Long Wave Propagation in Idealized Estuary

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Abstract
The paper outlines an analytical solution by Proudman to the partial differential equations of motion in an idealized estuary. The solution is obtained for an idealized estuary in which the channel is horizontal, of constant rectangular section, closed at one end and open at the other to tidal influence. The motion is considered to be one-dimensional, and the solution includes the effects of both the convective acceleration and friction terms. Proudman's work is developed in terms of working expressions for the tidal elevation and velocity at any point in the estuary. The limitations of this second-order solution are given in graphical form, in terms of four dimensionless numbers. Finally, the solution is compared with that obtained by solving Telegraphers equation, and Proudman's solution found to be more satisfactory.

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