Chaotic motion of fluid particles around a rotating elliptic vortex in a linear shear flow

Abstract

The motion of fluid particles around a rotating elliptic vortex in an external irrotational linear shear flow is examined both numerically and analytically. When the strain rate of the external flow, s, is small, fluid particles move chaotically only within two narrow regions. These regions are near the heteroclinic orbits of the Poincaré map of particle locations after every vortex rotation period in two special flows obtained in the limit s → 0 . The existence of these chaotic regions is confirmed by computing the Melnikov function for perturbed systems with small s. The widths of these chaotic regions are also estimated using this function. As s increases, these chaotic regions become larger and finally merge at s = s c . For s> s c, fluid particles near the vortex can move toward infinity. This critical value s c is larger for a vortex closer to a circular shape. By examining the residence time of fluid particles near the vortex for s> s c, we find its sensitive and complicated dependence on the particle initial positions.