Vortex Merging in a 11⁄2-Layer Fluid on an f Plane*

Mass, angular momentum, and energy budgets are examined in an analytical model of vortex merging relevant to midlatitude mesoscale eddies. The vortices are baroclinic and cyclogeostrophic. The fluid surrounding them is assumed to remain quiescent. It is shown that due to this surrounding fluid, angular momentum is conserved when expressed in both the inertial and rotating frames of reference. Lens-shaped solid-body vortices can conserve mass, angular momentum, and energy when they merge. If an upper-layer of thickness H1 is included in the model, the merged vortex must have either less energy or mass than the sum of the original two vortices. A more complex model of the vortex azimuthal structure is then considered, which includes a constant vorticity shell surrounding the solid-body core. If the shell is large compared to the core, the mass, angular momentum, and energy can all be conserved in the merged vortex. However, if the shell is small, the merged vortex must have less energy or mass than in the solid-body case.