Multilayer shallow-water model with stratification and shear

The purpose of this paper is to present a shallow-water-type model with multiple inhomogeneous layers featuring variable linear velocity vertical shear and startificaion in horizontal space time. This achieved by writing the layer buoyancy fields as functions depth, coefficients that depend arbitrarily on position generalization Ripa's (1995) single-layer an arbitrary number layers. Unlike models homogeneous able represent thermodynamics processes driven heat freshwater fluxes through surface or mixing resulting from fluid exchanges across contiguous By contrast inhomogeneous-layer depth-independent buoyancy, derived here can sustain explicitly at low frequency current thermal wind balance (between density gradient) within each layer. In absence external forcing dissipation, energy, volume, mass, variance constrain dynamics; conservation total zonal momentum requires addition usual symmetry topography domain. inviscid, unforced admits formulation suggestive generalized Hamiltonian structure, which enables classical connection between symmetries laws via Noether's theorem. A steady solution system involving one Ripa-like otherwise be proved formally (or Arnold) stable using above invariants. configuration only has been shown previously provide: very good representation exact normal modes up first internal mode; long-perturbation (free boundary) baroclinic instability; reasonable short-perturbation (classical Eady) instability. Here it substantially more accurate overall results respect calculations considering stack few similar behavior found ageostrophic Stone) instability describing accurately dependence solutions Richardson two