Transformed Eliassen Balanced Vortex Model

Abstract

We consider the axisymmetric balanced flow occurring in a thermally forced vortex in which the frictional inflow is confined to a thin boundary layer. Above the boundary layer the absolute angular momentum ½fR2=rv+½fr2 is conserved. We refer to R as the potential radius, i.e., the radius to which a particle must be moved (conserving absolute angular momentum) in order to change its tangential component v to zero. Using R as one of the dependent variables we review the equations of the Eliassen balanced vortex model. We next reverse the roles of the actual radius r and the potential radius R, i.e., we treat R as an independent variable and r as a dependent variable. Introducing transformed components (u*, w*) of the transverse circulation we obtain the transformed Eliassen balanced vortex equations, which differ from the original equations in the following respects: 1) the radial coordinate is R which results in a stretching of positive relative vorticity regions and a shrinking of negative relative vorticity regions; 2) the thermodynamic equation contains only the transverse circulation component w*, the coefficient of which is the potential vorticity q; 3) the equation for r contains only the transverse circulation component u*; 4) the transverse circulation equation contains only two vortex structure functions, the potential vorticity q and the inertial stability s, where pq=(?/f)(g/?0)(??/?Z) and ?s=f2R4/r4. The form of the transverse circulation equation leads naturally to a generalized Rossby radius proportional to (q/s)½. A typical distribution Of (q/s)½ is calculated using the composite tropical cyclone data of Gray. The fundamental dynamical role of (q/s)½ is then illustrated with a simple analytical example.