# Atmosphere Ocean Science Colloquium

#### The Geometric Interpretation of Eddy-Mean Flow Interaction in the Ocean

**Speaker:**
David Marshall, Oxford

**Location:**
Warren Weaver Hall 1302

**Date:**
Wednesday, March 30, 2016, 3:30 p.m.

**Synopsis:**

The ocean is populated by an intense geostrophic eddy field that is unresolved in most numerical ocean models used for climate prediction. A geometric framework for parameterising ocean eddy fluxes is developed that is consistent with conservation of energy and momentum. The framework involves rewriting the residual-mean eddy force, or eddy potential vorticity flux, as the divergence of an eddy stress tensor. The magnitude of the tensor is bounded by the eddy energy, allowing its components to be rewritten in terms of the eddy energy and non-dimensional parameters describing the mean "shape" of the eddies, analogous to "eddy ellipses" used in observational oceanography. These non-dimensional geometric parameters have strong connections with classical stability theory, for example, the new framework preserves the functional form of the linear Eady growth rate and, with one additional ingredient, Arnold's first stability theorem. This framework also leads to a simple model of "eddy saturation": the relative insensitivity of the ocean circulation and stratification to the magnitude of the surface wind stress in ocean models with explicit eddies. These results offer the prospect of improved eddy parameterisations that both preserve the underlying symmetries and conservation laws inherent in the unfiltered equations, and reproduce empirical results that have been obtained with eddy-permitting models.