Geometry of Advection, Diffusion, and Viscosity

Baylor Fox-Kemper, Brown University, Providence, RI, United States
Abstract:
Efforts to parameterize mesoscale, submesoscale, and boundary layer processes are often stymied at the application phase—how to convert processes into mathematical form and code them? I will present some existing parameterizations, as written compactly, and in arbitrary coordinate systems, using tensors and differential forms. In this form, I will show how advective, diffusive, dispersive, and other transport processes are contrasted from one another, and how enforcing physical symmetries helps in first discovering parameterizations. However, the main goal is a demonstration that relaxation of symmetries is a simple way to advance parameterizations and incorporate new processes efficiently. Examples and results will be introduced from applications in coarse-resolution climate models (anisotropic mesoscale and submesoscale eddy parameterizations), mesoscale-permitting models (enstrophy and potential enstrophy cascade models), submesoscale-permitting models (mixed layer and symmetric instability parameterizations), and representations of air-sea processes suitable in all of these model classes.