to the critical-layer structure involves a hydrodynamic ‘‘freezing’’ of the interface, which is accompanied by an interesting transition in the interfacial mass-transport characteristics, with the asymptotic Nusselt number changing from (Pe)1/2 abruptly to (Pe)1/3 dependency on the Péclet number Pe.