Experimental and Numerical Investigation on the Interactions between the Weakly Three-Dimensional Waves

Abstract

The results of laboratory experiments and numerical simulations were performed to investigate the interactions between the weakly three-dimensional waves in an ‘X’ configuration, which has a 16-degree approaching angle. In addition, another oblique two-dimensional experiment was also conducted for comparison with the ‘X’ configuration but in one single channel by removing a dummy wall in the interaction region. Our experimental results show that as the wave trains propagate into the interaction region, it is obvious that there is an increase in the wave height which reaches a maximum height of about 1.37H0 for different initial wave steepness at the center of the interaction region, and then decreases thereafter, where H0 is the input wave height. Then wave elevations at different positions downstream of the interaction region were also studied, indicating that the frequency and initial wave steepness were highly correlated with the wave-wave interaction between the weakly three-dimensional waves. For the wave with low frequency (f = 0.8 Hz), a crescent wave surface formed at the beginning of the interaction and then separated into two two-dimensional waves after the interaction, which illustrates that the waves can still keep their initial characteristic and propagate as their initial directions downstream of the interaction region. While the frequency increased (f = 1.2 Hz), three-dimensional effects appeared to dominate the interaction of weakly three-dimensional waves, especially for the large initial steepness, and the wave surfaces were also three-dimensional after interactions. Finally, numerical simulations with larger approaching angles were conducted to further understand the influence of propagation direction on the interactions between the weakly three-dimensional waves. The results suggest that intense interactions and strong three-dimensional characteristics of the wave trains downstream interactions can result from larger approaching angles.

Keywords

• wave-wave interactions
• experimental model
• non-hydrostatic model