Computational Analysis of Potential Vorticity and Quasi-Geostrophic Approximation for the Quasi-Hydrostatics Thermal Rotating Shallow Water Equations

Abstract

A novel idealized and incompressible fluid flow governing model is introduced, namely, the two-dimensional quasi-hydrostatics thermal rotating shallow water equations. The potential vorticity for the new model is computationally analyzed through the Hamiltonian formulation of the Eulerian variables using the noncanonical Poisson brackets. Both similarities and differences are observed between the new and standard shallow models.