On the largest wave height in water of constant depth

Abstract

Experimental evidence of the fact that, both in the laboratory and in the field, the largest wave height to water depth ratio realisable for oscillatory waves propagating in water of constant depth is about 0.55, has been published recently (Nelson, 1985); (Nelson, 1987); (Nelson, 1994). This paper presents various theoretical approaches to estimate this maximum value. In particular, the higher approximations of the Stokes and cnoidal theories give a much higher limiting wave height, close to 0.78 h, which is commonly used in engineering practice. However, the inclusion of higher harmonics, generated by a wave-maker paddle, into the analysis provides maximum wave height less than ≈ 0.6 h, which is in good agreement with observations.