Incident Wave Groups Research Articles

Forerunning mode transition in a continuous waveguide

We have discovered a forerunning mode transition as the periodic wave changing the state of a uniform continuous waveguide. The latter is represented by an elastic beam initially rested on an elastic foundation. Under the action of an incident sinusoidal wave, the separation from the foundation occurs propagating in the form of a transition wave. The critical displacement is the separation criterion. Under these conditions, the steady-state mode exists with the transition wave speed independent of the incident wave amplitude. We show that such a regime exists only in a bounded domain of the incident wave parameters. Outside this domain, for higher amplitudes, the steady-state mode is replaced by a set of local separation segments periodically emerging at a distance ahead of the main transition point. The crucial feature of this waveguide is that the incident wave group speed is greater than the phase speed. This allows the incident wave to deliver the energy required for the separation. The analytical solution allows us to show in detail how the steady-state mode transforms into the forerunning one. The latter studied numerically turns out to be periodic. As the incident wave amplitude grows the period decreases, while the transition wave speed averaged over the period increases to the group velocity of the wave. As an important part of the analysis, the complete set of solutions is presented for the waves excited by the oscillating or/and moving force acting on the free beam. In particular, an asymptotic solution is evaluated for the resonant wave corresponding to a certain relation between the load's speed and frequency.

Interaction between the fundamental lamb modes and the front edge of a crack in a metallic plate.

Numerical simulations followed by experimental validations were carried out to study the interaction of the fundamental Lamb modes when incident at the front edge of a horizontal crack in a metallic plate. During the interaction, the incident fundamental Lamb mode underwent mode conversion and started propagating in the main and sub-waveguides along with the mode-converted Lamb mode. The amplitude of the mode-converted Lamb mode propagating in the main waveguide was negligible compared with that of the incident wave group. It was found that the amplitude of the transmitted Lamb modes from the main waveguide to the sub-waveguides is nearly the same as the incident wave group's amplitude; wave groups propagating in the thicker sub-waveguides are found to be carrying higher power than their counterparts in the thinner sub-waveguides. Furthermore, it was observed that variation in power coefficients and amplitude-based factors with respect to frequency of excitation were not very significant. Moreover, it was also shown that amplitude of the reflected wave groups in the main waveguide depends on phase velocities of Lamb modes in the main waveguide and sub-waveguides for a given thickness ratio.

Low‐frequency characteristics of wave group–forced vortices

The dynamics of vorticity motions forced by wave groups incident on an alongshore‐uniform barred beach are analyzed. For both normally and obliquely incident wave groups, the potential vorticity and enstrophy equations reveal that the temporal variability of wave group–forced vortices is directly linked to the variability in the incoming wave groups rather than bottom friction, as previously hypothesized. Analysis of the lifespan of individual vortices further shows that the wave group forcing is responsible for not only the temporal variations of the vortices but also their eventual demise. Vortices in the simulations persist for 5 to 45 min, which is consistent with recent field observations. For oblique wave groups, the resulting vortices are advected by the mean current, yielding a signature in the frequency–wave number spectrum that is similar to that usually attributed to shear instabilities of the alongshore current. These results may explain previous observations of alongshore‐propagating vorticity motions in the presence of a stable alongshore current. For simulations involving an unstable alongshore current, we find that the inclusion of wave group forcing results in velocity spectra that are much broader compared to the simulations that neglect wave grouping, which could explain discrepancies between previously observed and modeled spectral widths of propagating vorticity motions. Finally, the potential enstrophy balance shows that vorticity production due to wave groups may be as important as that due to the instability process and that not all low‐frequency vortical motions observed during oblique wave incidence should be attributed to shear instabilities of the alongshore current.

海浜流の非定常過程に関する数値的検討

An analytical model for long shore transient current and a numerical model for transient current are proposed. The time evolution of long shore current by oblique incident waves shows analytically and asymptotic long shore velocity in the surf zone is defined the function of bottom friction coefficient. Numerical simulation of near shore current evolution by oblique incident wave groups shows periodic low-frequency current motion is driven by periodic and phase aligned motion of wave groups.

Local and far-field surface elevation around a vertical cylinder in unidirectional steep wave groups

The problem of diffraction of a unidirectional incident wave group by a bottom-seated cylinder is considered. We assume the amplitude of the incoming wave to be small in comparison with other linear scales of the problem, and develop the corresponding second-order perturbation theory. We use the Fourier transform to treat time variation and separate spatial variables when solving the non-homogeneous second-order problem. The resulting set of non-homogeneous Bessel equations is solved numerically. Solutions for various types of incoming wave spectrum are obtained including the Gaussian spectrum and the Pierson–Moskowitz spectrum. To validate the method, problems with gradually decreasing bandwidth of Gaussian spectrum are solved and it is shown that the corresponding solution approaches that for the monochromatic case. The Pierson–Moskowitz spectrum with a set of realistic physical parameters is used as an example of extreme wave interaction with an offshore structure. The corresponding first- and second-order solutions are obtained and the effect of non-linearity on the solution is discussed with the emphasis on the growth of maximum free-surface elevation on the cylinder’s surface and generation of high frequency free radiated waves.

