Effects of the earth's curvature on the dynamics of isolated objects. PartII: The uniformly translating vortex

Zonally propagating solutions of the primitive equations for an isolated vo lume of fluid are considered. In a moving stereographic projection (from th e antipode of the center of mass) geometric distortion enters at O(R-2), wi th R the radius of the earth, whereas planet curvature effects are O(R-t). The imbalance between the centrifugal force and the poleward gravitational force, due to the drift c, is equilibrated by the average Coriolis force, p roportional to beta. The results are valid for both homogeneous and stratif ied cases and the lowest-order solution need not be an axisymmetric vortex. The classical beta -plane approximation predicts correctly the leading ord er of c/beta, but makes large errors in the O(R ') term of the vortex struc ture. A method is developed to construct the correct O(R-1) term, starting from a ny steady solution of the f-plane equations, as the O(RO) term. The expansi on is exemplified starting with a homogeneous fluid, solid body rotating at an anticyclonic rate -nuf(0), with 0 < <nu> < 1. To O(R-1) particle orbits and isobaths belong to different families of nonconcentric circles. A wate r column moves faster and becomes taller the farther away it is from the eq uator. In order to keep its potential vorticity, the water column experienc es changes of relative vorticity equal to -(2 - <nu>)/(3 - 3 nu) times the variations of the ambient vorticity (Coriolis parameter). The physics of th is solution is compared with that of a circular and rigid disk, studied in Part I.