Numerical Simulation of Wave Transformation Across the Surf Zone Over a Steep Bottom

2010 ◽  
Author(s):  
Tai-Wen Hsu ◽  
Ta-Yuan Lin ◽  
Hwung-Hweng Hwung ◽  
Yaron Toledo ◽  
Aron Roland
Keyword(s):  
Energy Dissipation ◽  
Wave Breaking ◽  
Surf Zone ◽  
Numerical Models ◽  
Dissipation Factor ◽  
Wave Transformation ◽  
Bottom Slope ◽  
Mild Slope Equation ◽  
Efficient Scheme ◽  
Sloping Beach

The combined effect of shoaling, breaking and energy dissipation on a sloping bottom was investigated. Based on the conservation principle of wave motion, a combined shoaling and bottom slope coefficient is included in the mild-slope equation (MSE) which is derived as a function of the bottom slope perturbed to the third-order. The model incorporates the nonlinear shoaling coefficient and energy dissipation factor due to wave breaking to improve the accuracy of the simulation prior to wave breaking and in the surf zone over a steep bottom. The evolution equation of the MSE is implemented in the numerical solution which provides an efficient scheme for describing wave transformation in a large coastal area. The model validity is verified by comparison to accurate numerical models, laboratory experiments and analytical solutions of waves travelling over a steep sloping beach.

scholarly journals Extended Elliptic Mild Slope Equation Incorporating the Nonlinear Shoaling Effect

2016 ◽  
Vol 23 (s1) ◽  
pp. 44-51 ◽  
Author(s):  
Qian-lu Xiao ◽  
Chun-hui Li ◽  
Xiao-yan Fu ◽  
Mei-ju Wang
Keyword(s):  
Dispersion Relation ◽  
Nonlinear Wave ◽  
Surf Zone ◽  
Wave Dispersion ◽  
Structure Design ◽  
Coastal Engineering ◽  
Wave Transformation ◽  
Flume Experiments ◽  
Mild Slope Equation ◽  
Wave Shoaling

Abstract The transformation during wave propagation is significantly important for the calculations of hydraulic and coastal engineering, as well as the sediment transport. The exact wave height deformation calculation on the coasts is essential to near-shore hydrodynamics research and the structure design of coastal engineering. According to the wave shoaling results gained from the elliptical cosine wave theory, the nonlinear wave dispersion relation is adopted to develop the expression of the corresponding nonlinear wave shoaling coefficient. Based on the extended elliptic mild slope equation, an efficient wave numerical model is presented in this paper for predicting wave deformation across the complex topography and the surf zone, incorporating the nonlinear wave dispersion relation, the nonlinear wave shoaling coefficient and other energy dissipation factors. Especially, the phenomenon of wave recovery and second breaking could be shown by the present model. The classical Berkhoff single elliptic topography wave tests, the sinusoidal varying topography experiment, and complex composite slopes wave flume experiments are applied to verify the accuracy of the calculation of wave heights. Compared with experimental data, good agreements are found upon single elliptical topography and one-dimensional beach profiles, including uniform slope and step-type profiles. The results indicate that the newly-developed nonlinear wave shoaling coefficient improves the calculated accuracy of wave transformation in the surf zone efficiently, and the wave breaking is the key factor affecting the wave characteristics and need to be considered in the nearshore wave simulations.

Simulation of Water Wave Transformation Using Higher Order Mild-Slope Equation

2009 ◽  
Author(s):  
Tai-Wen Hsu ◽  
Ta-Yuan Lin ◽  
Kuan-Yu Hsiao ◽  
Shiao-Yin Chen
Keyword(s):  
Multiple Scale ◽  
Higher Order ◽  
Wave Transformation ◽  
Radiation Boundary Conditions ◽  
Depth Function ◽  
Mild Slope Equation ◽  
Scale Perturbation ◽  
Radiation Boundary ◽  
Wave Nonlinearity ◽  
Sloping Beach

A higher-order mild-slope equation (HOMSE) was developed using classical Galerkin method in which the depth function is expanded to the third-order. Wave nonlinearity and bottom slope parameters are involved in the depth function solved on the bases of the multiple-scale perturbation method. The equation is solved subject to the radiation boundary conditions by means of the procedure of parabolic formulation. Good agreement between numerical results and experimental data has been observed for wave propagation over a submerged obstacle and a sloping beach.

