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.

Infragravity waves induced by short-wave groups

1993 ◽  
Vol 247 ◽  
pp. 551-588 ◽  
Author(s):  
Hemming A. Schäffer
Keyword(s):  
Surf Zone ◽  
Break Point ◽  
Short Wave ◽  
Radiation Stress ◽  
Wave Groups ◽  
Infragravity Waves ◽  
Short Waves ◽  
Long Wave ◽  
Integrated Conservation ◽  
Infragravity Wave

A theoretical model for infragravity waves generated by incident short-wave groups is developed. Both normal and oblique short-wave incidence is considered. The depth-integrated conservation equations for mass and momentum averaged over a short-wave period are equivalent to the nonlinear shallow-water equations with a forcing term. In linearized form these equations combine to a second-order long-wave equation including forcing, and this is the equation we solve. The forcing term is expressed in terms of the short-wave radiation stress, and the modelling of these short waves in regard to their breaking and dynamic surf zone behaviour is essential. The model takes into account the time-varying position of the initial break point as well as a (partial) transmission of grouping into the surf zone. The former produces a dynamic set-up, while the latter is equivalent to the short-wave forcing that takes place outside the surf zone. These two effects have a mutual dependence which is modelled by a parameter K, and their relative strength is estimated. Before the waves break, the standard assumption of energy conservation leads to a variation of the radiation stress, which causes a bound, long wave, and the shoaling bottom results in a modification of the solution known for constant depth. The respective effects of this incident bound, long wave and of oscillations of the break-point position are shown to be of the same order of magnitude, and they oppose each other to some extent. The transfer of energy from the short waves to waves at infragravity frequencies is analysed using the depth-integrated conservation equation of energy. For the case of normally incident groups a semi-analytical steady-state solution for the infragravity wave motion is given for a plane beach and small primary-wave modulations. Examples of the resulting surface elevation as well as the corresponding particle velocity and mean infragravity-wave energy flux are presented. Also the sensitivity to the variation of input parameters is analysed. The model results are compared with laboratory experiments from the literature. The qualitative agreement is good, but quantitatively the model overestimates the infragravity wave activity. This can, in part, be attributed to the neglect of frictional effects.

scholarly journals UNDULAR BORE DEVELOPMENT OVER A LABORATORY FRINGING REEF

2018 ◽  
pp. 53 ◽  
Author(s):  
Marion Tissier ◽  
Jochem Dekkers ◽  
Ad Reniers ◽  
Stuart Pearson ◽  
Ap Van Dongeren
Keyword(s):  
Coral Reefs ◽  
Wave Field ◽  
Reef Flat ◽  
Wave Transformation ◽  
Undular Bore ◽  
Fringing Reef ◽  
Long Wave ◽  
Reef Type ◽  
Run Up ◽  
Infragravity Wave

Several studies have reported the development of undular bores over fringing coral reefs (e.g, Gallagher, 1976; Nwogu and Demirbilek, 2010) but the importance of this phenomenon for reef hydrodynamics has never been studied. Yet, the transformation of a long wave (e.g., swell or infragravity wave) into an undular bore leads to significant modifications of the wave field. The formation of undulations is for example associated to a significant increase of the leading bore height. Moreover, if the undulations have enough time to develop (i.e. if the reef flat is wide enough), the initial long wave will ultimately split into a series of solitons (e.g., Grue et al., 2008). All this is likely to affect wave run-up. As reeffronted coastlines are particularly vulnerable to flooding, a good understanding of long wave transformation over the reef flat, including their possible transformation into undular bores, is crucial. In this study, we investigate undular bore development over reef-type profiles based on a series of laboratory experiments. More specifically, we aim to characterize the conditions under which undular bores develop, and analyse how their development affect the hydrodynamics at the toe of the reef-lined beach and the resulting wave run-up.

scholarly journals TRANSFORMATION, BREAKING AND RUN-UP OF A LONG WAVE OF FINITE HEIGHT

2011 ◽  
Vol 1 (8) ◽  
pp. 5
Author(s):  
Tsutomu Kishi
Keyword(s):  
Approximate Solutions ◽  
Wave Transformation ◽  
Beach Profile ◽  
Parabolic Profile ◽  
Long Wave ◽  
Short Period ◽  
Run Up ◽  
Sloping Beach ◽  
Linear Shallow Water Theory ◽  
Considerable Deformation

On studying the transformation, breaking and run-up of a relatively steep wave of a short period, the theory for waves of permanent type has given us many fruitful results. However, the theory gradually loses its applicability as a wave becomes flat, since a considerable deformation of the wave profile is inevitable in its propagation. In § 1, a discussion concerning the transformation of a long wave in a channel of variable section is presented based on the non-linear shallow water theory. Approximate solutions obtained by G. B. Whitham's method (1958) are shown. Further, some brief considerations are given to the effects of bottom friction on wave transformation. In § 2, breaking of a long wave is discussed. Breakings on a uniformly sloping beach and on a beach of parabolic profile are considered and the effects of beach profile on breaking are clarified. Finally in § 3, experimental results on wave run-up over l/30 slope are described in comparing with the Kaplan's results.

