On two theories of fifth order Stokes waves

Two analytical wave theories of fifth order Stokes waves, one by Skjelbreia and Hendrickson (1960) and the other by Fenton (1985), are compared against a numerical wave theory at fifth order. Several interesting features of Fenton's theory are brought out using numerical examples. While having certain intrinsic advantages, e.g. it can predict the strength of evanescent modes of propagation as a function of wave height, it is shown to exhibit some anamolous features.