Diffraction and Instability of Short-Crested Limited-Length One-Dimensional Coherent Wave Trains

Alternative representations of the wave field (as opposed to superposition of Fourier components) are possible. In this paper, behaviour of short-crested limited-length one-dimensional coherent wave trains is investigated. Experiments were conducted in the three-dimensional wave tank of the University of Tokyo. Description of the directional wave tank and its capacity to generate short-crested coherent wave trains, including those concurrent, superposed and directionally-superposed is provided. If the crest is shorter than the lateral extent of the wave tank, diffraction tends to redistribute the wave energy into clear surfaces, and thus energy of the wave trains is reduced and the modulational instability bandwidth changes correspondingly. Rates of such nonlinear lateral spread are estimated, and they are proportional to mean wave steepness. To avoid the diffraction, in further tests concurrent trains were mechanically generated, each of which occupied half of the lateral width of the wave tank and had the same energy as another half. The trains had the same frequency, and in order to keep them separate phase shift of 180 degrees was used. Sideband growth was significantly impaired by comparison with the long-crested evolution of the train with the same steepness.