ON CHAPLYGIN INVESTIGATIONS OF 2-DIMENSIONAL VORTEX STRUCTURES IN AN INVISCID FLUID

This paper describes exact solutions of two-dimensional vortex structu res that were published by Chaplygin (1899, 1903) at the turn of the l ast century, which seem to have escaped the attention of later investi gators in this field. Chaplygin's solutions include that of an ellipti cal patch of uniform vorticity in an exterior field of pure shear and that of a (symmetric or non-symmetric) dipolar vortex with a continuou s distribution of vorticity translating steadily along a straight path . In addition, a solution is presented for a non-symmetric vortex dipo le moving along a circular trajectory. A concise account of Chaplygin' s solutions is given, complemented by a more detailed analysis of some of their relevant properties.