Linearized solution of a flow over a nonuniform bottom

摘要

A linearized theory is presented for determining the shape of the free surface of a running stream which is disturbed by some irregularities lying on the bottom. The bottom is represented in integral form using Fourier's double-integral theorem. Then following Lamb [3], a linear free-surface profile is obtained for the supercritical and subcritical cases.The results are plotted for the two cases of the flow for different shapes of the bottom, and different values of the Froude number. The effect of the Froude number, the bottom height and the shape of the bottom are discussed.