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.

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.

Long wave generation by the shoaling and breaking of transient wave groups on a beach

2006 ◽  
Vol 462 (2070) ◽  
pp. 1853-1876 ◽  
Author(s):  
T.E Baldock
Keyword(s):  
Shallow Water ◽  
Water Waves ◽  
Surf Zone ◽  
Laboratory Data ◽  
Short Wave ◽  
Long Waves ◽  
Transient Wave ◽  
Wave Groups ◽  
Spatial Gradients ◽  
Long Wave

This paper presents new laboratory data on the generation of long waves by the shoaling and breaking of transient-focused short-wave groups. Direct offshore radiation of long waves from the breakpoint is shown experimentally for the first time. High spatial resolution enables identification of the relationship between the spatial gradients of the short-wave envelope and the long-wave surface. This relationship is consistent with radiation stress theory even well inside the surf zone and appears as a result of the strong nonlinear forcing associated with the transient group. In shallow water, the change in depth across the group leads to asymmetry in the forcing which generates significant dynamic setup in front of the group during shoaling. Strong amplification of the incident dynamic setup occurs after short-wave breaking. The data show the radiation of a transient long wave dominated by a pulse of positive elevation, preceded and followed by weaker trailing waves with negative elevation. The instantaneous cross-shore structure of the long wave shows the mechanics of the reflection process and the formation of a transient node in the inner surf zone. The wave run-up and relative amplitude of the radiated and incident long waves suggests significant modification of the incident bound wave in the inner surf zone and the dominance of long waves generated by the breaking process. It is proposed that these conditions occur when the primary short waves and bound wave are not shallow water waves at the breakpoint. A simple criterion is given to determine these conditions, which generally occur for the important case of storm waves.

On the modulation of water waves on shear flows

1976 ◽  
Vol 347 (1651) ◽  
pp. 537-546 ◽  
Keyword(s):  
Water Waves ◽  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Vries Equation ◽  
Harmonic Wave ◽  
Short Wave ◽  
Long Wave ◽  
Stokes Waves ◽  
The Stability ◽  
Wave Limit

The method of multiple scales is used to examine the slow modulation of a harmonic wave moving over the surface of a two dimensional channel. The flow is assumed inviscid and incompressible, but the basic flow takes the form of an arbitrary shear. The appropriate nonlinear Schrödinger equation is derived with coefficients that depend, in a complicated way, on the shear. It is shown that this equation agrees with previous work for the case of no shear; it also agrees in the long wave limit with the appropriate short wave limit of the Korteweg-de Vries equation, the shear being arbitrary. Finally, it is remarked that the stability of Stokes waves over any shear can be examined by using the results derived here.

scholarly journals SURF BEAT GENERATION ON A MILD-SLOPE BEACH

1988 ◽  
Vol 1 (21) ◽  
pp. 79 ◽  
Author(s):  
Hemming A. Schaffer ◽  
Ib A. Svendsen
Keyword(s):  
Surf Zone ◽  
Beat Generation ◽  
Radiation Stress ◽  
Inhomogeneous Wave ◽  
Wave Groups ◽  
Forcing Function ◽  
Long Wave ◽  
Inhomogeneous Wave Equation ◽  
Slope Beach ◽  
Resonant Generation

Two dimensional generation of surf beats by incident wave groups is examined theoretically. An inhomogeneous wave equation describes the amplitude of the surf beat wave. The forcing function is the modulation of the radiation stress. The short waves are amplitude modulated both outside and inside the surf zone causing the long wave generation to continue right to the shore line. Resonant generation as shallow water is approached is included. The analytical solution is evaluated numerically and shows a highly complicated amplitude variation of the surf beat depending on the parameters of the problem.

