Wave propagation modeling in coastal engineering

Coastal Engineering, 2013

The energy dissipation in the surf-zone due to wave breaking is inherently accounted for in shock-capturing non-hydrostatic wave models, but this requires high vertical resolutions. To allow coarse vertical resolutions a hydrostatic front approximation is suggested. It assumes a hydrostatic pressure distribution at the front of a breaking wave which ensures that the wave front develops a vertical face. Based on the analogy between a hydraulic jump and a turbulent bore, energy dissipation is accounted for by ensuring conservation of mass and momentum. Results are compared with observations of random, uni-directional waves in wave flumes, and to observations of short-crested waves in a wave basin. These demonstrate that the resulting model can resolve the relevant near-shore wave processes in a short-crested wave-field, including wave breaking and wave-driven horizontal circulations.

2008

Oceans and seas, which cover a large percentage of the Earth, interact with the atmosphere at their upper boundary. The generation, growth and breaking of wind waves are the most prominent physical processes that occur at water surface. In this study the transformation of waves groups in a medium water of coastal zone towards breaking point is investigated in two dimensional case. The governing equations are Navier-Stokes, continuity and Fractional VOF function equations. The fluid flow is assumed to be viscous and incompressible, and the turbulence effect has been considered in wave evolution using a two equation k-ε model. The DDAR-VOF method which is a kind of SLIC method defined by Moradi [Moradi Larmaei M, Simulation of waves groups propagation and breaking in medium water depth using VOF method. M.Sc. thesis (Distinct). Iran: Amirkabir University of Technology; 2006] is used by employing a finite volume method based on the PISO algorithm. To validate the numerical model, different tests such as led-driven cavity, a simple translation test, rotation test, dam-break, turbulent pattern and plunging breaking are performed. These tests show that this model is a powerful and reliable tool to simulate free water surface in wave motion with breaking process. The numerical results obtained indicate the existence of the waves group inducing set-down in the form of long wave in a medium water depth due to passage of high waves group. Comparison of the results with the experimental data shows that the current modified model is able to predict this complicated phenomenon accurately.

The correct representation of depth-induced wave breaking is important for understanding coastal morphology and for design andmanagement in the coastal zone. Although numerous studies have demonstrated the applicability of a constant scaling of the Battjes and Janssen (1978) dissipationmodel for depth-induced breaking, recent studies have shown its inability to sufficiently reproduce wave dissipation over complex field cases. In the present study, we contrast the application of such a constant scaling to two alternative wave breaking parameterizationswith a variable scaling based on either thewave nonlinearity (the φparameterization) oronbothbottomslope and normalizedwavelength supplementedwithwave directionality (the β−kd parameterization).We consider three field data sets characteristic of a simple beach-bar profile, a bay partially protected by a shoal and a complex intertidal region.We demonstrate that in these cases the β−kd parameterization provides a better alternative to the use of a constant scaling or the φ parameterization. To illustrate the operational consequences, we up-scale the conditions over the case of the intertidal region to correspond to design conditions for the Dutch coast (storm conditions with a 4000 year return period). Under these extreme conditions, for locally generated waves both the β−kd and φ parameterizations predict qualitatively similar increased significant wave heights but the β−kd parameterization increased the waves twice as much as the φ parameterization. Under other conditions, when non-locally generated waves (swell) dissipates over a gently sloping bottom, the β−kd parameterization predicts lower significant wave heights compared to either the constant scaling or φ parameterization.

Coastal Engineering, 2007

A deterministic combination of numerical and physical models for coastal waves is developed. In the combined model, a Boussinesq model MIKE 21 BW is applied for the numerical wave computations. A piston-type 2D or 3D wavemaker and the associated control system with active wave absorption provides the interface between the numerical and physical models. The link between numerical and physical models is given by an ad hoc unified wave generation theory which is devised in the study. This wave generation theory accounts for linear dispersion and shallow water non-linearity. Local wave phenomena (evanescent modes) near the wavemaker are taken into account. With this approach, the data transfer between the two models is thus on a deterministic level with detailed wave information transmitted along the wavemaker.

