A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Engineering

Thesis (Ph.D.) - Asian Institute of Technology, 1975

In this thesis the transformation of the solitary wave in two different processes is discussed from theoretical and practical point of view. The processes are the damping due to bottom friction and the overtopping at a seadike. They have the common feature of subtracting an amount of energy of the wave, although the modes of subtraction are quite different. The effect of the bottom friction to the deformation of the finite amplitude long waves on a horizontal bed, is mathematically modelled by associating the empirical friction term of steady flows with the irrotational, Boussinesq's equations. For the waves travelling in one direction only, the modified Korteweg-de Vriea equation (Kdv equation) is derived. In dimensionless variables, this equation is written as: Nt + NNs + Nsss + B = o Some characteristics of the modified Kdv equation is analytically discussed for the initial solitary wave. Various features of the solitary wave damping are studied through laboratory and computer experiments with the modified Kdv equation. The frictional behaviour of the bed in the motion of the solitary wave, is analysed by considering the analogy with the steady flow past a flat plate. A friction factor diagram for the solitary wave, which is based on the available laboratory data, is proposed. The problem of overtopping of the solitary wave at a seadike of idealized geometry, is analytically treated by adopting the analogy with the steady flow over a sharp crested weir. The values of two empirical parameters which appear in the analytical expression for the volume of overtopping, are determined from the laboratory data on 5 different dike shapes. The characteristics of the reflected waves which are formed after the overtopping of the solitary wave, and their further evolution, are discussed with reference to the measured results.