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Title: Tales from topological oceans
Author: Stanley, Geoff
ISNI:       0000 0004 7652 7503
Awarding Body: University of Oxford
Current Institution: University of Oxford
Date of Award: 2018
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Functional relationships between variables can offer great illumination to hard problems. In geophysical fluid dynamics these often arise via alignment of gradients, in which case the functional relationship is multivalued; its branches are determined by a topological analysis of the connectedness of level sets, accomplished by the Reeb graph. The neutral tangent plane, along which mixing in the ocean predominantly occurs, is defined by ∇nρ = ρpn p, thus a multivalued function relates the in-situ density ρ and the pressure p. With topological analysis, a new approximately new surface is presented, called a topobaric surface. This surface possesses an exact geostrophic stream function, namely the exact geostrophic stream function for neutral surfaces, which ΜcDougall (1989) proved must exist. A closed form expression for this stream function is presented. For a steady, inviscid, buoyancy conserving fluid, a multivalued function relates the potential vorticity Q and the Bernoulli potential B on buoyancy surfaces. In the Antarctic Circumpolar Current (ACC), level sets of B are dominated by one circumpolar contour, so Q is studied as a single-valued function of B. A tight linear relationship is discovered. Its slope, appropriately non-dimensionalised, provides information about the degree of PV homogenisation on a buoyancy surface, and about the shear stability of the flow regime via Arnol'd's stability theorems. The real ocean does not obey these assumptions, and Q is not exactly materially conserved. In the time-mean ACC, it is found that Q can vary along streamlines by up to 50%. The causes for these fluctuations are studied, revealing a balance between two large and opposite-signed forcings---mean vertical advection and eddy interfacial form stress---with friction significant near topography. Variation of Q along B contours adds complexity on top of a background state defined by constant Q along B contours.
Supervisor: Marshall, David Sponsor: Clarendon Fund ; Clarendon Canadian Alumni Scholarship
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: Oceanography