Numerical studies of motion of vortex filaments - Implementing the asymptotic analysis

A computational code is developed for the integro-differential equations governing the motion of the centerlines of vortex filaments submerged in a background potential flow. These equations, which are derived from the method of matched asymptotic analysis, include the effect of the decaying large-magnitude circumferential and axial velocity components in the vortical cores. Numerical examples are presented to assess the effect of a large axial velocity and that of nonsimilar initial profiles in the vortical cores. The initial configurations of the filaments are chosen so as to fulfill the basic assumption of the asymptotic analysis, which is that the effective vortical core size is much smaller than all the other length scales in the flowfield, e.g., the radius of curvature and the interfilament distance. The computations are continued until the basic assumption is no longer valid, that is when the merging or intersection of filaments has begun. A classification of the various types of local or global merging or intersection of filaments is made and demonstrated by numerical examples. It is then shown that the asymptotic solution not only provides the initial data but also can be used to formulate the appropriate boundary conditions for the numerical solution of a merged region.