EXTENDED-GEOSTROPHIC HAMILTONIAN MODELS FOR ROTATING SHALLOW-WATER MOTION

By using a small Rossby number expansion in Hamilton's principle for s hallow water dynamics in a rapidly rotating reference frame, we derive new approximate extended-geostrophic equations with pressure, or surf ace height, as the dynamical variable. By introducing modeling paramet ers into the relation between the ageostrophic velocity and surface he ight, we obtain a family of models for which the functional form of th e potential vorticity, conserved on fluid particles, and of the kineti c energy contribution to the globally conserved energy can be prescrib ed. The particular approximate equations which result when the ageostr ophic velocity is chosen to be in full agreement with an asymptotic sm all Rossby number expansion of the rotating shallow water equations gi ve a new model with apparently higher-order dynamical consistency than either quasigeostrophy or geostrophic momentum. The geostrophic momen tum model is recovered as a special case among these new models.