POTENTIAL FLOW PROBLEMS

Abstract

For many years the effect of the shape of the bottom on surface wave has received considerable attention. Several methods, both experimentally and theoretically have been used to solve this problem.

In this thesis, all problems are solved wtder the assumption that the fluid is inviscid and incompressible and that the flow is two-dimensional, irrotational and steady.

Chapter I mentioned a historical survey for the subjects dealing with the flow over various bottom topographies.

The principal mathematical methods are reviewed in Chapter II such as Linearization method, Perturbation method, Relaxation method, Finite difference method, Finite element method, Bowtdary-integral equation method, Kantorovich method, Hilbert's Method, Hodograph method and Cauchy integral equation method.

The free surface flow past a submerged periodic bottom of different shapes is considered in Chapter ill. Following the linearized method suggested by Thomson and Lamb the free­ . surface profile is obtained for the supercritical and subcritical cases.

The effect of the surface tension is taken into account for the two kinds of flow. The parameters governing the flow such as the Froude number F, the periodic length L and the shape of the bottom are discussed in both cases of the presence or absence of the surface tension.

The results are in good agreement with those obtained by other previous methods.