Energy flux and quasi-geostrophic theory

The energy flux vector in fluid dynamics is the product of the pressure and the velocity vector. In linear systems, the energy flux is also the product of the energy and group velocity. Quasi-geostrophic theory is made consistent with these two definitions by the specification of a second-order pressure field that is proportional to the meridional gradient of the Coriolis parameter and the first-order dynamic pressure field. This second-order pressure field contributes a second-order geostrophic wind. Several analytic applications of the theory in both linear and nonlinear contexts are presented. Specification of the second-order pressure formally closes the theory so all first- and second-order fields may be derived directly from the geostrophic stream function. The theory provides a physical explanation for the difference in the direction of the zonal energy propagation for long and short Rossby waves.