Masataka Yamaguchi


The aim of this paper is to analytically clarify the interrelation among- all of the existing cnoidal wave theories of the third order approximation. The result is that the Chappelear theory expressed with two expansion parameters is found to include the other theories. This means that they are able to be derived from the Chappelear theory by changing expansion parameters in the expressions of wave characteristics and integral properties and identifying the definition for wave celerity to be used in the theory. The expressions for the trajectory of a water particle, mass transport velocity and integral properties of waves are newly derived using these theories, and the wave characteristics and integral properties are examined based on the numerical computation and comparison with the experiments. As a result, use of the theory expressed with a single expansion parameter is recommended from a practical viewpoint. The figures describing a limiting range of wave parameters for the application of the above-mentioned theory are also provided by comparing wave characteristics and integral properties of the theory with those of Fenton's Fourier approximation wave theory.


theory interrelation; cnoidal theory; wave theory

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