Seminar Event Detail


Applied Interdisciplinary Mathematics (AIM)

Date:  Friday, February 08, 2019
Location:  1084 East Hall (3:00 PM to 4:00 PM)

Title:  Vortex dynamics on the surface of a torus

Abstract:   Interactions of vortex structures play an important role in the understanding of complex evolutions of fluid flows. Incompressible and inviscid flows with point-wise vorticity distributions in two-dimensional space, called point vortices, have been used as a theoretical model to describe such vortex interactions. The motion of point vortices has been investigated well in unbounded planes with boundaries as well as on a sphere owing to their physical relevance. On the other hand, it is of a theoretical interest to investigate how geometric nature of curved surfaces and the number of holes gives rise to different vortex interactions that are not observed in vortex dynamics in the plane and on the sphere. In this talk, we consider the dynamics of point vortices on a toroidal surface, which is a compact, orientable 2D Riemannian manifold with a non constant curvature with a handle structure. Deriving the equation of motion of point vortices, we obtain some stationary point-vortex configurations and describe the interactions of two point vortices in order to cultivate an insight into vortex interactions on this manifold. We will also discuss the stability of the ring configuration of N point vortices aligned along the line of latitude.

Files:


Speaker:  Takashi Sakajo
Institution:  Kyoto University

Event Organizer:   Robert Krasny    krasny@umich.edu

 

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