## 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 ½*fR*^{2}=*rv*+½*fr*^{2} 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*=(ζ/*f*)(*g*/θ_{0})(∂θ/∂*Z*) and ρ*s*=*f*^{2}*R*^{4}/*r*^{4}.

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.