On the laboratory generation of two-dimensional, progressive, surface waves of nearly permanent form on deep water

Recent experiments by Hammack et al. (J. Fluid Mech., vol. 532, 2005, p. 1) on deepwater waves with two-dimensional, periodic surface patterns showed several features, some of which were unsteady. Fuhrman & Madsen (J. Fluid Mech., vol. 559, 2006, p. 391) explained three of these as being the consequence of sinusoidal forcing by the wavemaker array that did not include forced harmonics, either in time or in the direction parallel to the wavemaker. They predicted that neglected third-harmonic terms cause more serious consequences than neglected second-harmonic terms when the generated wavefields have two-dimensional surface patterns. This paper presents experiments that provide strong evidence that their explanation is correct: including the third-harmonic terms in the wavemaker forcing results in wave patterns that propagate with nearly permanent form.