The effect of a single resonant expansion chamber on the propagation of long waves in a channel.

Abstract

The study of the effect of resonant expansion systems on the propagation of long waves is presented in this thesis as a design problem in coastal hydraulics. Two previous studies which have been made on similar systems are presented in Chapter I to provide background material on the subject. The first study presented was made by Lamb (1916); and it demonstrates that reflection of long waves can be obtained by an expansion system and that the amount of wave energy that is reflected is a function of the geometry of the system. The second study presented was made by Valembois (1953) and is based on a hydrodynamic impedance theory. An important point to note in Chapter I is that both of these studies use a scalar equation of pressure continuity and a vector equation for the conservation of mass to obtain a solution. A new solution is derived in Chapter 2 by formulating a boundary value problem which incorporates the same type of boundary condition equations noted earlier. The problem is formulated in considerable detail to demonstrate the type of problem solution technique which is required to solve problems arising in coastal hydraulics. The details given in the problem statement become important later when the effect of geometrical changes of the resonant system are evaluated. Chapter 3 discusses the interdependance required between Civil Engineering and Oceanography to effect a complete solution to a design problem in coastal hydraulics. Several methods for presenting wave data are given, and one of these methods is selected for the design problem being considered. Finally, a linear analysis is employed in Chapter 4 to evaluate the effect of the resonator on the propagation of long waves by combining the solution derived in Chapter 2 with the spectral method of wave data presentation selected in Chapter 3. The results of the linear analysis are presented in graphical form as a measure of the amount of wave energy that is reflected and transmitted by the resonator.