TABLE OF CONTENTS This application yields various parameters of wave motion as predicted by first-order (Isobe, 1985) and second-order (Hardy and Kraus, 1987) approximations for cnoidal wave theory. It provides estimates for common items of interest such as water surface elevation, general wave properties, kinematics, and pressure as functions of wave height and period, water depth, and position in the wave form.
The accurate description of waves in the nearshore region is an important element in the design and analysis process. The complexity of nonlinear wave theories has apparently discouraged their common application, especially for reconnaissance level investigations; yet they often provide significant improvements over linear wave theory descriptions. Today s common desktop microcomputers offer adequate computational power to implement many nonlinear wave theories.
Solutions for wave attributes described by this theory are expressed in terms of the Jacobian elliptic function cn, thus providing an explanation for the theory s name. The original source for the theory was a paper by the Dutch mathematicians Korteweg and de Vries (1895). More recent derivations for cnoidal wave theory include those of Keulegan and Patterson (1940), Keller (1948), Laitone (1960), Chappelear (1962), Fenton (1979), and Isobe and Kraus (1983) among others. Differences between the derivations consist primarily of choices in perturbation parameter, definition of celerity, and order of the solution. The following discussion is taken principally from Hardy and Kraus (1987), and Isobe and Kraus (1983).
A representative cnoidal wave profile is illustrated in Figure 2 2 1.
