Stokes' equations are presented, but the use of higher order approximations is 

 sometimes justified for the solution of practical problems. 



For shallow-water regions, cnoidal wave theory, originally developed by 

 Korteweg and De Vries (1895), provides a rather reliable prediction of the 

 waveform and associated motions for some conditions. However, cnoidal wave 

 theory has received little attention with respect to the actual application in 

 the solution of engineering problems. This may be due to the difficulties in 

 making computations. Recently, the work involved in using cnoidal wave theory 

 has been substantially reduced by the introduction of graphical and tabular 

 forms of functions (Wiegel, 1960; Masch and Wiegel, 1961); however, appli- 

 cation of the theory is still complex. At the limit of cnoidal wave theory, 

 certain aspects of wave behavior may be described satisfactorily by the 

 solitary wave theory. Unlike the cnoidal wave theory, the solitary wave 

 theory is easy to use because it reduces to functions that may be evaluated 

 without recourse to special tables. 



The development of individual wave theories is omitted, and only the 

 results are presented since the purpose is to present only that information 

 that may be useful for the solution of practical engineering problems. Many 

 publications are available, such as Wiegel (1964), Kinsman (1965), and Ippen 

 (1966a), which cover in detail the development of some of the theories 

 mentioned above, as well as others. The mathematics used here generally is 

 restricted to elementary arithmetic and algebraic operations. Emphasis is 

 placed on the selection of an appropriate theory in accordance with its 

 application and limitations. 



Numerous example problems are provided to illustrate the theory involved 

 and to provide some practice in using the appropriate equations or graphical 

 and tabular functions. Some of the sample computations give more significant 

 digits than are warranted for practical applications. For instance, a wave 

 height could be determined to be 3.048 meters for certain conditions purely 

 based on theoretical considerations. This accuracy is unwarranted because of 

 the uncertainty in the basic data used and the assumption that the theory is 

 representative of real waves. A practical estimate of the wave height given 

 above would be 3.0 meters. When calculating real waves, the final answer 

 should be rounded off. 



2. Wave Fundamentals and Classification of Waves . 



Any adequate physical description of a water wave involves both its sur- 

 face form and the fluid motion beneath the wave. A wave that can be described 

 in simple mathematical terms is called a simple wave. Waves that are com- 

 posed of several components and difficult to describe in form or motion are 

 termed complex waves . Sinusoidal or simple havmonia waves are examples of 

 simple waves since their surface profile can be described by a single sine or 

 cosine function. A wave is periodic if its motion and surface profile recur 

 in equal intervals of time. A waveform which moves relative to a fixed point 

 is called a progressive wave; the direction in which it moves is termed the 

 direction of wave propagation . If a waveform merely moves up and down at a 

 fixed position, it is called a 'complete standing wave or a clapotis. A 

 progressive wave is called a wave of permanent form if it is propagated 

 without experiencing any changes in free-surface configuration. 



2-3 



