Session Ci - Vortex Dynamics.
ORAL session, Sunday, November 23
309, Moscone Center
A vortex ring is characterized by two nondimensional parameters, i.e. the slenderness ratio of core radius to ring radius and Reynolds number. When the slenderness ratio is small and the Reynolds number is large, there are various different time scales in the motion of a vortex ring, which are lifetime of vortex ring, moving time scale and revolution time scale of fluid particle and so on. The phenomena of vortex dynamics ( i.e. stretching, vanishing, the cut-and-connect of vortex lines ) in the interaction of two vortex rings are also characterized by these time scales. In addition, the estimation of far-field acoustic pressure excited by a time-dependent localized vorticity distribution will strongly be related to these time scales. In order to study these relationship, the numerical simulations of oblique collisions of two same vortex rings with various angles have been done. Two slenderness ratios( 0.1 and 0.2) are chosen. Time evolution of the vorticity field is obtained by solving a viscous incompressible vorticity equation with a vorticity-potential method. The rings with different slenderness ratio and/or with different collision angles experience the cut-and-connect or vanishing of vortex lines in the different time stages of collision of rings. As the results, the different time histories of strength of multipole sound modes are obtained , while they have peaks at the mostly same time. Using these data, we discuss the relationship between the vortical phenomena and the emitted vortex sound.