A cnoidal approximation wave theory

Periodic progressive waves in shallow to transitional water are described by a cnoidal approximation wave theory. The formulation is analytical and largely classical. Periodic waves are assumed, so that the theory does not extend to solitary waves. The solution is completed numerically, as a problem in non-linear optimisation. The suitability of the theory in shallow to transitional water is demonstrated to 88% of the limit wave height.