Steep. Short-Crested Waves and Related Phenomena

Abstract

Steep, short-crested waves, as well as a large variety of three-dimensional propagating wave patterns have been created in laboratory, utilizing a plunging half-cone. Monochromatic waves, over a range of frequencies and amplitudes through breaking and including soliton wave groups near resonance, have been observed and studied in a small wave flume. This monochromatic wavemaker creates complex wave patterns which depend upon the wavemaker shape, its frequency, and the tank width. The theory is presented along with computer simulation and experimental data to describe these three-dimensional waves. The effect of viscosity at the wall is taken into account to explain the attenuation of wave energy down-tank. In the neighborhood of the first cut-off frequency, strong nonlinear-effects were observed. Symmetric-standing sloshing waves generated at the wavemaker spontaneously form a moving hump (soliton), which propagates very slowly down-tank. The hump then builds up again in time at the wavemaker and the process is repeated. In the case of two-mode propagation, waves produced are diamond-shaped patterns and propagate in such a way that the amplitude of individual wave crests oscillate with distance down-tank. As a result, intermittent breaking can be caused to occur at specific locations away from the wavemaker. The inception of breaking was found to occur over a range of wave steepness, from a minimum (consistent with other experiments, and decreasing with short-crestedness) to a maximum (close to the Stokes limiting steepness). Breaking was observed to occur, providing: (i) the wave steepness exceeds a threshold (minimum) value; and, simultaneously, (ii) the propagating wave crest reaches a maximum and begins to decline. These observations suggest a new criteria for the inception of breaking.