| Summary: | Ocean mesoscale (10-100km) turbulence is integral to the complex and interconnected climate system. Many of the assumptions made in classical turbulence theory are inappropriate for describing the characteristic features of geophysical flows. In particular, when the fluid flow is both forced and dissipative. With increased interest in stochastic parameterization of ocean eddies, it becomes pertinent to consider what the statistics of ocean turbulence should look like as well as consider what statistical physics concepts can be used to further the theoretical understanding of the ocean mesoscale. In this thesis, we examine mesoscale turbulence from both a theoretical and empirical perspective employing both idealized models and realistic ocean model data. The statistical nature of a turbulent barotropic jet is explored empirically in the context of an idealized model as well as for realistic ocean model data. Additionally, an entropic and statistical mechanics framework is investigated in the context of force-dissipative flow. It is shown that: ocean jets which exhibit strong mixing barriers have a profound effect on the statistics, leading to multi-modal probability distributions and pointing to the importance asymmetry and extreme values in the statistics; an eddy-mixing entropy, which quantifies turbulent disorder, is a useful metric in describing turbulent motions and evidence is found for the maximization of this entropy in a forced-dissipative fluid flow. Further, across the separate studies presented in this thesis, it is shown that Lagrangian information is useful in distinguishing large-scale coherent structures from the more stochastic small-scale turbulence; and high-order Casimir invariants of motion are important for describing forced-dissipative geophysical flows in a statistical mechanics framework.
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