The Influence of Energy Grouping and Undulation on Sediment Suspension in the Surf Zone

A field experiment was conducted to investigate the effects of the wave energy grouping and undulating on the sediment suspension in the surf zone at Taichung, Taiwan, in 1995.Instruments were deployed in line with the wave front, including one acoustic current meter, one pressure sensor, and four optical turbidity monitors were arranged in line and perpendicular to the bed. During the experiments he water depth was varied from 0.7m to 3.6m due to the tide level variations. The instruments were fixed to the ground to have data collected throughout the surf zone while the relative position of the station in the surf zone was varied with the tide level. Sediment suspension events associated with the group wave motions reached peak concentrations were 2-3 times larger than that associated with waves without grouping. A new approach using Hilbert transform and Intrinsic Mode Functions(IMF)analysis to explore the effect of energy grouping and undulating on sediment suspension is presented. It gives a close insight to the suspended sediment distribution and wave characteristics in the surf zone. n interesting bursting phenomenon of bed concentration was found dominating in the surf zone, which was closely related to the incident wave groups.

Observations of nearshore infragravity waves: Seaward and shoreward propagating components

The variation of seaward and shoreward infragravity energy fluxes across the shoaling and surf zones of a gently sloping sandy beach is estimated from field observations and related to forcing by groups of sea and swell, dissipation, and shoreline reflection. Data from collocated pressure and velocity sensors deployed between 1 and 6 m water depth are combined, using the assumption of cross‐shore propagation, to decompose the infragravity wave field into shoreward and seaward propagating components. Seaward of the surf zone, shoreward propagating infragravity waves are amplified by nonlinear interactions with groups of sea and swell, and the shoreward infragravity energy flux increases in the onshore direction. In the surf zone, nonlinear phase coupling between infragravity waves and groups of sea and swell decreases, as does the shoreward infragravity energy flux, consistent with the cessation of nonlinear forcing and the increased importance of infragravity wave dissipation. Seaward propagating infragravity waves are not phase coupled to incident wave groups, and their energy levels suggest strong infragravity wave reflection near the shoreline. The cross‐shore variation of the seaward energy flux is weaker than that of the shoreward flux, resulting in cross‐shore variation of the squared infragravity reflection coefficient (ratio of seaward to shoreward energy flux) between about 0.4 and 1.5.

Nonlinear and 3D effects in leaky infragravity waves

In this paper, infragravity (IG) waves, forced by normally and obliquely incident wave groups, are studied using the quasi-3D (Q3D) nearshore circulation model SHORECIRC [Van Dongeren, A.R., I.A. Svendsen, 1997b. Quasi 3-D modeling of nearshore hydrodynamics. Research report CACR-97-04. Center for Applied Coastal Research, University of Delaware, Newark, 243 pp.], which includes the Q3D effects. The governing equations that form the basis of the model, as well as the numerical model and the boundary conditions, are described. The model is applied to the case of leaky IG waves. It is shown that the Q3D terms have a significant effect on the cross-shore variation of the surface elevation envelope, especially around the breakpoint and in the inner surf zone. The effect of wave groupiness on the temporal and spatial variation of all Q3D terms is shown after which their contribution to the momentum equations is analyzed. This reveals that only those Q3D coefficients, which appear in combination with the largest horizontal velocity shears make a significant contribution to the momentum equations. As a result of the calculation of the Q3D coefficients, the IG wave velocity profiles can be determined. This shows that in the surf zone, the velocity profiles exhibit a large curvature and time variation in the cross-shore direction, and a small — but essential — depth variation in the longshore direction.

Propagation of incident modulated waves past impermeable semi-infinite breakwaters

A possible source of resonant problems in a harbor is the long waves generated due to incident wave groups. For harbors protected by vertical breakwaters the diffraction of the group could generate free long waves. Using a multiple-scale perturbation method, the diffraction and reflection of a wave group past an impermeable semi-infinite vertical thin breakwater in horizontal bottom is studied. The relationship between the incident wave group and the generated free and locked long waves is derived and an analytical solution is presented. It is shown that free long waves could be generated due to the wave group propagation past the breakwater and that the range of angles for potential free long waves increases when the value of the relative depth decreases.

The Generation of Alongslope Currents by Breaking Internal Waves

Abstract Internal gravity waves propagating in a fluid of constant buoyancy frequency and approaching a uniform sloping boundary from a direction that is not in a plane normal to the boundary, and dissipating energy on reflection, generate alongslope currents. The net radiation stress or momentum flux into the breaking region is proportional to the flux of energy lost from the waves. It is supposed that the stress is balanced by a frictional boundary stress so that a steady alongslope current is generated. The dependence of the strength of the current on the steepness, AIMI, of the incident wave and on its propagation direction is examined as a function of α and β, the inclination of the boundary to the horizontal and the angle between the incident wave group velocity vector and the horizontal, respectively. Alongslope currents of several centimeters per second, generally exceeding the Lagrangian drift produced by wave reflection alone, may be generated in the ocean or in lakes. Reflection of subcritical ...

