In this talk, we present recent development of vortex-body interactions. We introduce an invicsid vortex shedding model which regards separated vortex from a body as point vortices or vortex sheets. Analytical and computational issues of the model are discussed and its applications to various problems such as insect flights and fish swimming will be presented.
We also consider geophysical flows on a sphere and discuss mainly on the modeling of the polar jet stream. The polar jet stream strongly affects weather and aviations, and the understanding of its stability is highly important. We describe the jet stream by a barotropic vortex strip and present the linear stability and the nonlinear evolution of the vortex strip.