Vorticity, Vortex Dynamics and Rotating Flows

Vorticity characterizes the local rotation within a fluid. It can be continuously distributed or nonzero only on singular lines: the study of such “vortex filaments” suggests an analogy with distributions of magnetic fields and currents. The transport of vorticity in a fluid is then discussed from the point of view of the velocity circulation dynamics (Kelvin’s theorem); the governing Helmholtz equation for the vorticity then is derived. The dynamics of a system of vortex lines is described and applied to the propulsion problems (animal, mobiles). The last part of the chapter is devoted to rotating flows, where a global rotation is superimposed onto the vorticity (like in atmospheric and oceanographic flows). An appendix deals with superfluid Helium.