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Abstract

This thesis is concerned with free surface flow in a non-rotating or rotating shallow laterally heated cavity which is assumed to be of infinite length in the third dimension. The flow is driven by a horizontal temperature difference: the two vertical walls are kept at constant, but different, temperatures, giving rise in general to a large scale circulation known as a Hadley cell. The flow is considered to be subdivided into three main regions: a parallel-flow core region away from the end walls and two end zones close to the vertical walls where the fluid is turned through 180 degrees. This study is concerned with identifying the main features of both the basic flow and temperature fields generated in the cavity and, in the non-rotating case, with the stability of that flow.

There are two main parts to this thesis: the first part is dedicated to the flow in the non-rotating cavity and, in the second part, the flow in the rotating cavity is considered. In each case the steady-state free surface problem is initially studied. An analytical solution for the parallel-flow core is found; the flow in the end regions close to the vertical walls is then investigated. Results are presented which determine the extent of these regions. These complement asymptotic results which are found for large Rayleigh number (based on the temperature difference between the vertical walls and cavity depth) in the non-rotating case and small Rayleigh number in the limit of large rotation rate. Asymptotic solutions are also found in the limit of large Rayleigh number and rotation rate where a novel boundary layer structure is identified near the horizontal surfaces.

The linear stability of the non-rotating parallel-flow core is investigated. Here the neutral curves which delineate the boundary for which instabilities persist are found and an investigation of the large Rayleigh number behaviour of the neutral curves is undertaken.

Numerical and analytical methods are used to give complete solutions for the flow in the end regions from the small rotation rate limit where the solutions match with the non-rotating results to the large rotation rate limit where the double vertical boundary-layer structure identified by the asymptotic analysis evolves.

Publication Type:	Thesis (Doctoral)
Subjects:	Q Science > QA Mathematics
Departments:	School of Science & Technology > Mathematics School of Science & Technology > School of Science & Technology Doctoral Theses Doctoral Theses

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