Vortex Motion on a Sphere
The problem of N-point vortices moving on the surface of a sphere is not as well understood as the corresponding planar problem, yet in some sense it is more general, since the planar problem can be obtained from the spherical problem in the limit as the radius of the sphere becomes large. This limit will be discussed in more detail later in the chapter. The spherical model is used in geophysical fluid dynamics when considering large-scale atmospheric and oceanographic flows with coherent structures that persist over long periods of time and move over such large distances that the spherical geometry of the earth’s surface becomes important. In addition, when considering the streamline patterns generated by a given vorticity field, the spherical geometry is important to take into account if one wants to make statements that are relevant to atmospheric weather patterns. These issues are discussed later in the chapter. For a general introduction to geophysical fluid dynamics, see Pedlosky (1987) or Gill (1982).
KeywordsPhase Plane Stagnation Point Great Circle Relative Equilibrium Stereographic Projection
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