A 3-DIMENSIONAL BALANCE THEORY FOR RAPIDLY ROTATING VORTICES

A three-dimensional balance formulation for rapidly rotating vortices, such as hurricanes, is presented. The asymmetric balance (AB) theory represents a new mathematical framework for studying the slow evolutio n of rapidly rotating fluid systems. The AB theory is valid for large Rossby number; it makes no formal restriction on the magnitude of the divergence or vertical advection, which need not be small. The AB is a n ordered expansion in the square of the ratio of orbital to inertial frequencies, the square of a local Rossby number. The approximation fi lters gravity and inertial waves from the system. Advantage is taken o f the weak asymmetries near the vortex core as well as the tendency fo r low azimuthal wavenumber asymmetries to dominate. Linearization abou t a symmetric balanced vortex allows the three-dimensional asymmetric dynamics to be deduced properly. The AB formulation has a geopotential tendency equation with a three-dimensional elliptic operator. The AB system has a uniformly valid continuation to nonlinear quasigeostrophi c theory in the environment. It includes the full inertial dynamics of the vortex core, and reduces to Eliassen's formulation for purely axi symmetric flow. It has a full set of conservation laws on fluid parcel s analogous to those for primitive equations, including conservation o f potential temperature, potential vorticity, three-dimensional vortic ity, and energy. A weakly nonlinear extension of the formulation in th e near-vortex region is presented, Appropriate physical applications f or the AB system, as well as its limitations, are discussed.