Theoretical studies in mesoscale jets and vortices

Mesoscale vortices in the mid-ocean are known to move large distances without loss of coherence, preserving their speed and (usually westward) direction. Still open are the questions of how an eddy is able to preserve its structure during many turnaround times and what is the role in this process of the specific perturbations of the circular basic state. To investigate the effect of the rectilinear motion of the isolated eddies, we construct several analytical steady state models and examine the realizability in time of those solutions using the initial-value numerical calculations.; To gain a preliminary understanding of the process, we first consider the barotropic f-plane model. It is demonstrated using linearized (about the circular basic state) calculations that for almost any eddy with compact basic velocity we can find a small amplitude disturbance of the first azimuthal harmonic ({dollar}m=1{dollar} mode) that results in the rectilinear motion of an eddy. If such a disturbance is sufficiently small, the vortex can propagate many diameters away from its origin, as shown by a weak non-linear theory. This conclusion is confirmed by the spectral calculations using the full two dimensional vorticity equation.; A more realistic representation of the ocean eddies is given by the equivalent-barotropic model, which includes effects of the passive lower layer and the ambient potential vorticity gradient (the {dollar}beta{dollar}-effect). Analytical theory is developed to construct a wide class of stable quasi-monopolar vortecies propagating in the westward direction with the supercritical ({dollar}U<{lcub}-{rcub}beta Rsbsp{lcub}d{rcub}{lcub}2{rcub}{dollar}) velocities. A remarkable similarity is found between the structure of the solutions in barotropic and equivalent-barotropic models for all values of the propagation velocity. The numerical spectral calculations, initiated by our analytical solutions, indicate that the (supercritical) vortices initially move with the predicted velocity, but later slow down to the speed of the long planetary waves. The period of time during which an eddy is propagating with its initial velocity is analyzed as a function of its strength and (initial) speed. It is also suggested that any strong vortex placed on the beta-plane will eventually develop to a structure described by our analytical model.; We also introduce analytical models of the propagating vortices in the shallow water reduced-gravity system of equations. The realizability in time of these ageostrophic solutions, in sense of initial value calculations, is tested using the isopycnal numerical model of Bleck and Boudra.