Abstract
This chapter presents the equations of motion in rotating cylindrical polar coordinates and develops the classical axisymmetric theory of vortices relevant to understanding the primary and secondary circulations of a tropical cyclone forced by diabatic heating and tangential momentum forcings such as near-surface friction. It derives a general form of the thermal wind equation and introduces the concept of generalized buoyancy in a rapidly-rotating vortex. It goes on to discuss the tropical cyclone eye, vortex spin up, stability of baroclinic vortices, symmetric instability, absolute angular momentum, scale analysis, gradient wind balance, hydrostatic balance, Eliassen's balance theory for the forced secondary circulation, toroidal vorticity, potential toroidal vorticity, the geopotential tendency equation, relation between Eliassen theory and potential vorticity inversion, the spin-up function and extensions to Eliassen's balance theory.
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