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Rip currents on a circular beach. O'Rourke, John Cameron


A mathematical model is developed which extends the theory of rip currents developed by Bowen (1969b) for a straight beach to curved beaches where radii of curvature are large relative to the width of the surf zone. Nine forcing terms are found to cause rip current systems. The terms are functions of the longshore variation in wave height and angle of incidence of the incoming waves at the breakers. The model is applied to the case of a circular beach with conical nearshore bottom topography. A large rip current component is found to exist which is inversely proportional to the radius of curvature of the beach. Another significant rip current component is found to be proportional to the variation in the angle of incidence of the waves at the breakers. This component would cause rip currents on a straight beach where some irregular offshore topography caused some variation in the incident angle of the incoming waves. Another component rip current was found which was essentially the same as the one predicted by Bowen (1969b).

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