Motion of a Vortex in a Rotating Layer of Fluid Between Rigid Concentric Spheres (Classic Reprint) - Softcover

Inhaltsangabe

Excerpt from Motion of a Vortex in a Rotating Layer of Fluid Between Rigid Concentric Spheres

This preliminary report is concerned with an approximate description of the two dimensional vortical motion in a thin spherical layer of a gravitating, incompressible, inviscid fluid. We suppose that the fluid is contained between an inner rigid ball and an outer rigid concentric sphere and that the fluid, along with the inner spherical surface, has been rotating with constant angular velocity w about a polar axis until a reference time t O. Thereafter we suppose that the motion is due to the gravitational attraction of the rotating ball and to the sudden creation at t O of concentrated vortices with axis normal to the spheres.

The general objective is to discuss the subsequent motion of these isolated vortices, including the case for which w 0. However, in this report we confine the discussion primarily to the motion of a single concentrated vortex in the northern hemi sphere when certain equatorial boundary conditions are imposed. The differential equations for the motion of such a vortex appear below; and they are followed by an approximate description of its geometric path for a period of time of such duration that it is not necessary to use a computer for the numerical integration of the equations.

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