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A cnoidal approximation wave theory

The extreme wave credibility of analytical solutions for cnoidal waves (periodic progressive waves in shallow transitional water) reaches only to about 50% of the limit wave height in very shallow water. Higher order analytical theories become prohibitively complicated in application. A Cnoidal Approximation theory is introduced for shallow water. It is a hybrid analytical–numerical extension of the cnoidal theory where the analytical formulation follows the cnoidal approach with the unknowns of the theory assigned numerically rather than analytically. Credibility at very moderate order extends to about 88% of the limit wave.