Effects of coastal topography on lake currents: Using three-dimensional boundary-fitted coordinates

Date of Award




Degree Name

Doctor of Philosophy (Ph.D.)


Mechanical Engineering

First Committee Member

Subrata Sengupta, Committee Chair


A three-dimensional boundary-conforming co-ordinate system has been developed as a combination of an algebraic stretching transformation in the vertical and through the use of elliptic operators in the horizontal. The combined transformation maps a domain of variable depth and any arbitrary shape in the horizontal to a parallelpiped. The stretching transformation also accounts for the moving free-surface. Thus, although the physical boundary changes with time the transformed domain remains the same. The stretching transformation and hence, the three-dimensional boundary-fit transformation, are valid only when the depth at all locations is nonzero.The three-dimensional transformation has been used to study the unsteady, three-dimensional, wind-driven flow in a shallow, homogeneous lake in the f-plane of square cross-section of side 100km, with a cape present midway along one of its coasts. Solutions were obtained for both constant depth and variable topography basins and for capes of different shapes, sizes, and aspect ratios. The horizontal velocity structure was affected by the cape geometry only in the transient condition but the upwelling and downwelling patterns in the entire lake were affected by the cape geometry. The solutions for the constant depth and the variable depth cases showed that the effects of coastline geometry were about as significant as the effects of bottom topography.Studying the effects of the cape geometry on flow at E$\sb{\rm V}$ = 2.0 and E$\sb{\rm V}$ = 0.4 showed that the solutions were qualitatively similar at both Ekman numbers, but the quantitative effect of the cape on the upwelling and downwelling was significantly greater at E$\sb{\rm V}$ = 0.4.


Engineering, Mechanical

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