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Necessary conditions are derived for a spherical vortex in a perfect fluid to be stationary in the case when the velocities depend on a single surface harmonic. The motion is indeterminate unless an additional condition is imposed. In the case when this condition is incompressibility, the equations are solved, yielding a class of stationary spherical vortices.

A theory is given to explain the observed dependence on Reynolds number of the decay of turbulent line vortices. It is argued that the turbulent vortex has a triple structure. There is an outer region for r > r1 (r1 is the radius of maximum tangential velocity) with a logarithmic distribution of circulation, and for r < r1 an inner region and viscous core in both of which the motion is close to solid body rotation. It is predicted that r1 ~ (vT1 t2)1/4, where 1 is the circulation at r1. Further, T1/T0 is predicted to be a slowly decreasing function of T0/v, where T0 is the strength of the vortex. The development of an overshoot of circulation in the outer region is discussed, and the axial velocities produced by growth of a trailing vortex are calculated.

In this paper it is shown that the shear fields on either side of the westerlies are dynamically unstable and will roll up to form discrete eddies. A study of the stable vortex systems into which these eddies might collect shows that a "vortex street" is stable for a certain range of the ratio of width to vortex spacing. It is also shown that a formation with vortices placed on the corners of a regular polygon is stable if the number of vortices is less than seven. This still holds if the effect of the shear field north of the westerlies is stimulated by a fixed polar cyclone. It further appears that with a strong general circulation, i.e. strong westerlies, only two or three high pressure cells should be found while the numbers, up to six, should be found with weaker circulations. This conclusion is verified by Northern Hemisphere mean pressure charts.