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.

A particle image velocimetry investigation on laboratory surf-zone breaking waves over a sloping beach

2007 ◽  
Vol 588 ◽  
pp. 353-397 ◽  
Author(s):  
O. KIMMOUN ◽  
H. BRANGER
Keyword(s):  
Particle Image Velocimetry ◽  
Velocity Field ◽  
Water Waves ◽  
Particle Image ◽  
Surf Zone ◽  
Wave Transformation ◽  
Time Step ◽  
Complete Space ◽  
Image Velocimetry ◽  
Sloping Beach

Particle image velocimetry (PIV) measurements were performed in a wave tank under water waves propagating and breaking on a 1/15 sloping beach. The wave transformation occurred in the surf zone over a large domain covering several wavelengths from incipient breaking to swash zone beyond the shoreline. PIV spatial interrogation windows must be small enough to obtain accurate velocities, and one window covers only a small part of the domain. To overcome this problem and to measure the instantaneous velocity field over the whole surf zone area, we have split the full field into 14 overlapping smaller windows of the same size. Local measurements were synchronized with each other using pulsed TTL triggers and wave gauge data. The full velocity field was then reconstructed at every time step by gathering the 14 PIV fields. We then measured the complete space–time evolution of the velocity field over the whole surf zone. We determined also the ensemble-period-average and phase-average components of the flow with their associated fluctuating parts. We used the PIV images and velocity measurements to estimate the void fraction in each point of the surf zone. Special attention was given to the calculation of the spatial derivatives in order to obtain relevant information on vorticity and on the physical terms that appear in the fluctuating kinetic energy transport equation.

scholarly journals NUMERICAL COMPUTATION OF INFRAGRAVITY WAVE DYNAMICS AND VELOCITY PROFILES USING A FULLY NONLINEAR BOUSSINESQ MODEL

2011 ◽  
Vol 1 (32) ◽  
pp. 48 ◽  
Author(s):  
Rodrigo Cienfuegos ◽  
L. Duarte ◽  
L. Suarez ◽  
P. A. Catalán
Keyword(s):  
Wave Propagation ◽  
Complex Dynamics ◽  
Velocity Profiles ◽  
Wave Generation ◽  
Type Model ◽  
Random Wave ◽  
Boussinesq Model ◽  
Frequency Wave ◽  
Fully Nonlinear ◽  
Infragravity Wave

We present experimental and numerical analysis of nonlinear processes responsible for generating infragravity waves in the nearshore. We provide new experimental data on random wave propagation and associated velocity profiles in the shoaling and surf zones of a very mild slope beach. We analyze low frequency wave generation mechanisms and dynamics along the beach and examine in detail the ability of the fully nonlinear Boussinesq- type model SERR1D (Cienfuegos et al., 2010) to reproduce the complex dynamics of high frequency wave propagation and energy transfer mechanisms that enhance infragravity wave generation in the laboratory.

Infragravity Waves Induced by Short-Wave Groups in Coastal Regions Characterized by General Bottom Topography

2011 ◽  
Author(s):  
K. A. Belibassakis
Keyword(s):  
Water Waves ◽  
Wave Equations ◽  
Present Model ◽  
Surf Zone ◽  
Bottom Topography ◽  
Short Wave ◽  
Coastal Regions ◽  
Wave Groups ◽  
Infragravity Waves ◽  
Long Wave

The free long-wave generation by short-wave groups over a sloping bottom is studied both experimentally and theoretically by various authors showing important results concerning the modelling of energy transfer from the short waves to subharmonics. In the present work, the coupled-mode model developed by Athanassoulis & Belibassakis (1999) for the propagation of water waves over variable bathymetry regions, as generalized to include dissipation due to bottom friction and breaking effects, is applied to calculate the spatial evolution of short-wave groups propagating over a shoaling area, characterized by general bottom topography. Following Scha¨ffer (1993), the present model is appropriately modified in the surf zone in order to destroy the short-wave modulation, keeping the wave height decay in proportion to the local water-depth, and is then used to calculate radiation stresses associated with shoaling and breaking of short-wave groups in the area of general bathymetry and in the surf zone. Subsequently, the system of long wave equations, corresponding to zero (set-down/set-up) and first few harmonics, forced by the radiation stresses, is numerically solved. Results are presented showing that the present model provides reasonable predictions, supporting the study of infragravity waves induced by shortwave groups and their effects on harbors and mooring systems of large vessel operating in nearshore/coastal regions.

