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In this study, analytical solutions and physical interpretations are presented for the Riemann wave equation (RWE), which has an important physical property in fluid dynamics. The solutions of the RWE, which models the formation, interaction and breaking of the waves that occur as a result of any external effect on the ocean surface, are examined using the generalized exponential rational function method (GERFM). Bright (nontopological) soliton, singular soliton and solitary wave solutions are produced with advantages of GERFM over other traditional exponential methods. The factors in which solitary wave solutions cause breaking of wave are examined. The effects of parameters on wavefunctions and the physical interpretations of these effects are discussed and supported by graphics and simulations.

In order to model nonlinear breaking waves with moving boundary and coastal sandbar migration; we presented a morphodynamic model, where hydrodynamic equations (free surface flows) and sediment transport equation are solved in a coupled manner. The originality lies in the development of an innovative approach, in which, we project the horizontal velocity onto a basis functions depending only on the variable z and we calculate analytically the vertical velocity and the nonhydrostatic pressure. The choice of basis depends on the problem under consideration. This model is numerically stable because there is no mesh in the vertical direction. This model is accurate because we can directly introduce functions that best fits the physical nature of the flow. Our model is validated through laboratory measurements carried out by Dingemans [1994, J. Comput. Phys. 231, 328–344], Cox and Kobayashi [2000, J. Geophys. Res. 105(c6), 223–236. and Dette et al. [2002, Coast. Eng.47, 137–177].

A set of predictive models is formulated for computing suspended sediment concentration in and outside the surf zone under three different mechanisms:

(1) suspension due to turbulence motion over sand ripples,

(2) suspension from sheet flow layer, and

(3) suspension due to turbulence motion under breaking waves

Dimensional analysis and best-fit technique are the main methods for the formulation of reference concentration and diffusion coefficient and the model parameters are calibrated with the help of a large amount of published data. Time-averaged concentration profiles are derived from the steady diffusion equation. Published experimental data from 19 sources from 1977 to 1996 are better explained by the proposed formulae than the preceding formulae of Sleath [1982], Nielsen [1986 and 1988] and, Rattanapitikon and Shibayama [1994]. Due to scale effects, models are given for small-scale and large-scale cases separately. Predominance of each suspension mechanism is verified with a newly developed explicit formula. Finally, the applicability of the above sub models for irregular waves is also confirmed by the measured data sets.

This paper reports the cross-shore variations of a pressure gradient observed on a fixed barred beach in a large-scale laboratory wave flume. The data sets include measurements of the free water surface elevation, the near-bottom velocity and the near bottom pressure and the pressure gradient for one irregular wave and three regular wave cases. The cross-shore variation of the pressure gradient showed that the maximum value of pressure gradient appeared in the area of wave breaking, and the pressure gradients were influenced by the fluctuation of water surface elevation. The exceedance probabilities of pressure gradient were analyzed using irregular wave case data. Comparison of the onshore and offshore directions of the exceedance probability showed that the onshore direction dominant in this experiment; its values were generally large over the bar. The distribution of the exceedance probability of pressure gradient could be evaluated by the Weibull distribution.

A Corrected Moving Particle Semi-implicit (CMPS) method is proposed for the accurate tracking of water surface in breaking waves. The original formulations of standard MPS method are revisited from the view point of momentum conservation. Modifications and corrections are made to ensure the momentum conservation in a particle-based calculation of viscous incompressible free-surface flows. A simple numerical test demonstrates the excellent performance of the CMPS method in exact conservation of linear momentum and significantly enhanced preservation of angular momentum. The CMPS method is applied to the simulation of plunging breaking and post-breaking of solitary waves. Qualitative and quantitative comparisons with the experimental data confirm the high capability and precision of the CMPS method. A tensor-type strain-based viscosity is also proposed to further enhanced CMPS reproduction of a splash-up.

