Vortex Patches: A Short History

Start: 09/24/2014 - 4:15pm
End  : 09/24/2014 - 5:15pm


Jim Kelliher, University of California at Riverside


A vortex patch is a 2D velocity field whose scalar curl (vorticity) is the characteristic function of a bounded domain. Taking this as the initial velocity for an incompressible, inviscid fluid, the patch remains a patch as the fluid evolves, but the geometry of the boundary of the patch can become quite convoluted. By the mid 1980s computers had developed just enough power to make numerical exploration of the evolution of the patch possible, but those numerics provided conflicting evidence. Some seemed to indicate that a patch with an initially smooth boundary can lose regularity in finite time, but the proper interpretation of the numerics was much disputed. Analytic evidence from model problems led to conjectures that such loss does, in fact, occur. I will discuss the history of this problem, from its roots in the 1870s to its resolution in the early 1990s, and up through some more recent results.

Freeburg Forum, Kravis Center (LC 62), Claremont McKenna College

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