Free Long Wave – Short Wave Interaction in a Surf Zone

2001 ◽  
Author(s):  
T. J. O'Hare ◽  
T. E. Baldock ◽  
D. A. Huntley ◽  
P. A. D. Bird ◽  
G. N. Bullock
Keyword(s):  
Surf Zone ◽  
Wave Interaction ◽  
Short Wave ◽  
Long Wave

scholarly journals WAVE GROUPINESS AS A SOURCE OF NEARSHORE LONG WAVES

1986 ◽  
Vol 1 (20) ◽  
pp. 38 ◽  
Author(s):  
Jeffrey H. List
Keyword(s):  
Wave Amplitude ◽  
Cross Correlation ◽  
Surf Zone ◽  
Low Frequency ◽  
Long Waves ◽  
Progressive Wave ◽  
Wave Groups ◽  
Long Wave ◽  
Cross Correlation Analysis ◽  
Limited Usefulness

Data from a low energy swell-dominated surf zone are examined for indications that observed low frequency motions are simply group-forced bounded long waves. Time series of wave amplitude are compared to filtered long wave records through cross-spectral and cross-correlation analysis. These methods are found to have limited usefulness until long waves are separated into seaward and shoreward components. Then a clear picture of a rapidly shoaling bounded long wave emerges, with a minimum of nearly one fourth of the long wave amplitude being explainable by this type of motion close to shore. Through the zone in which waves were breaking, and incident wave amplitude variability decreased by 50%, the contribution from the bounded long wave continued to increase at a rate much greater than a simple shoaling effect. Also present are clear signs that this amplified bounded long wave is reflected from a position close to the shoreline, and is thus released from wave groups as a free, offshore-progressive wave.

scholarly journals Experimental study of particle trajectories below deep-water surface gravity wave groups

2019 ◽  
Vol 879 ◽  
pp. 168-186 ◽  
Author(s):  
T. S. van den Bremer ◽  
C. Whittaker ◽  
R. Calvert ◽  
A. Raby ◽  
P. H. Taylor
Keyword(s):  
Gravity Wave ◽  
Deep Water ◽  
Water Waves ◽  
Wave Equations ◽  
Stokes Drift ◽  
Surface Gravity ◽  
Return Flow ◽  
Surface Gravity Wave ◽  
Wave Groups ◽  
Wave Induced

Owing to the interplay between the forward Stokes drift and the backward wave-induced Eulerian return flow, Lagrangian particles underneath surface gravity wave groups can follow different trajectories depending on their initial depth below the surface. The motion of particles near the free surface is dominated by the waves and their Stokes drift, whereas particles at large depths follow horseshoe-shaped trajectories dominated by the Eulerian return flow. For unidirectional wave groups, a small net displacement in the direction of travel of the group results near the surface, and is accompanied by a net particle displacement in the opposite direction at depth. For deep-water waves, we study these trajectories experimentally by means of particle tracking velocimetry in a two-dimensional flume. In doing so, we provide visual illustration of Lagrangian trajectories under groups, including the contributions of both the Stokes drift and the Eulerian return flow to both the horizontal and the vertical Lagrangian displacements. We compare our experimental results to leading-order solutions of the irrotational water wave equations, finding good agreement.

scholarly journals Effect of Varying Bottom Topography on the Radiation of Water Waves by a Floating Rectangular Buoy

Fluids ◽  
2021 ◽  
Vol 6 (2) ◽  
pp. 59
Author(s):  
Kshma Trivedi ◽  
Santanu Koley
Keyword(s):  
Water Waves ◽  
Bottom Topography ◽  
Oscillation Amplitude ◽  
Added Mass ◽  
Short Wave ◽  
Wave Regime ◽  
Damping Coefficients ◽  
Oscillatory Pattern ◽  
Reverse Pattern ◽  
Incident Waves

In the present study, the effect of an undulated bottom topography on the radiation of water waves by a floating rectangular buoy is analyzed. Various physical quantities of interest such as the added mass and damping coefficients associated with the surge, heave, and pitch motions are analyzed for a variety of parameters associated with the incident waves and bottom undulations. The study reveals that the added mass and damping coefficients associated with the surge and pitch motions of the floating buoy vary in an oscillatory manner with the variation in wavenumber for a sinusoidally varying bottom topography. Moreover, the oscillation amplitude is higher around the primary Bragg value. Further, this oscillatory pattern and oscillation amplitude increase with an increase in the ripple amplitude and the number of ripples for a sinusoidally varying bottom. However, a reverse pattern is formed with an increase in the depth ratio. In the long-wave regime, the added mass and damping coefficient corresponding to the surge motion become higher for a protrusion-type bed profile and lower for a depression-type bed profile. However, a reverse pattern is observed in the intermediate- and short-wave regimes.

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.

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