Conserving quantities related to potential vorticity in numerical models.

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In the ideal, invscid limit, the equations of fluid dynamics conserve mechanical energy and the potential vorticity on fluid particles. In computer models of the Earth's atmosphere and ocean, the conservation of potential enstrophy (the average, squared potential vorticity) is known to prevent a spurious transfer of energy to the smallest spatial scales of the model. Numerical models that fail to conserve potential enstrophy have an unrealistically large dissipation of energy due to the sub-grid-scale viscosity that is added. Despite this, virtually all of the models which are currently used to compute large-scale flow in the atmosphere and the ocean do not conserve potential enstrophy in the inviscid limit. In this study, a scientist at Scripps Institution of Oceanography will design numerical models for the atmosphere and ocean that conserve energy, potential enstrophy and other quantities related to potential vorticity. These models are expected to be more stable and less dissipative than the current generation of numerical models in use. A PhD student will be involved. The project therefore will have a broad impact on the future of model development.