ON THE INSTANTANEOUS CUTTING OF A COLUMNAR VORTEX WITH NONZERO AXIAL-FLOW

A study of the response of a columnar vortex with non-zero axial flow to impulsive curling has been performed. The flow evolution is compute d based on the vorticity-velocity formulation of the axisymmetric Eule r equation using a Lagrangian vorticity collocation method. The vortex response is compared to analytical predictions obtained using the plu g-flow model of Lundgren & Ashurst (1989). The plug-flow model indicat es that axial motion on a Vortex core with variable core area behaves in a manner analogous to one-dimensional gas dynamics in a tube, with the vortex core area playing a role analogous to the gas density. The solution for impulsive cutting of a vortex obtained from the plug-flow model thus resembles the classic problem of impulsive motion of a pis ton in a tube, with formation of an upstream-propagating vortex 'shock ' (over which the core radius changes discontinuously) and a downstrea m-propagating vortex 'expansion wave' on opposite sides of the cutting surface. Direct computations of the vortex response from the Euler eq uation reveal similar upstream-and downstream-propagating waves follow ing impulsive cutting for cases where the initial vortex flow is subcr itical. These waves in core radius are produced by a series of vortex rings, embedded within the columnar vortex core, having azimuthal vort icity of alternating sign. The effect of the compression and expansion waves is to bring the axial and radial velocity components to nearly zero behind the propagating vortex rings, in a region on both sides of the cutting surface with ever-increasing length. The change in vortex core radius and the variation in pressure along the cutting surface a gree very well with the predictions of the plug-flow model for subcrit ical flow after the compression and expansion waves have propagated su fficiently far away. For the case where the ambient vortex flow is sup ercritical, no upstream-propagating wave is possible on the compressio n side of the vortex, and the vortex axial flow is observed to impact on the cutting surface in a manner similar to that commonly observed f or a non-rotating jet impacting on a wall. The flow appears to approac h a steady state near the point of impact after a sufficiently long ti me. The vortex response on the expansion side of the cutting surface e xhibits a downstream-propagating vortex expansion wave for both the su bcritical and supercritical conditions. The results of the Vortex resp onse study are used to formulate and verify predictions for the net no rmal force exerted by the vortex on the cutting surface. An experiment al study of the cutting of a vortex by a thin blade has also been perf ormed in order to verify and assess the limitations of the instantaneo us vortex cutting model for application to actual vortex-body interact ion problems.