Modified Extended Hyperbolic Mild-Slope Equations

2014 ◽  
Vol 522-524 ◽  
pp. 995-999
Author(s):  
Hua Chen Pan ◽  
Zhi Guang Zhang
Keyword(s):  
Wave Propagation ◽  
Energy Dissipation ◽  
Wave Breaking ◽  
Nonlinear Dispersion ◽  
Modifying Factors ◽  
Nonlinear Dispersion Relation ◽  
Mild Slope Equation ◽  
Breaking Mechanism ◽  
Wind Input ◽  
Rapidly Varying Topography

A form of hyperbolic mild-slope equations extended to account for rapidly varying topography, nonlinear dispersion relation, wind input and energy dissipation during the process of wave propagation, has been derived from the mild-slope equation modified first in this paper. With the inclusion of the input of wind energy, the resultant model can be applied in some areas where the effect of wind could not be neglected. The wave-breaking mechanism which will cause energy dissipation remarkably, as well as the bottom friction, is introduced and discussed during this derivation. Since the modifying factors have taken plenty of aspects into consideration, the extended equations hold enlarged application and increased accuracy.

Research and Analysis on the Wave Transformation and Irregular Wave Breaking Criterion on the Shore

2016 ◽  
Vol 858 ◽  
pp. 354-358
Author(s):  
Tao You ◽  
Li Ping Zhao ◽  
Zheng Xiao ◽  
Lun Chao Huang ◽  
Xiao Rui Han
Keyword(s):  
Theoretical Model ◽  
Wave Height ◽  
Wave Breaking ◽  
Surf Zone ◽  
Breaking Waves ◽  
Wave Transformation ◽  
Breaking Wave ◽  
Height Distribution ◽  
Flume Experiments ◽  
Irregular Wave

Within the surf zone which is the region extending from the seaward boundary of wave breaking to the limit of wave uprush, breaking waves are the dominant hydrodynamics acting as the key role for sediment transport and beach profile change. Breaking waves exhibit various patterns, principally depending on the incident wave steepness and the beach slope. Based on the equations of conservation of mass, momentum and energy, a theoretical model for wave transformation in and outside the surf zone was obtained, which is used to calculate the wave shoaling, wave set-up and set down and wave height distributions in and outside the surf zone. The analysis and comparison were made about the breaking point location and the wave height variation caused by the wave breaking and the bottom friction, and about the wave breaking criterion under regular and irregular breaking waves. Flume experiments relating to the regular and irregular breaking wave height distribution across the surf zone were conducted to verify the theoretical model. The agreement is good between the theoretical and experimental results.

scholarly journals Second-Order Time-Dependent Mild-Slope Equation for Wave Transformation

2014 ◽  
Vol 2014 ◽  
pp. 1-15
Author(s):  
Ching-Piao Tsai ◽  
Hong-Bin Chen ◽  
John R. C. Hsu
Keyword(s):  
Wave Equation ◽  
Wave Field ◽  
Surf Zone ◽  
Linear Time ◽  
Second Order ◽  
Time Dependent ◽  
Wave Transformation ◽  
Stokes Wave ◽  
Perturbation Scheme ◽  
Mild Slope Equation

This study is to propose a wave model with both wave dispersivity and nonlinearity for the wave field without water depth restriction. A narrow-banded sea state centred around a certain dominant wave frequency is considered for applications in coastal engineering. A system of fully nonlinear governing equations is first derived by depth integration of the incompressible Navier-Stokes equation in conservative form. A set of second-order nonlinear time-dependent mild-slope equations is then developed by a perturbation scheme. The present nonlinear equations can be simplified to the linear time-dependent mild-slope equation, nonlinear long wave equation, and traditional Boussinesq wave equation, respectively. A finite volume method with the fourth-order Adams-Moulton predictor-corrector numerical scheme is adopted to directly compute the wave transformation. The validity of the present model is demonstrated by the simulation of the Stokes wave, cnoidal wave, and solitary wave on uniform depth, nonlinear wave shoaling on a sloping beach, and wave propagation over an elliptic shoal. The nearshore wave transformation across the surf zone is simulated for 1D wave on a uniform slope and on a composite bar profile and 2D wave field around a jetty. These computed wave height distributions show very good agreement with the experimental results available.

scholarly journals SERRE GREEN-NAGHDI MODELLING OF WAVE TRANSFORMATION BREAKING AND RUN-UP USING A HIGH-ORDER FINITE-VOLUME FINITE-DIFFERENCE SCHEME