Nearshore Side-Scan Sonar Studies

Side-scan sonars operating at 80–250 kHz have been deployed to produce narrow beams directed parallel and normal to shore on a gently sloping beach. These provide measurements of processes (such as wave propagation) seaward of the edge of the surf zone. Shoreward propagation of sound into the surf zone and hence useful information retrieval from this zone is prevented, however, by high bubble or suspended sediment absorption at its outer edge, as found in earlier Doppler sonar studies at 195 kHz by J.A. Smith. The Shoreward limit of acoustic propagation has a variable structure related to incident wave groups, the position at which waves break, and to dynamical processes within the surfzone determining the position of the bubble or suspended sediment boundary.

Propagation and trapping of obliquely incident wave groups over a trench with currents

The analytical solutions of secord-order long waves generated by the diffraction of short wave groups by a combination of depth and current velocity discontinuities are presented. The incident wave groups consist of two co-linear short waves with slightly different frequencies. These incident short wave groups are reflected partially by the abrupt changes in depth and current velocity. The incident, reflected, and transmitted wave groups are accompanied by the second-order locked long waves, which propagate together with the wave envelopes of the short waves at their group velocity. Because of the discontinuity in the second-order free surface displacement of the locked long waves, free long waves are generated, which propagate at the shallow-water phase speed and in a direction different from those of short waves and wave envelopes. With certain combinations of angle of wave incidence, depth ratios and current velocity, the free long waves can be trapped in the vicinities of depth and current discontinuities. Several examples are given to illustrate the resonance of trapped free long waves.

Harbour excitations by incident wave groups

By using the multiple-scales perturbation method, analytical solutions are obtained for the second-order low-frequency oscillations inside a rectangular harbour excited by incident wave groups. The water depth is a constant. The width of the harbour entrance is of the same order of magnitude as the wavelength of incident carrier (short) waves, but small in comparison with the wavelength of the wave envelope. Because of the modulations in the wave envelope, a second-order long wave is locked in with the wave envelope and propagates with the speed of the group velocity. Outside the harbour, locked long waves also exist in the reflected wave groups, but not in the radiated wave groups. Inside the harbour, the analytical expressions for the locked long waves are obtained. Owing to the discontinuity of the locked long waves across the harbour mouth, second-order free long waves are generated. The free long waves propagate with a speed of (gh)½ inside and outside the harbour. The free long waves inside the harbour may be resonated in a low-frequency range which is relevant to the harbour resonance.

Long-Wave Generation Due to the Refraction of Short-Wave Groups over a Shear Current

The generation of long waves by short-wave groups propagating over a shear current is studied. The incident wave groups consist of two co-linear short waves with slightly different frequencies. These short waves are refracted by the shear currents. For certain angles of incidence caustics may exist and the short waves are reflected back by the shear current. Similarly, caustics could also appear in the wave envelope, which propagates in a different direction from that of the short waves. In the present paper, the treatment of caustics is not considered. In the region where the shear current vanishes, the short-wave groups are accompanied by locked long waves that propagate with the wave envelope of short waves at their group velocity. In the shear current region, the refraction effects not only separate the propagation directions of the short waves and the wave envelope but also generate free long waves, which propagate at the speed of.gh. The free long waves could also be trapped over the shear current region.

SURF BEAT GENERATION ON A MILD-SLOPE BEACH

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.

SWASH ON STEEP AND SHALLOW BEACHES

Extensive field observations of swash on natural beaches are used to relate the magnitudes of swash oscillations to incident wave conditions and the beach slope. Swash fluctuations at wind wave frequencies (defined here as f > .05 Hz) appear to be "saturated." As in laboratory experiments with monochromatic waves, wave breaking prevents the magnitudes of swash oscillations at incident wave frequencies from increasing past a certain level which depends on the beach slope. All data sets considered support this conclusion. In contrast, the magnitude of swash oscillations at surf beat frequencies (defined as f < .05 Hz) varies between data sets. Possible reasons for the discrepancy are discussed. Despite their differences, all data sets show that motions at surf beat frequencies dominate the swash spectrum on dissipative beaches. As in previous studies, the frequencies of spectral hills and valleys in the spectra of surf zone sensors suggests that a significant fraction of the surf beat energy is contained in motions which are standing in the cross-shore direction. Preliminary analysis indicates that shoreward propagating surf beat is coupled to incident wave groups.

Longshore motion due to an obliquely incident wave group

We consider longshore motion generated within the surf zone by obliquely incident breaking waves, and seek to describe the effect on such motion of variations, caused by wave grouping, in the incident longshore momentum flux. The effects of associated variations in set-up are not considered.We use the linear long-wave equations to describe the motion resulting from the longshore momentum contained in a wave group. This consists of a succession of edge waves which disperse along the beach, and, for the example considered, an eventual steady circulation cell at the position of the wave group. We suggest that such a cell is always likely to be formed if the wave group is sufficiently localized, and that higher-modenumber edge waves are more likely to be excited.We find timescales for the dispersal of the edge waves, and for the decay, due to bottom friction, of the circulation cell: we suggest that the latter may more generally be used, as a timescale for the effect of friction on longshore motion.