Numerical entropy conservation without sacrificing Charney-Phillips grid optimal wave propagation

Abstract

Conservation of entropy or potential temperature and accurate representation of wave propagation without computational modes are both desirable properties for a numerical model of the atmosphere. However, they appear to require different model formulations, forcing model developers to choose between them. Here it is shown that, by a straightforward modification of the horizontal entropy fluxes, numerical entropy conservation can be achieved without sacrificing accurate wave propagation. The result is confirmed by a numerical linear normal mode analysis for a simple but suitably modified finite volume scheme, and by buoyant bubble and gravity wave test cases in a vertical slice model using a suitably modified conservative semi-Lagrangian transport scheme.