Journal of Geophysical Research, 1999

A third-generation numerical wave model to compute random, short-crested waves in coastal regions with shallow water and ambient currents (Simulating Waves Nearshore (SWAN)) has been developed, implemented, and validated. The model is based on a Eulerian formulation of the discrete spectral balance of action density that accounts for refractive propagation over arbitrary bathymetry and current fields. It is driven by boundary conditions and local winds. As in other third-generation wave models, the processes of wind generation, whitecapping, quadruplet wave-wave interactions, and bottom dissipation are represented explicitly. In SWAN, triad wave-wave interactions and depth-induced wave breaking are added. In contrast to other third-generation wave models, the numerical propagation scheme is implicit, which implies that the computations are more economic in shallow water. The model results agree well with analytical solutions, laboratory observations, and (generalized) field observations.

Journal of Marine Science and Technology

The objective of the present work is to illustrate the performances of the numerical wave models in ocean and coastal environment. Third generation wave models are considered nowadays the most appropriate for such task. These are full spectral models based on the integration on the wave energy (or alternatively wave action) balance equation. In order to cover more aspects related with the modelling process hindcast, nowcast and forecast schemes are discussed and illustrated along six case studies. The major model used was SWAN (acronym for Simulating Waves Nearshore) which is a very flexible model that can be applied in a wide range of coastal applications being effective from high resolution coastal areas up to quasi oceanic scales. In both hindcasts and forecasts the wave forcing was provided by generation models (WAM and WW3), while in nowcast schemes buoy data were used. Various coastal environments that are rather different from the point of view of the bathymetric features and of the characteristics of the environmental matrix were considered. These are the Portuguese continental nearshore with higher resolution sub domains, Madeira Archipelago, the nearshore of Sardinia Island in the Mediterranean Sea and the Black Sea. A general conclusion of this work would be that, despite some limitations, the wave models provide an effective framework in predicting wave conditions in ocean and coastal environment.

Ocean Modelling, 2016

Field-scale modeling of wave-breaking-induced turbulence and mean circulation is still challenging. Although Boussinesq-type models have been successfully used to study field-scale wave transformation and breaking-driven circulation, they cannot provide turbulence or the vertical structure of velocity field. In addition, the applicability of such models is limited to shallow water. In Part 1 (Derakhti et al., 2016b) of this study, we showed that the non-hydrostatic σ-coordinate RANS model NHWAVE, as described by Derakhti et al. (2016a), accurately predicts organized wave motions and total wave-breaking-induced energy dissipation from deep water up to the swash zone using a few vertical σ-layers. In this paper, our goal is to examine what level of detail of wave-breaking-induced turbulence and mean circulation, both in depth-and steepness-limited breaking waves, can be reproduced by NHWAVE. Further, effects of modeled turbulent eddy viscosity on the pre

Coastal Engineering, 2009

A two-dimensional numerical model of nearshore waves, currents, and sediment transport was developed. The multi-directional random wave transformation model formulated by Mase [Mase, H., 2001. Multi-directional random wave transformation model based on energy balance equation. Coastal Engineering Journal 43 (4) (2001) 317] based on an energy balance equation was employed with an improved description of the energy dissipation due to breaking. In order to describe surface roller effects on the momentum transport, an energy balance equation for the roller was included following Dally-Brown [Dally, W. R., Brown, C. A., 1995. A modeling investigation of the breaking wave roller with application to cross-shore currents. Journal of Geophysical Research 100(C12), 24873]. Nearshore currents and mean water elevation were modeled using the continuity equation together with the depth-averaged momentum equations. Sediment transport rates in the offshore and surf zone were computed using the sediment transport formulation proposed by Camenen-Larson

Applied Mathematical Modelling, 2021

The present paper aims to incorporate nonlinear amplitude dispersion effects in parabolic and hyperbolic approximation models. First, an explicit and analytical method for considering nonlinearities in parabolic approximation models is investigated. This method follows the concept of calculating spatially and temporally varying wave phase celerities within the simulation. The nonlinear dispersion relation to be applied is dependent on the local Ursell number and wave steepness, in relation to valid regions of analytical wave theories. Furthermore, nonlinearities are introduced in a hyperbolic approximation model by proposing a novel method which combines a parabolic and a hyperbolic model without a significant loss in accuracy, leading to a substantial reduction in the required simulation time. This is achieved by inputting initial boundary conditions into the hyperbolic model based on the output of the parabolic model, which is used for an initial calculation of the spatial distribution of nonlinear dispersion effects over the entire numerical domain. Numerical results were compared with measurements obtained via demanding experimental setups and illustrated satisfactory performance of the models. These concerted nonlinear models offer ease in implementation, short simulation times, and accurate results while incorporating the majority of wave transformation processes including shoaling, refraction, diffraction, reflection, bottom friction and depth-induced wave breaking.

