**Geoffrey Vallis**

Geophysical Fluid Dynamics Laboratory, Princeton University

### Baroclinic Turbulence: The Long Road from Quasi-geostrophic Theory to the Primitive Equations.

Geostrophic turbulence is ubiquitous in both atmosphere and ocean, and a fundamental question is, how does such flow equilibrate? Specifically, what determines the scale and magnitude of baroclinic eddies in a fluid that is forced to be potentially baroclinically unstable? Quasi-geostrophic theory is the starting point for such a discussion, and various theories, or phenomenologies, based on geostrophic turbulence theory have been put forward. Note that even if quasi-geostrophic arguments work, they cannot be the whole story because the stratification is imposed, and not allowed to vary. In addition, various types of 'baroclinic adjustment' arguments have been made that posit that the fluid should equilibrate near a state of marginal supercriticality, a consequence of which would be that there is little or no inverse cascade of energy to larger scales.

We will discuss these various theories, and describe some numerical experiments exploring geostrophic turbulence in primitive equation model.