-Layer Hamiltonian Toy Models for Stratospheric Dynamics

A two-layer Hamiltonian toy model consisting of two isentropic stratospheric layers is simplified using perturbation analysis while preserving the Hamiltonian structure. These two layers are neutrally and stably stratified. The first approximation applies when the Froude number of the upper isentropic layer is small, such that the upper surface is approximately rigid, and this upper layer is much thicker than the lower layer. A conservative 1 1 2 -layer isentropic model emerges when leading-order perturbation theory is used in the Hamiltonian formulation of the isentropic two-layer model. Furthermore, Hamiltonian theory directly leads to (Salmon’s) L1-dynamics for the novel 1 1 2 -layer model, following a more concise derivation than shown before, when the Rossby number in the upper stratospheric layer is small and leads to a geostrophic constraint.