The Geostrophic Momentum Approximation and the Semi-Geostrophic Equations

Abstract

Consideration of flows in which the rate of change of momentum is much smaller than the Coriolis force suggests that the advected quantity momentum may be approximated by its geostrophic value but that trajectories cannot be so approximated. The resulting set of equations imply full forms of the equations for potential temperature, three-dimensional vorticity, potential vorticity and energy. A transformation of horizontal coordinates products the “semi-geostrophic” system in which conservation of potential vorticity and potential temperature suffice to determine the motion. The system is capable of describing the formation of fronts, jets, and the growth of baroclinic waves into the nonlinear regime. It sheds some light on the success and failure of the quasi-geostrophic equations. Abstract Consideration of flows in which the rate of change of momentum is much smaller than the Coriolis force suggests that the advected quantity momentum may be approximated by its geostrophic value but that trajectories cannot be so approximated. The resulting set of equations imply full forms of the equations for potential temperature, three-dimensional vorticity, potential vorticity and energy. A transformation of horizontal coordinates products the “semi-geostrophic” system in which conservation of potential vorticity and potential temperature suffice to determine the motion. The system is capable of describing the formation of fronts, jets, and the growth of baroclinic waves into the nonlinear regime. It sheds some light on the success and failure of the quasi-geostrophic equations.