Coastal Engineering Proceedings, 2014

With the objective of modeling coastal wave dynamics taking into account nonlinear and dispersive effects, an accurate nonlinear potential flow model is studied. The model is based on the time evolution of two surface quantities: the free surface position and the free surface velocity potential (Zakharov, 1968). The spectral approach of Tian and Sato (2008) is used to resolve vertically the velocity potential in the whole domain, by decomposing the potential using the orthogonal basis of Chebyshev polynomials. The model mathematical theory and numerical development are described, and the model is then validated with the application of three 1DH test cases: (1) propagation of nonlinear regular wave over a submerged bar, (2) propagation of nonlinear irregular waves over a barred beach, and (3) wave generation and propagation after an abrupt deformation of the bottom boundary. These three test cases results agree well with the reference solutions, confirming the model's ability to simulate accurately nonlinear and dispersive waves.

Journal of Physics: Conference Series, 2019

This study simulates shallow water waves using the Navier-Stokes equation. This simulation uses the MatLab application, especially Quickersim with 2-dimensional output. Mesh in simulation is made using Gmsh. Research about shallow water has an essential role in studying the characteristics of ocean waves. The depth of the sea influences this characteristic. Data obtained from this simulation is in the wave height and velocity positions at any time. The limitations in the data collected are not comparable with the experimental results because there are no experimental Navier-Stokes simulations, but these simulation results have shown the phenomenon of seawater movement. In future work, the results of this study can be used to analyse its application in tsunami waves.

1997

Physics of Fluids, 2017

The present work represents the research continuation on the semi-integrated method proposed by Antuono and Brocchini 1 , this being composed by a subset of depthaveraged equations (like the popular Boussinesq-like models) and by a Poisson equation that accounts for the vertical dynamics. On the theoretical side, the subset of depth-averaged equations has been reshaped in a conservative-like form with inherent advantages when applied at the discrete level. On the numerical side, the Poisson equation has been inspected in both formulations proposed in Antuono and Brocchini 1 : a Poisson equation for the vertical component of the velocity (formulation A) and a Poisson equation for a specific depth semi-averaged variable, Υ (formulation B). The studies showed that formulation A is prone to instabilities as the problem nonlinearities increase. On the contrary, formulation B allows for an accurate and robust numerical implementation. Some relevant test cases derived from the scientific literature on Boussinesq-type models-i.e. solitary and Stokes wave analytical solutions for linear dispersion and nonlinear evolution and experimental data for shoaling properties-have been used to assess the proposed solution strategy and to highlight its features and characteristics. The method proved to predict reliable results for wave solutions in shallow to intermediate waters, both in terms of semi-averaged variables and conservation properties.

A third-generation spectral wave model (Simulating Waves Nearshore (SWAN)) for small-scale, coastal regions with shallow water, (barrier) islands, tidal flats, local wind, and ambient currents is verified in stationary mode with measurements in five real field cases. These verification cases represent an increasing complexity in twodimensional bathymetry and added presence of currents. In the most complex of these cases, the waves propagate through a tidal gap between two barrier islands into a bathymetry of channels and shoals with tidal currents where the waves are regenerated by a local wind. The wave fields were highly variable with up to 3 orders of magnitude difference in energy scale in individual cases. The model accounts for shoaling, refraction, generation by wind, whitecapping, triad and quadruplet wave-wave interactions, and bottom and depth-induced wave breaking. The effect of alternative formulations of these processes is shown. In all cases a relatively large number of wave observations is available, including observations of wave directions. The average rms error in the computed significant wave height and mean wave period is 0.30 m and 0.7 s, respectively, which is 10% of the incident values for both.