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Physical oceanography: an applied mathematician's approach

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NWWW01 - Nonlinear water waves

In this talk we present the problem, based on the Euler equation, which is at the heart of any mathematical description of the motion of our oceans. This involves the prescription of a suitable model for the fluid (e.g. inviscid but with vorticity), together with an appropriate set of boundary conditions (and associated initial data that is consistent with our solutions will be assumed to exist). The approach is based on classical ideas of fluid mechanics, involving non-dimensionalisation and scaling, leading to a reasonable and suitable reduction of the system that is amenable to further analysis. The aim is to show that such methods, which involve relatively little conventional ‘physical oceanographic modelling’, can uncover some fundamental processes that underpin many of the observed movements of the oceans (typically, on the large scale). However, in addition to approximate (asymptotic) versions of the various problems of interest, we find that this systematic approach also enables some relevant and useful exact solutions of the system to be developed. In particular, we will show how problems can be formulated that relate to: linear waves in the presence of a thermocline over an arbitrary flow (near the Pacific Equator); exact solutions associated with the Antarctic Circumpolar Current and a corresponding equatorial flow; a three-dimensional flow, with a thermocline, appropriate to a neighbourhood of the Pacific Equatorial Undercurrent; a representation of gyres of any size.

This talk is part of the Isaac Newton Institute Seminar Series series.

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