Abstract:

The Antarctic Circumpolar Current is the strongest persistent oceanic current; it flows all the way around Antarctica and plays a crucial role in determining the Earth's climate, as it drives the water exchange between the Atlantic, Pacific, and Indian basins. In this talk, we will discuss a model of this flow that has been studied extensively over the past few years. All previous results concern the stationary case, mostly focusing on properties of particular zonal (i.e., exclusively latitude-dependent) flows; however, we will consider the full time-dependent model and obtain global-in-time existence and uniqueness of a classical solution to sufficiently regular initial data. Moreover, we will discuss the stability of a certain family of stationary zonal flows, which is obtained by exploiting appropriate conservation laws to construct a Lyapunov functional. Finally, if time permits, I will explain how the theory of local bifurcations can be applied to construct non-zonal stationary solutions.

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