The circulation induced by a steady uniform stress acting on the surface of a liquid in a closed basin of uniform depth is considered for Reynolds Numbers (surface current x depth) (dynamic viscosity) from 0-400. The main work is the numerical solution of the two—dimensional Navier Stokes equation for circulation in a vertical plane parallel to the wind stress. It is found that the circulation near the two ends of the basin is very different. At the windward end, it becomes vary slack, while at the leeward end, oscillations occur which decrease in amplitude from an end maximum (eddy) near the wall. These oscillations extend further from the wall, and increase in amplitude as the Reynolds Number it increased. At about Reynolds Number 500, they lead to reversed flow in the lee of the end eddy, and imply instability of the steady—state flow. At higher Reynolds Numbers, steady—state solutions still appear to be possible, but for finite basins the ' effects of the end walls and of the side walls will interact to give a. necessarily three—dimensional and complex streamline field.. The Numerical method of solution, which becomes progressively more difficult to apply as the Reynolds Number is increased, is basically the relaxation of finite difference approximations to the vorticity equation by the Liebmann process, using an electronic computer. The vorticity equation has also been solved in special cases by a series expansion. in the last Chapter on the grounds of similarity theory, and the rather sparse experimental evidence, the results are qualitatively applied to tho mean lake circulation.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:602158 |
| Date | January 1962 |
| Creators | Bye, John Arthur Tristram |
| Contributors | Eady, E. T. ; Charnock, H. |
| Publisher | Imperial College London |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | http://hdl.handle.net/10044/1/13650 |
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