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

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Abstract

The shallow-water equations may be posed in the form dF/dt - {F, H, Z}, where H is the energy, Z is the plential 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. © 2007 American Meteorological Society.

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Salmon, R. (2007). A general method for conserving energy and potential enstrophy in shallow-water models. Journal of the Atmospheric Sciences, 64(2), 515–531. https://doi.org/10.1175/JAS3837.1

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