Shallow flow over an isolated obstacle

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Abstract
This is a study of how certain geometrical and flow parameters affect the tendency of a fluid to flow around rather than over a single obstacle of simple shape in a homogeneous non-rotating fluid. A series of numerical experiments was conducted with a finite-difference model of such a shallow flow, assuming a hydrostatic pressure distribution. The results demonstrate how the flow over a three-dimensional obstacle deviates from the patterns established for a two-dimensional ridge. Measures are suggested for quantitative assessment of the tendency to flow around as a function of relative hill height and Froude number.A series of laboratory experiments was also performed, examining the motions of two superposed homogeneous layers of fluid past an isolated obstacle in a towing tank. The resulting motion of the interface was found to agree with the results of the numerical experiments. The laboratory experiments also extended the understanding gained from the numerical experiments. Flow-visualization techniques were employed to aid in the qualitative assessment of the flow around the obstacles and its dependence on hill and flow parameters. In particular, these techniques demonstrated the impingement of the interface on the obstacle, and its dependence on flow speed and hill height.