#### Multiple equilibria for flow over topography in a β-plane channel

*Supervised by Dr Michael Davey, 2011*

The occurrence of blocked flows in the atmosphere causes anomalous circulations and severe weather patterns both upstream and downstream of the block. Inspired by the words of Namias (1964), who wrote that climatic fluctuations are *‘due to feedback phenomena between the atmosphere and the underlying surface, and without considering the latter, meteorologists cannot hope to solve the problems of climatic abnormalities’*, we will examine the existence of multiple equilibria caused by topography as an explanation for blocking.

We will begin with quasi-geostrophic flow over topography in a β-channel using the quasi-linear theory that was first developed by Davey (1980). A first quasi-linear approximation will be obtained by looking at steady flow and neglecting all non-linear terms and this approximation will then be refined by retaining the zonally averaged shear, but ignoring eddy-eddy interactions. We will see that these approximations give rise to multiple solutions, which correspond to blocked and unblocked flows. We then restate the problem as a Fokker-Planck equation to be solved numerically to give the stationary probability density function of the system. Finally, we will look to extend the one layer problem to two layers and will study some of the results obtained when solving the governing equations.

*You can download a copy of my Master’s thesis here.*