الفهرس 
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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 WIder 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 IT such as Linearization method, Perturbation method, Relaxation method, Finite difference method, Finite element method, Bowulary-integral equation method, Kantorovich method, Hilbert’s Method, Hodograph method and Cauchy integral equation method.
The free swface flow past a submerged periodic bottom of different shapes is considered in Chapter m. 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 offlow. The parameters governing the flow such as the Froude number F, the periodic length L and the shape of the bottom arc 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
A numerical method based on series truncation and Sohwarlz-ehristoffel transformation is presented in Chapter IV to lve the problem of a flow over a polygon, lying on the bottom fOf the nmning stream. The suggested numerical method for the ;solution of the fully nonlinear problem is presented for critical IOlutions in which the flow is subcritical upstream and isupercritical downstream. In this case the speed and the height cof the flow before and after the obstacle are not equal. As a ~specia1 case a two cascade triangular obstacle is considered. The ,results are plotted and discussed for different triangular shapes.
In Chapter V, the solution of the nonlinear problem is ’presented for which the flow is supercritical both upstream and ’downstream. It is fOWld that solutions exist for the case of :aymmetric two triangules of arbitrary size. The results are lplotted for different triangular shapes and different values of ’Froude number F > 1. The effect of the Froude number and the shape of the obstacle on the free surface are discussed.
General discussions, comments, conclusions and proposals for futw-e extension are presented in Chapter 6.