| Summary: | Climate modelling fails to accurately represent the global oceans in a number of ways. One area where models are consistently flawed is in the Atlantic Water Layer of the Arctic Ocean, by failing to predict the predominantly cyclonic circulation observed. In this thesis we discuss the most likely explanation for this failing, namely that most, if not all, climate models fail to have a physically consistent representation of mesoscale eddies, whether resolved or parameterised. We will explore recent developments in eddy-mean interaction theory, and use it to investigate eddy-mean interactions over topography. To do this we will use an idealised stacked shallow water model in which large topographic slopes and realistic mesoscale eddy fields can be well represented. The effect of these eddy fields on the larger scale is diagnosed using the theory to determine how the eddy-mean interaction is characterised by both the topography and the properties of the eddy field. It is shown that the eddy energy and eddy enstrophy provide useful bounds. In the specific configurations explored in this thesis, the eddy energy is shown to be a highly constraining bound and hence an important factor for the structure of the eddy stresses. Also, despite the two definitions of mean potential vorticity allowed by eddy-mean interaction theory, we show that these definitions are effectively identical in our configurations, and hence that the eddy enstrophy bound is applicable to both definitions. These results will hopefully contribute to developing a dynamically-consistent parameterisation of eddies over variable topography. And hence, help to improve the ability of ocean models to reproduce circulation patterns observed in the Atlantic Water Layer of the Arctic.
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