Evaluation of a Model for Estimating Infragravity Waves in Shallow Water: Accuracy and Suitability for Long-Term Climatologies

2009 ◽  
Author(s):  
Matthijs Bijl ◽  
Ad Reniers ◽  
Kevin Ewans ◽  
Stephen Masterton ◽  
Rene´ Huijsmans
Keyword(s):  
Shallow Water ◽  
Surf Zone ◽  
The United States ◽  
Design Criteria ◽  
Data Set ◽  
Infragravity Waves ◽  
North West ◽  
Wave Heights ◽  
Infragravity Wave

With interest in developing shallow-water facilities on the increase, primarily for offloading LNG, there is also growing interest in infragravity waves. In particular, it is recognized that infragravity waves can have an important influence on the motions of tankers in shallow-water regions exposed to the open ocean, and therefore they need to be considered in the design and operation of the moorings and offloading facilities. Accordingly, there is a need to model infragravity waves both for design calculations and to be able to estimate the design criteria themselves. This paper is concerned with the later — setting infragravity wave design criteria, or more precisely on details involved in establishing an appropriate infragravity wave database from which design criteria can be estimated. The focus is on the accuracy of using the 1D linear Surf Beat model (IDSB) for estimating nearshore infragravity wave heights. The study has focused on field measurements made by U.S. Corp of Army Engineers Field Research Facility location at Duck on the east coast of the United States, and another location at Baja on the north west coast of Mexico. At the Duck location, the study involved data recorded in shallow water (8 meters water depth) with a pressure transducer array, while at the Baja location, data from a directional Waverider buoy with GPS are used. The “short wave” directional spectra from the measured data are used as input to the IDSB model, to compute the total infragravity response generated by the transformation of the grouped short waves through the surf zone including bound long waves, leaky waves and edge waves. The computed root mean square infragravity wave heights have been compared with measured infragravity waves at the respective sites, and assessment has been made of the accuracy of the predictions. The computed results show good agreement with the measured infragravity waves and provide confidence that the IDSB is a suitable tool for developing a long-term infragravity data set for developing design criteria.

Nonlinear Effect on Wave-Structure Interaction

2012 ◽  
Author(s):  
J. M. Chen ◽  
D. Liang
Keyword(s):  
Free Surface ◽  
Nonlinear Effect ◽  
Surf Zone ◽  
Wave Structure ◽  
Diffraction Theory ◽  
Structure Design ◽  
Wave Transformation ◽  
Type Model ◽  
Surface Motion ◽  
And Performance

Accurate prediction on the behaviour of the nonlinear waves in a coastal environment is vital to the safe design and performance of coastal defence. This paper is concerned with the description of tsunami wave-island interaction, and includes both linear and nonlinear modelling of the maximum free surface motion arising within distorted flow field. A deterministic nonlinear effect on the predicted maximum runup is examined using a Boussinesq-type model. Statistics of the predicted maximum leading-crest motion are obtained and discussed in light of linear diffraction theory. The results show that the predicted maximum runup and free surface motion by the quaternary-islands is affected by nonlinear wave transformation. The numerical simulations suggest that the present model describes the wave field very accurately even for extreme events. The present study provides a critical insight into the free surface elevation maxima at surf zone, thus safeguarding the structure design.

scholarly journals A STUDY ON WAVE TRANSFORMATION INSIDE SURF ZONE

1966 ◽  
Vol 1 (10) ◽  
pp. 14 ◽  
Author(s):  
Kiyoshi Horikawa ◽  
Chin-Tong Kuo
Keyword(s):  
Experimental Data ◽  
Wave Height ◽  
Surf Zone ◽  
The Other ◽  
Wave Transformation ◽  
Analytical Treatment ◽  
Numerous Data ◽  
Wave Height Attenuation ◽  
Sloping Beach ◽  
Horizontal Bottom

The wave transformation inside surf zone is treated analytically m this paper under the several appropriate assumptions. The theoretical curves computed numerically have a consistant agreement with the experimental data in the case of wave transformation on a horizontal bottom. On the other hand, m the case of wave transformation on a uniformly sloping beach, the analytical treatment seems to be inadequate to clarify the actual phenomena. Besides them the numerous data on wave height attenuation and others are presented m the graphical forms.

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