ASYMPTOTIC VORTICITY STRUCTURE AND NUMERICAL-SIMULATION OF SLENDER VORTEX FILAMENTS

A new asymptotic analysis of slender vortices in three dimensions, bas ed solely on the vorticity transport equation and the non-local vortic ity-velocity relation gives new insight into the structure of slender vortex filaments. The approach is quite different from earlier analyse s using matched asymptotic solutions for the velocity field and it yie lds additional information. This insight is used to derive three diffe rent modifications of the thin-tube version of a numerical vortex elem ent method. Our modifications remove an O(1) error from the node veloc ities of the standard thin-tube model and allow us to properly account for any prescribed physical vortex core structure independent of the numerical vorticity smoothing function. We demonstrate the performance of the improved models by comparison with asymptotic solutions for sl ender vortex rings and for perturbed slender vortex filaments in the K lein-Majda regime, in which the filament geometry is characterized by small-amplitude-short-wavelength displacements from a straight line. T hese comparisons represent a stringent mutual test for both the propos ed modified thin-tube schemes and for the Klein-Majda theory. Importan tly, we find a convincing agreement of numerical and asymptotic predic tions for values of the Klein-Majda expansion parameter epsilon as lar ge as 1/2. Thus, our results support their findings in earlier publica tions for realistic physical vortex core sizes.