On the structure and stability of slender viscous vortices.

Abstract

The phenomenon of vortex breakdown, in which the flow near the axis of a rotating fluid suffers a sudden disruption, was first observed in the late 1950s. Despite having been the subject of intensive research since then, a fundamental understanding of the phenomenon has not yet been achieved. This thesis is an attempt at achieving such by way of a unified approach to each aspect which may be involved, the working hypothesis being that breakdown may best be understood as a nonlinear evolution problem. Treated in detail are the first two steps in such a program, which are first to understand the structure of the steady flows which may give rise to breakdown and then to investigate their stability. A family of similarity solutions to the Navier-Stokes equations, modelling the flows in leading-edge-type vortices, is presented. These solutions show a strong retardation of the axial flow in the core when the flow is subject to an adverse axial pressure gradient. The stability of several types of swirling base flows to three-dimensional disturbances is studied, revealing a rich variety of neutral and exponentially growing eigenmodes of both an inviscid and viscous character. The above axial retardation is also shown to be capable of inducing a linear instability of the flow, indicating the possibility of a secondary instability phenomenon. Implications of these results for the study of the full breakdown itself are discussed.