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.

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 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 MEASUREMENTS OF SURF BEAT AND SET-DOWN BENEATH WAVE GROUPS

1984 ◽  
Vol 1 (19) ◽  
pp. 49 ◽  
Author(s):  
J.K. Kostense
Keyword(s):  
Surf Zone ◽  
Time Varying ◽  
Equal Frequency ◽  
Wave Groups ◽  
Free Wave ◽  
Wave Channel ◽  
Long Wave ◽  
The Difference ◽  
Active Wave ◽  
Good Agreement

A laboratory study was conducted to measure the amplitudes of long waves In shallow water as induced by wave grouping. In a 55 m long wave channel with a plane beach at the end, two primary waves of nearly equal frequency were generated. Due to a sophisticated control of the wave paddle - including second order wave generation as well as active wave absorption at the paddle face - the wave action at the difference frequency was limited to an incident forced wave, propagating at the group velocity, and a reflected free wave generated in the surf zone. For the incident forced - or bound - wave, also known as set-down, the experimental results show good agreement with the existing theory. Furthermore, the experiments confirm qualitatively a theoretical model by Symonds et al. (198 2) explaining two-dimensional surf beat as a result of the time-varying breakpoint of the incident primary waves.

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.

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.

Low Frequency Surf Zone Response to Wave Groups

1999 ◽  
Author(s):  
Merrick C. Haller ◽  
Uday Putrevu ◽  
Joan Oltman-Shay ◽  
Robert A. Dalrymple
Keyword(s):  
Surf Zone ◽  
Low Frequency ◽  
Wave Groups

Unsteady disturbances of streaming motions around bodies

1989 ◽  
Vol 209 ◽  
pp. 385-403 ◽  
Author(s):  
H. M. Atassi ◽  
J. Grzedzinski
Keyword(s):  
Wave Equation ◽  
Body Surface ◽  
Source Term ◽  
The Body ◽  
Entire Body ◽  
Two Dimensional ◽  
Mean Flow ◽  
Inhomogeneous Wave ◽  
Inhomogeneous Wave Equation ◽  
The Mean

For small-amplitude vortical and entropic unsteady disturbances of potential flows, Goldstein proposed a partial splitting of the velocity field into a vortical part u(I) that is a known function of the imposed upstream disturbance and a potential part ∇ϕ satisfying a linear inhomogeneous wave equation with a dipole-type source term. The present paper deals with flows around bodies with a stagnation point. It is shown that for such flows u(I) becomes singular along the entire body surface and its wake and as a result ∇ϕ will also be singular along the entire body surface. The paper proposes a modified splitting of the velocity field into a vortical part u(R) that has zero streamwise and normal components along the body surface, an entropy-dependent part and a regular part ∇ϕ* that satisfies a linear inhomogeneous wave equation with a modified source term.For periodic disturbances, explicit expressions for u(R) are given for three-dimensional flows past a single obstacle and for two-dimensional mean flows past a linear cascade. For weakly sheared flows, it is shown that if the mean flow has only a finite number of isolated stagnation points, u(R) will be finite along the body surface. On the other hand, if the mean flow has a stagnation line along the body surface such as in two-dimensional flows then the component of u(R) in this direction will have a logarithmic singularity.For incompressible flows, the boundary-value problem for ϕ* is formulated in terms of an integral equation of the Fredholm type. The theory is applied to a typical bluff body. Detailed calculations are carried out to show the velocity and pressure fields in response to incident harmonic disturbances.

scholarly journals VORTEX FORMATION IN PLUNGING BREAKER

1986 ◽  
Vol 1 (20) ◽  
pp. 54 ◽  
Author(s):  
T. Sakai ◽  
T. Mizutani ◽  
H. Tanaka ◽  
Y. Tada
Keyword(s):  
Flow Visualization ◽  
Particle Velocity ◽  
Vortex Formation ◽  
Water Particle ◽  
Mac Method ◽  
Long Wave ◽  
Wave Celerity ◽  
Maximum Water ◽  
Slope Beach ◽  
Plunging Breaker

By a flow visualization of a plunging breaker on 1/20 slope beach in a wave tank, an existence of 2nd and 3rd horizontal vortices(Miller, 1976) and slanting vortex (Nadaoka et al., 1986) is confirmed. A MAC method is applied to simulate a violent motion after an impinging of a jet from a crest of a plunging breaker on the trough surface. The calculated maximum water particle velocity in the jet is found to reach three times the linear long wave celerity. Values of circulation of the first four horizontal vortices are calculated and their changes in time are discussed.

Time‐domain behavior of wide‐angle one‐way wave equations

Geophysics ◽  
1991 ◽  
Vol 56 (3) ◽  
pp. 382-384
Author(s):  
A. H. Kamel
Keyword(s):  
Wave Equation ◽  
Wave Equations ◽  
Source Function ◽  
Plane Waves ◽  
Wide Angle ◽  
Wave Processes ◽  
Inhomogeneous Wave ◽  
Dirac Delta ◽  
Inhomogeneous Wave Equation ◽  
Standard Tool

The constant‐coefficient inhomogeneous wave equation reads [Formula: see text], Eq. (1) where t is the time; x, z are Cartesian coordinates; c is the sound speed; and δ(.) is the Dirac delta source function located at the origin. The solution to the wave equation could be synthesized in terms of plane waves traveling in all directions. In several applications it is desirable to replace equation (1) by a one‐way wave equation, an equation that allows wave processes in a 180‐degree range of angles only. This idea has become a standard tool in geophysics (Berkhout, 1981; Claerbout, 1985). A “wide‐angle” one‐way wave equation is designed to be accurate over nearly the whole 180‐degree range of permitted angles. Such formulas can be systematically constructed by drawing upon the connection with the mathematical field of approximation theory (Halpern and Trefethen, 1988).

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