VORTICITY FLUX ON FREE-SURFACE BOUNDARIES OF IRROTATIONAL VISCOUS FLOWS: SUBSURFACE DISTURBANCE

摘要

The oblique collision of a vortex ring with a bounding free surface is a canonical problem the solution of which underlies the understanding of free-surface turbulence. In this problem a bounded vortical structure, surrounded by initially irrotational flow, is made to interact with the irrotational flow free surface. The part of the problem involving the disconnection of the ring to form a vortex loop attached to the free surface has been studied experimentally (Bernal, 1989; Gharib, et al., 1992; Gharib, 1994), computationally (Leighton and Swean, 1991; Dommermuth, 1993; Lugt and Ohring, 1994; Yue, 1995), and analytically (Rood, 1994a, 1994b, 1995a). The disconnection event is characterized by a flux of opposite-sign vorticity generated by the accelerated free surface during the collision of the vortex core with the free surface. The theoretical explanation for the process suggests that in general a flux of vorticity is generated whenever the free surface is accelerated. Any subsurface disturbance accelerating the free surface should produce a vorticity flux through the free surface, and, in particular, the initial irrotational flow acceleration of the free surface by a submerged vortex ring prior to the disconnection event should produce a flux of secondary vorticity from the free surface and into the bulk fluid. In this case, the acceleration is produced by the irrotational flow induced by the rising vortex ring. Analytical considerations predict a flow acceleration in the downstream direction (relative to the upstream translational motion of the vortex) that consists of both a temporal and an advective component. The temporal component provides the net flux of positive or negative vorticity to the subsurface flow, whereas the advective component provides equal amounts of flux of positive and negative vorticity. The fluxes from the temporal and advective components combine prior to the disconnection event to produce a net flux of like-sign vorticity (relative to the primary vortex) Upon the initiation of the disconnection event, the net flux of vorticity becomes of opposite-sign as required for vorticity annihilation at the free surface as the ring transforms to a loop. The analytical predictions are consistent with measurements obtained from experiments.