AbstractWe explore the simultaneous use of potential radius and potential temperature coordinates in the Eliassen balanced vortex model of tropical cyclones. This results in a simple flux form for the equation governing the inverse potential vorticity. the fluxes are accomplished byRand θ, which are given in terms of the angular momentum and heat sources. If the sources are specified functions ofRand θ, analytic solutions for the time evolution of the potential vorticity distribution can be obtained. the solutions illustrate how latent heat release generates potential vorticity at low levels, destroys it at upper levels, and through vertical advection causes a deepening of the low‐level potential vorticity maximum and a pinching off of the upper‐level potential vorticity minimum. to recover the tangential wind and mass fields from the known potential vorticity, one must solve a second‐order nonlinear partial differential equation. Numerical solutions of this equation result in tangential wind fields which are similar in many ways to observed tropical c