Interaction of vortex sheet with a finite vortex

The rollup of a vortex sheet of elliptic span loading in the presence of a vortex of finite core size is studied in the Trefftz plane. The vorticity in the finite vortex is taken to be uniform and sign opposite to that of the sheet and the flow is assumed to be inviscid and incompressible. A numerical scheme is developed to determine the evolution of (a) the finite vortex using the Contour Dynamics technique, (b) the vortex sheet using an algorithm developed by Krasny. The interaction is shown to substantially affect the development of the vortex sheet rollup. The vortex sheet undergoes significant deformation at the rolling up tip region due to its devouring the vortex patch as well as due to the formation of secondary rollup features on the sheet. These features are believed to be important in inhibiting rollup considerably. The interaction is quantified by using a criterion developed to measure the extent of the tip vortex rollup and its characteristics are studied for a range of flow parameters. The strength of the rolling up tip region of the vortex sheet is found to be highly dependent on the location and the vorticity in the finite vortex.