A general method for conserving energy and potential enstrophy in shallow-water models

Citation:
Salmon, R.  2007.  A general method for conserving energy and potential enstrophy in shallow-water models. Journal of the Atmospheric Sciences. 64:515-531.

Date Published:

Feb

Keywords:

dynamics, equations, scheme

Abstract:

The shallow-water equations may be posed in the form dF/dt = {F, H, Z}, where H is the energy, Z is the potential enstrophy, and the Nambu bracket {F, H, Z} is completely antisymmetric in its three arguments. This makes it very easy to construct numerical models that conserve analogs of the energy and potential enstrophy; one need only discretize the Nambu bracket in such a way that the antisymmetry property is maintained. Using this strategy, this paper derives explicit finite-difference approximations to the shallow-water equations that conserve mass, circulation, energy, and potential enstrophy on a regular square grid and on an unstructured triangular mesh. The latter includes the regular hexagonal grid as a special case.

Notes:

n/a

Website

DOI:

10.1175/jas3837.1