Vortex Motion on Riemann Surfaces

초록

Vortex motion of an incompressible inviscid flow on a infinitely thin curved shell specified as a Riemann surface is studied. The intrinsic dynamical equations are derived and compared on two conformally equivalent Riemann surfaces. In particular, the relations for the streamfunction, velocity, and vorticity are found by using explicit computations. Then, the result is applied to the problem of motion of point vortex dipoles on Riemann surfaces whose trajectories in time turn out to be a geodesic. Also, the case of more complicated surfaces with a boundary, is discussed with an example.

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