The Large-scale Semi-Geostrophic Equations (LSGE, Salmon[73]) are three-dimensional equations valid for an ocean with a rigid lid and length scales much greater than the internal deformation radius (about 40km). In this thesis I reduce the LSGE to a pair of two-dimensional equations via the ansatz that the temperature is independent of the vertical co-ordinate. I refer to these as the Depth-Independent-Temperature (DIT) equations. Whilst this is regarded as a paradigm for the entire ocean, the reduction is similar in spirit to that utilised by many authors for modelling the mixed layer of the ocean. The equations of this thesis differ from the work of such mixed layer models because they involve no ad hoc vertical averaging and so solutions to these equations are also solutions to the full three-dimensional LSGE. The DIT are arguably the simplest equations for ocean circulation to include the effects of inertia, topography and baroclinicity. The DIT are studied both analytically and numerically. It is shown that the model exhibits baroclinic instabilities and analogies are drawn with classical Rayleigh-Benard convection. It is shown that both viscosity and thermal diffusivity are required to avert an ultra-violet catastrophe. Numerical simulations of turbulence demonstrate that the long-time behaviour resembles barotropic flow and that the temperature is reduced to the role of a passive tracer unless large-scale thermal structure is imposed externally on the flow. One of the advantages of the current model over the more widely used quasi-geostrophic models is that there is no restriction on the vertical extent of the bottom topography. This allows the simulation of idealised oceanic basin circulations in which the depth of the ocean vanishes smoothly at boundaries. These ocean simulations are used to study the sensitivity of the model to the Rossby Number, Ekman Number and forcing parameters. Comparison of a barotropic and a DIT ocean reveals the influence of baroclinicity in the latter model. Characteristic features of the Gulf Stream such as meandering, recirculation gyres and the shedding of warm and cold core rings are reproduced by the DIT model and the simple nature of the equations permits an interpretation of these features.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:313023 |
| Date | January 1999 |
| Creators | Shepherd, James Robert |
| Contributors | Ford, Rupert ; Salmon, Rick |
| Publisher | Imperial College London |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | http://hdl.handle.net/10044/1/51559 |
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