REPRESENTATION OF CORE DYNAMICS IN SLENDER VORTEX FILAMENT SIMULATIONS

The numerical description of slender vortex motion faces several major obstacles: (i) The stiffness induced by the rapid rotatory motion in the vortex core, where peak velocities are an order of magnitude large r than the filament velocity. In a vorticity-velocity formulation, thi s stiffness is reflected by the singular behavior of the line-Biot-Sav art integral as one approaches the vortex geometry. Regularization occ urs physically by viscous smoothing of the vorticity. (ii) The vortex core vorticity distribution has a crucial influence on the vortex fila ment motion. Thus, an accurate description of the core structure evolu tion due to vortex stretching and vorticity diffusion is necessary. We propose a numerical scheme that allows an accurate description of the effects of axial flow in the core, viscosity and vortex stretching on slender vortex filament motion. The approach is based on incorporatin g the detailed asymptotic analyses of the vortex core structure evolut ion by Callegari and Ting [SIAM J. Appl. Math. 15, 148 (1978)] and Kle in and Ting [Appl. Math. Lett. 8, 45 (1995)] for stretched viscous sle nder vortices into the improved thin-tube vortex element schemes of Kl ein and Knio (1995). The resulting schemes overcome the difficulties m entioned above except for the issue of temporal stiffness, which we le ave for future work. (C) 1996 American Institute of Physics.