Applications of Improved 2‐D Numerical Wave Tanks in Wave Breaking

Abstract

Song and Banner (2002, henceforth referred to as SB02) used a numerical wave tank (developed by Drimer and Agnon, and further refined by Segre, henceforth referred to as DAS) to study the wave breaking in deep water, and proposed a dimensionless breaking threshold based on the behaviour of the wave energy modulation and focusing during the evolution of the wave group. In this paper, two modified DAS models are used to further test the SB02's results, the first one (named to MDAS1) corrected many integral calculation errors appeared in the DAS code, and the second one (named MDAS2) replaced the linear boundary element approximation of DAS into the cubic element on the free surface. Researches show that the results of MDAS1 are the same as those of DAS for the simulations of deep water wave breaking, but the different values of the wavemaker amplitude, breaking time and the maximum local average energy growth rate ‐max for the marginal breaking cases are generated by MDAS2 in comparison with MDAS1. However, MDAS2 still satisfies the SB02's breaking threshold. Furthermore, MDAS1 is utilized to study the marginal breaking case at the intermediate water depth when wave passes over a submerged slope, where the slope is given by 1:500, 1:300, 1:150 or 1:100. It is found that the maximum local energy density μ increases significantly if the slope becomes steeper, and the ‐max decreases weakly and increases intensively for the marginal recurrence case and marginal breaking case, respectively. SB02's breaking threshold is still valid for the wave passing over a submerged slope that is gentler than 1:100 at the intermediate water depth.