Abstract

Co-author: Colin Cotter (Imperial College)

A variational framework is defined for vertical slice models with three dimensional velocity depending only on horizontal $x$ and vertical $z$. The models that result from this framework are Hamiltonian, and have a Kelvin-Noether circulation theorem that results in a conserved potential vorticity in the slice geometry. These results are demonstrated for the incompressible Euler—Boussinesq equations with a constant temperature gradient in the $y$-direction (the Eady—Boussinesq model), which is an idealised problem used to study the formation and subsequent evolution of weather fronts. We then introduce a new compressible extension of this model for testing compressible weather models running in a vertical slice configuration. (Joint work with CJ Cotter, Imperial College).