VORTICITY COORDINATES, TRANSFORMED PRIMITIVE EQUATIONS, AND A CANONICAL FORM FOR BALANCED MODELS

A potential pseudodensity principle is derived for the quasi-static pr imitive equations on the sphere. An important step in the derivation o f this principle is the introduction of ''vorticity coordinates''-that is, new coordinates whose Jacobian with respect to the original spher ical coordinates is the dimensionless absolute isentropic vorticity. T he vorticity coordinates are closely related to Clebsch variables and are the primitive equation generalizations of the geostrophic coordina tes used in semigeostrophic theory. The vorticity coordinates can be u sed to transform the primitive equations into a canonical form. This f orm is mathematically similar to the geostrophic relation. There is fl exibility in the Choice of the potential function appearing in the can onical momentum equations. This flexibility can be used to force the v orticity coordinates to move with some desired velocity, which results in an associated simplification of the material derivative operator. The end result is analogous to the way ageostropbic motions become imp licit when geostrophic coordinates are used in semigeostrophic theory.