The Eliassen balanced vortex model assumes gradient balance of the azimuthal mean flow. This assumption was tested by calculating mean and eddy terms in the radial momentum equation in the synoptic-scale environments of two tropical cyclones. The azimuthally averaged gradient balance was accurate to within 15%–25% in the free atmosphere outside the core, even in the asymmetric outflow layer. Balanced secondary circulations correlated well with circulations that included gradient thermal wind imbalance terms. Although the balanced model lacks Galilean invariance, balanced circulations were largely insensitive to use of a fixed coordinate or a coordinate moving with the storm. This occurred because changes in eddy heat and angular momentum fluxes largely offset one another. The two-dimensional balanced solutions provide a reasonably robust measure of circulations induced by azimuthal eddy processes in the tropical cyclone environment.
Nevertheless, individual forcing functions, such as the commonly examined lateral eddy flux convergence of angular momentum, often varied enormously between fixed and moving coordinates. Logic and available evidence suggest that such terms are meaningful only in a coordinate system moving with the storm.