On the Forced Tangentially-Averaged Radial- Vertical Circulation within Vortices Part Ⅰ: Concepts and Equations

A linear partial differential equation is derived in cylindrical-isobaric coordinates on the earth for the diagnostic study of the tangentially-averaged radial-vertical circulation within translating vortices. In the hydrodynamic stable atmosphere, the circulation will be forced through many dynamic and thermodynamic processes. These processes are associated with frictional torque, inertial torque, the horizontal and vertical divergence of eddy angular momentum, diabatic heating, adiabatic heating, and eddy temperature advection. For a given forcing, the intensity of circulation will increase with the decrease of static, inertial,and baroclinic stabilities. This paper also presents an explanation on the data interpolation from the latitude-longitude grid to the vortex volume gird and a brief discussion on the forcing processes.