2011 ◽  
Vol 1 (32) ◽  
pp. 13 ◽  
Author(s):  
Marion Tissier ◽  
Philippe Bonneton ◽  
Fabien Marche ◽  
Florent Chazel ◽  
David Lannes
Keyword(s):  
Energy Dissipation ◽  
Finite Difference ◽  
Finite Volume ◽  
Wave Breaking ◽  
Ad Hoc ◽  
Laboratory Data ◽  
Breaking Waves ◽  
Wave Transformation ◽  
Finite Volume Schemes ◽  
Boussinesq Model

In this paper, a fully nonlinear Boussinesq model is presented and applied to the description of breaking waves and shoreline motions. It is based on Serre Green-Naghdi equations, solved using a time-splitting approach separating hyperbolic and dispersive parts of the equations. The hyperbolic part of the equations is solved using Finite-Volume schemes, whereas dispersive terms are solved using a Finite-Difference method. The idea is to switch locally in space and time to NSWE by skipping the dispersive step when the wave is ready to break, so as the energy dissipation due to wave breaking is predicted by the shock theory. This approach allows wave breaking to be handled naturally, without any ad-hoc parameterization for the energy dissipation. Extensive validations of the method are presented using laboratory data.

scholarly journals FULLY NONLINEAR BOUSSINESQ-TYPE MODELLING OF INFRAGRAVITY WAVE TRANSFORMATION OVER A LOW-SLOPING BEACH

2012 ◽  
Vol 1 (33) ◽  
pp. 28 ◽  
Author(s):  
Marion Tissier ◽  
Philippe Bonneton ◽  
Gerben Ruessink ◽  
Fabien Marche ◽  
Florent Chazel ◽  
...  
Keyword(s):  
Surf Zone ◽  
Field Studies ◽  
Wave Transformation ◽  
Type Model ◽  
Infragravity Waves ◽  
Fully Nonlinear ◽  
Complex Interactions ◽  
Long Wave ◽  
Sloping Beach ◽  
Infragravity Wave

Recent field studies over low sloping beaches have shown that infragravity waves could dissipate a significant part of their energy in the inner surf zone. This phenomenon and the associated short- and long-wave transformations are not well-understood. In this paper, we assess the ability of the fully nonlinear Boussinesq-type model introduced in Bonneton et al. (2011) to reproduce short and long wave transformation in a case involving a strong infragravity wave dissipation close to the shoreline. This validation study, based on van Dongeren et al. (2008)’s laboratory experiments, suggests that the model is able to predict infragravity wave breaking as well as the complex interactions between short and long waves in the surf zone.

Analysis of Numerical Oscillation Problems in a Non Linear Time Dependent Mild Slope Model and First Developments for the Implementation of Wave Breaking

2008 ◽  
Author(s):  
Ana Catarina Zo´zimo ◽  
Conceic¸a˜o Fortes
Keyword(s):  
Energy Dissipation ◽  
Wave Breaking ◽  
Linear Time ◽  
Momentum Equation ◽  
Time Dependent ◽  
Theoretical Formulation ◽  
Dissipative Term ◽  
Mild Slope Equation ◽  
Non Linear ◽  
Work Done

In this paper, a description of the numerical model NMLSE is presented. This model solves the time dependent non linear mild slope equation, without including energy dissipation due to wave breaking [1]. Some modifications are made in the boundary conditions of the original version of the model in order to overcome the numerical oscillation problems detected in the work done by [2]. To evaluate the effectiveness of the new versions of the model, they are applied to test cases of the bibliography and to a bar-trough profile beach for which there are data from physical model tests. The basic theoretical formulation of a new momentum equation that includes energy dissipation due to wave breaking is also presented. The energy dissipation due to wave breaking is included through the addition of a dissipative term based in the eddy viscosity concept.

Wave Height Variation Across Surf Zone of Bar Type Profile

2009 ◽  
Author(s):  
Tai-Wen Hsu ◽  
Kun-Sian Lai
Keyword(s):  
Energy Dissipation ◽  
Wave Height ◽  
Analytical Solutions ◽  
Wave Energy ◽  
Hydraulic Jump ◽  
Surf Zone ◽  
Wave Transformation ◽  
Height Variation ◽  
Wave Energy Dissipation ◽  
Theoretical Results

Analytical solutions for wave height decay due to shoaling and breaking on a bar type profile are presented. A macroscopic analogy between an idealized surf zone and a hydraulic jump are incorporated in the theory to account for wave transformation and energy dissipation in the surf zone. The theoretical results are fairly compared with laboratory observations. Key parameters that influence wave energy dissipation in the surf zone are investigated.

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