A Pseudoenergy Conservation Law for the Two-Dimensional Primitive Equations

Abstract

Unbalanced frontogenesis studies frequently employ a mathematical model known as the two-dimensional primitive equations, a reduction of the full three-dimensional primitive equations made by ignoring variations in the meridional direction. Such a model is interesting from a theoretical standpoint because it can describe both frontal systems and gravity waves simultaneously, and the process of gravity wave generation during frontogenesis can be investigated. In the past, theoretical studies of complex flows have benefitted from an exploitation of the underlying Hamiltonian structure of the relevant governing equations. In this article, the two-dimensional primitive equations are shown to be Hamiltonian as well (for the case of uniform background shear), and a symplectic representation, Casimir invariants, and a pseudoenergy conservation law are all determined.