Application of Stokes, Cnoidal, and Fourier Wave Theories

Abstract

A consistent framework for the selection and application of higher‐order steady wave theories is presented. Fifth‐order formulations for cnoidal (shallow water) and the corrected Stokes (deep water) wave theories are reviewed, in addition to Fourier approximation theory (deep, transitional, and shallow water). All three theories are developed in a standardized fashion with respect to coordinate transformations, notation, and presentation of results, so as to facilitate their application in engineering practice. A coflowing uniform current is accommodated by all three theories, which is essential in maintaining consistency at higher orders. The cnoidal theory has been specifically extended to include current to fifth order. Consideration is given to the calculation of integral parameters, forces and moments from the O'Brien‐Morison equation, in addition to field velocities, accelerations, and pressures. Comparative predictions from the three theories for several depth and current conditions illustrate characteristic features, predictive capabilities, and limitations of the separate theories.