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Model of frictional two-layer exchange flow Zaremba, Lillian

Abstract

An unsteady model is developed for two-layer exchange through a channel with friction on the bottom, sidewalls, surface and interface. Steady or time-varying barotropic forcing can be specified. The unsteady model is first used to solve for the steady solution with zero barotropic forcing starting from initial conditions of the lock exchange problem. The effects of friction on steady exchange are investigated for four channel configurations: a contraction with constant depth and with an offset sill, and a constant-width channel with constant depth and with a sill near one end. Exchange flow decreases substantially with increasing friction. The interface position and locations of internal hydraulic control are affected by varying friction. Solutions are asymmetrical when surface friction is absent. Internal hydraulic jumps form when friction is increased. Flow becomes hydraulically uncontrolled for high friction in all channel geometries considered. The model predictions are compared to experiments in a constant-width channel with constant depth and with a sill. The model is also applied to the Burlington Ship Canal which connects Hamilton Harbour to Lake Ontario. The exchange in the Burlington Ship Canal is modeled with zero and net steady barotropic components. Field observations from boat-mounted instruments show barotropic components and unsteadiness in flows. The magnitude of the observed barotropic variations is not great enough to influence exchange so that friction is the dominant factor governing exchange in the Burlington Ship Canal. The unsteady model is finally used with a periodic barotropic forcing in the contraction geometry. Exchange increases with forcing period and magnitude for the frictionless case. The model results are inconclusive for the effect of increasing friction with the periodic barotropic forcing. The numerical methods of the model do not' allow it to be generally applied to other channel geometries with time-varying barotropic forcing.

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