On the Forcing of the Radial-vertical Circulation within Cyclones-Part 1: Concepts and Equations

Following the theoretical result of Eliassen, the Sawyer-Eliassen equation for frontal circulations and the equa-tion for forcing the meridional circulation within a circum polar vortex are extended in isentropic coordinates to des-cribe the forcing of the azimuthaHy averaged mass-weighted radial-vertical circulation within translating extratropical and tropical cyclones. Several physical processes which are not evident in studies employing isobaric coordinates are isolated in this isentropic study. These processes include the effects of pressure torque, inertia! torque and slorm translation that are associated with the asymmetric structure in isentropic coordinates. This isentropic study also includes the effects of eddy angular momentum transport, diabatie heating and fractional torque that are common in both isentropic and isobaric studies. All of the processes are modulated by static, inertial and baroclinic stabilities. Consistent with the theoretical result of Eliassen, the numerical solution from this isentropic study shows that the roles of torque, diabatic heating and hydrodynamic stability in forcing the radial-vertical circulation within stable vortices are that 1) positive (negative) torque which results in the counterclockwise (clockwise) rotation of vortices al?so forces the outflow (inflow) branch of the radial-vertical circulation, 2) diabatic heating (cooling) forces the ascent (descent) branch of the radial-vertical circulation and 3) for given forcing, the weaker hydrodynamic stability results in a stronger radial-vertical circulation. It is the net inflow or convergence (net outflow or divergence), vertical mo?tions and the associated redistribution of properties that favor the evolution of vortices with colorful weather events. Numerical solutions of this isentrcpic study ate given in companion articles. The relatively important contribu?tion of various physical processes to the forcing of the aamulhally-averaged mass-weighted radial-vertical circula?tion within different translating cyclones and in their different stages of development will be investigated.