Session JH - Vortex Dynamics IV.
ORAL session, Monday afternoon, November 24
Triple Crown, SMH
The properties of viscous and inviscid approximations of 3D normal modes of an axisymmetrical vortex with axial flow are examined in the limit of large Reynolds numbers. These approximations are known to exhibit critical point singularities. In this work, these singularities are resolved in a viscous critical layer. We demonstrate that the viscous critical layer analysis is similar to what has been done for stratified shear flows with unitary Prandtl number. The analysis provides the matching conditions of the different approximations across the critical points, as well as the Stokes multipliers. The results are applied to the Batchelor vortex. As an illustration, it is shown how approximations of viscous centre modes can be constructed.