Vortex dynamics in complex domains on a spherical surface

✍ Scribed by Amit Surana; Darren Crowdy

• Publisher: Elsevier Science
• Year: 2008
• Tongue: English
• Weight: 494 KB
• Volume: 227
• Category: Article
• ISSN: 0021-9991
• DOI: 10.1016/j.jcp.2008.02.027

✦ Synopsis

We consider the motion of both point vortices and uniform vortex patches in arbitrary, possibly multiply connected, regions bounded by impenetrable walls on the surface of a sphere. By exploiting knowledge of the functional form of the relevant Green's function in a pre-image circular domain that is conformally equivalent to a stereographic projection of the fluid domain on the spherical surface, we first generalize Kirchhoff-Routh theory for point vortex motion in the plane to point vortex motion on a spherical shell. Next, we study vortex patch motion and show that there is a contour dynamics formulation for the evolution of uniform vortex patches in any finitely connected domain on a spherical shell bounded by impenetrable walls. We describe a novel numerical scheme whereby this motion can be computed. Some illustrative calculations are shown.