Breaking Criterion and Characteristics for Solitary Waves on Slopes

Abstract

Shoaling and breaking of solitary waves is computed on slopes 1:100 to 1:8 using an experimentally validated fully nonlinear wave model based on potential flow equations. Characteristics of waves are computed at and beyond the breaking point, and geometric self-similarities of breakers are discussed as a function of wave height and bottom slope. No wave breaks for slopes steeper than 12. A breaking criterion is derived for milder slopes, based on values of a nondimensional slope parameter S o. This criterion predicts both whether waves will break or not and which type of breaking will occur (spilling, plunging, or surging). Empirical expressions for the breaking index and for the depth and celerity at breaking are derived based on computations. All results agree well with laboratory experiments. The NSW equations fail to predict these results with sufficient accuracy at the breaking point. Pre-breaking shoaling rates follow a more complex path than previously realized. Post-breaking behaviors exhibit a rapid (non-dissipative) decay, also observed in experiments, associated with a transfer of potential energy into kinetic energy. Wave celerity decreases in this zone of rapid decay.

A 3d Isogeometrical Boundary Element Analysis for Non-Linear Gravity Wave Propagation

“…8a and b). For the cubic NURBS model the wave reaches a maximum height of 6.85 · 10 −1 h which is very close to the reported in [2] (6.89 · 10 −1 h), while for the quadratic NURBS model is lightly lower (6.81 · 10 −1 h) due to the lower degree of accuracy. In Fig.…”

“…9 we compare the central section of the cubic NURBS model and the results presented by Grilli et al [2] at the breaking time. The relative errors for volume and energy are v = 1.21 · 10 −4 and e = 7.62 · 10 −5 , respectively, and the shape is in very good agreement with the data reported in [2]. …”

“…We also analysed the numerical stability of the same solitary wave propagating over a 1:15 slope that starts at the initial position of the crest (x = 7.5h). This configuration, that produces the overturn of the wave, was studied in detail by Grilli et al [2] using a 2D BEM mode. Later these results have been used used to validate a 3D BEM formulation [3].…”

“…These models have been applied to simulated tsunami generation and [1] overturning waves [2][3][4], to design breakwaters [5,6], to predict the wave pressure impact on structures [7], or to study radiation and diffraction waves produced by a wave-maker [8][9][10][11]. Nowadays, because of the increasing interest on the ocean renewable energy, in which the generation systems are installed near-shore or off-shore, new applications of such models are being used to study the fluid-structure interaction considering the effect of the waves [12][13][14][15][16].…”

“…These authors presented a successful comparison between the numerical results obtained by a 2D-BEM model and experimental results in a water tank. It is worth to mention the studies reported by Grilli et al [2,24,25] who developed an advanced approach using 2D high order BEM. Later, Grilli et al [3] and Guyenne and Grilli [4] extended the model to three-dimensional (3D) geometries to analyse overturning waves over an arbitrary bottom.…”