The accurate prediction of shallow water breaking heights is paramount to better understanding complex nonlinear near shore coastal processes. Over the past 150 years, numerous empirical relationships have been proposed based on scaled laboratory datasets. This study utilizes a newly available field collected full-scale dataset of breaking wave conditions to investigate the accuracy of published empirical models and a novel artificial neural networks (ANN) model in predicting the final breaking wave-height for laboratory-scaled and full-scaled ocean waves. Performance is measured by comparison against both the field datasets and 465 separate datasets from 11 independent laboratory studies. The relationship of Rattanapitikon and Shibayama [2000 “Verification and modification of breaker height formulas,” Coastal Eng. J.42(4), 389–406.] outperformed all available empirical models when tested against only laboratory datasets, but was superseded by the relationship of Robertson et al. [2015 “Remote sensing of irregular breaking wave parameters in field conditions,” J. Coastal Res.31(2), 348–363.] when tested against only field datasets. However, this study noted that models developed based on scaled laboratory tests tend to underestimate the ocean full-scale breaking wave-heights. The training and testing of the ANN model were accomplished using 75% and 25% of the combined field and laboratory datasets. The ANN models consistently outperformed predictive accuracy of empirical models. Sensitivity analysis of the trained ANN models quantified the relative impact of individual wave parameters on the final breaking wave-height.

The forces and loading resulting from shallow water breaking waves are one of the most important drivers in coastal engineering design and morphological change. The importance of accurately and precisely predicting breaking wave conditions cannot be overstated. Using a novel dataset of laboratory and field scale breaking wave conditions, this study assesses the performance of widely applied empirical relationships for breaking waves and uses newly available artificial neural networks and gene expression programming (GEP) numerical methods to develop an accurate and easily applied predictor of breaking conditions for coastal engineers and planners. A novel GEP model is developed and shown to: provide excellent predictive ability at all scales, greatly improve prediction compared with previous works at laboratory scale, and clearly identify the relevant importance of seafloor slope and the water depth to wavelength ratio.

Wave breaking processes inducing violent transition of wave shapes and internal kinematics are investigated through laboratory experiments using flow visualization techniques, and through numerical computations using the BIM (Boundary Integral Method) for non-breaking waves and the VOF method for breaking waves. The results show the importance of the plunging jet from wave crest into the front face, and clarify the relationships of the jet size to the characteristic values of the resultant large scale deterministic eddies, entrained air bubbles and wave height decay.

The paper presents a three-dimensional Corrected MPS (3D-CMPS) method for improvement of water surface tracking in breaking waves. The Corrected MPS (CMPS; Khayyer and Gotoh, 2008) has been extended to three dimensions and a 3D-CMPS method has been developed on the basis of the 3D-MPS method by Gotoh et al. (2005b). The improved performance of the 3D-CMPS method with respect to the 3D-MPS method has been shown by simulating a plunging breaking wave and resultant splash-up on a plane slope. Furthermore, the parallelization of 3D-CMPS method with two different solvers of simultaneous linear equations, namely, namely, the PICCG-RP (Parallelized ICCG with Renumbering Process; Iwashita and Shimasaki, 2000) and SCG (Scaled Conjugate Gradient; Jennings and Malik, 1978) techniques, has been performed to enhance the computational efficiency of the calculations. This study also applies a simple dynamic domain decomposition for an optimized load balancing among the processors.

When a planar water jet obliquely splashes on still water, a secondary jet is ejected from the front face of the initial jet and is extended to be so-called finger jets. The formation of finger jets and evolution into sprays were visualized using a fluorescent imaging technique. Two different mechanisms to form sprays have been found in this study: (A) The sprays ejected by a moving contact between the splashing jet and receiving water surface, and (B) fragmentation of the finger jets into the sprays due to surface tension effect. The sprays formed in (A), having small diameter and high velocity, precede those formed in (B). Size distributions of the both fingers and sprays are found to be approximated by log-normal distributions. Transport and dispersion of the finger jets and sprays are described by the three representative velocities of (i) the moving contacts, (ii) the wave front preceding the moving contact and (iii) the secondary jet.