A Generalized Transport Equation for Use with Meteorological Coordinate Systems

Abstract

A generalized transport equation for a variety of meteorological coordinate systems is derived. Through its application, the commonality of modes of convective and nonconvective flux of mass, momentum and energy is identified between the specific coordinate systems. Generalized forms for pressure gradient and frictional forces (?·?) in the momentum equation are presented that directly integrate to boundary stresses (τ) while in the total energy equation the sum of mechanical [U·(?·&Pi)] and thermodynamic work (?:?U) readily integrates to boundary work (?·[?·U]). Additional degrees of freedom for the nonconvective flux of properties are identified with the inclination of information surfaces. The vertical transfer of momentum and energy by this means is discussed in regard to the time rate of change of the dynamic circulation (Bjerknes, 1937). The results reveal that views of the forcing of circulation become coordinate dependent. Variant and invariant aspects of the physical and mathematical meaning of the generalized transport equation and forcing of the circulation are presented.