Wave groupiness variations in the nearshore

This paper proposes a new definition of the groupiness factor, GF, based on the envelope of the incident-wave time series. It is shown that an envelope-based GF has several important advantages over the SIWEH-based groupiness factor, including objective criteria for determining the accuracy of the envelope function and well-defined numerical limits.Using this new GF, the variability of incident wave groupiness in the field is examined both temporally, in unbroken waves at a fixed location, and spatially, in a cross-shore array through the surf zone. Contrary to previous studies using the SIWEH-based GF, results suggest that incident wave groupiness may not be an independent parameter in unbroken waves; through a wide range of spectral shapes, from swell to storm waves, the groupiness did not vary significantly. As expected, the groupiness decreases rapidly as waves break through the surf zone, although significant wave height variability persists even through a saturated surf zone. The source of this inner surf zone groupiness is not identified; however, this observation implies that models of long wave generation must account for nonsteady radiation stress gradients landward of some narrow zone near the mean breakpoint.     

Breakpoint generated surf beat induced by bichromatic wave groups

This paper presents new experimental data on 2-D surf beat generation by a time-varying breakpoint induced by bichromatic wave groups. The experimental investigation covers a broad range of wave amplitudes, short wave frequencies, group frequencies and modulation rates. The data include measurements of incident and outgoing wave amplitudes, breakpoint position, shoreline run-up and the cross-shore structure of both the short and long wave motion. Surf beat generation is shown to be in good agreement with theory [Symonds, G., Huntley, D.A., Bowen, A.J., 1982. Two dimensional surf beat: long wave generation by a time-varying breakpoint. J. Geophys. Res. 87, 492–498]. In particular, surf beat generation is dependent on the normalised surf zone width, which is a measure of the phase relationship between the seaward and shoreward breakpoint forced long waves, and linearly dependent on the short wave amplitude. The cross-shore structure of the long wave motion is also consistent with theory; at maximum and minimum surf beat generation, the mean breakpoint coincides with the nodal and anti-nodal points, respectively, for a free long wave standing at the shoreline. A numerical solution, using measured data as input, additionally shows that the phase relationship between the incident bound long wave and the outgoing breakpoint forced wave is consistent with the time-varying breakpoint mechanism.     

Numerical study of pollutant movement in waves and wave-induced long-shore currents in surf zone

Water waves, wave-induced long-shore currents and movement of pollutants in waves and currents have been numerically studied based on the hyperbolic mild-slope equation, the shallow water equation , as well as the pollutant movement equation, and the numerical results have also been validated by experimental data. It is shown that the long-shore current velocity and wave set-up increase with the increasing incident wave amplitude and slope steepness of the shore plane ; the wave set-up increases with the in- creasing incident wave period;and the pollutant morement proceeds more quiekly with the increasing incident wave amplitude and slope steepness of the shore palane. In surf zones, the long-shore currents induced by the inclined incident waves have effectively affected the pollutant movement.     

Some properties of surf-beats

Long ocean waves with periods of several minutes (surf-beats) were observed at a marine observation tower. We have analysed time series data of an envelope of incident swell, long period current velocity and surface elevation fluctuations. Current velocity was measued by an electromagnetic flow meter. Surf-beats amplitudeH ^(l) is shown to be proportional to 3/2 power of incident swell amplitudeH ^(s), and decreases with increase of depthh in proportional toh ^–1/2 such thatH ^(l) H ^(s) (H ^(s)/h)^1/2. Frequency energy density functionP _LL (f) of surface elevation had two dominant peaks whose frequencies were highly stable through the entire observational period. Cross-spectral analysis suggested that those peaks correspond to traveling edge waves caused by the excess momentum and mass flux in the surf zone. The forced long ocean waves predicted byLonguet-Higgins andStewart (1964) was ditected. Phase-shift and wave height of the wave with respect to those of incident swell envelope are shown to be in remarkable agreement with the predictions. However the forced long wave is only a minor component in the total energy of surf-beats. Current fields are shown to be largely composed of non-surface modes.     

Optimal configurations of wave energy device arrays

In this paper, the influence of the spatial configuration of a wave energy device array upon total power output is investigated. Hydrodynamic interactions are computed using a method capable of producing the linear wave theory solution to arbitrary accuracy. The overall performance of devices with two different power take-off arrangements is maximised at one incident wave frequency and direction by altering the formation of the array. Minimisation of the power is also carried out in a third case in order to demonstrate potential array-related losses. The optimisation is applied using two different approaches in each case: the Parabolic Intersection (PI) method and a Genetic Algorithm (GA). The former is a heuristic technique that has been devised for this study to enable rapid array construction using only simple calculations. The latter is an existing method, applied here with a novel crossover operator. Although considerably more computational effort is required, superior results may be obtained using the GA compared to the PI method. All of the arrays are subsequently analysed under incident waves of different frequency and direction, the resulting behaviour explained in terms of certain geometrical features of the arrangements.     

Surf zone dynamics simulated by a Boussinesq type model. Part II: surf beat and swash oscillations for wave groups and irregular waves

This is the second of three papers on the modelling of various types of surf zone phenomena. In the first paper the general model was described and it was applied to study cross-shore motion of regular waves in the surf zone. In this paper, part II, we consider the cross-shore motion of wave groups and irregular waves with emphasis on shoaling, breaking and runup as well as the generation of surf beats. These phenomena are investigated numerically by using a time-domain Boussinesq type model, which resolves the primary wave motion as well as the long waves. As compared with the classical Boussinesq equations, the equations adopted here allow for improved linear dispersion characteristics and wave breaking is modelled by using a roller concept for spilling breakers. The swash zone is included by incorporating a moving shoreline boundary condition and radiation of short and long period waves from the offshore boundary is allowed by the use of absorbing sponge layers. Mutual interaction between short waves and long waves is inherent in the model. This allows, for example, for a general exchange of energy between triads rather than a simple one-way forcing of bound waves and for a substantial modification of bore celerities in the swash zone due to the presence of long waves. The model study is based mainly on incident bichromatic wave groups considering a range of mean frequencies, group frequencies, modulation rates, sea bed slopes and surf similarity parameters. Additionally, two cases of incident irregular waves are studied. The model results presented include transformation of surface elevations during shoaling, breaking and runup and the resulting shoreline oscillations. The low frequency motion induced by the primary-wave groups is determined at the shoreline and outside the surf zone by low-pass filtering and subsequent division into incident bound and free components and reflected free components. The model results are compared with laboratory experiments from the literature and the agreement is generally found to be very good. Finally the paper includes special details from the breaker model: time and space trajectories of surface rollers revealing the breakpoint oscillation and the speed of bores; envelopes of low-pass filtered radiation stress and surface elevation; sensitivity of surf beat to group frequency, modulation rate and bottom slope is investigated. Part III of this work (Sørensen et al., 1998) presents nearshore circulations induced by the breaking of unidirectional and multi-directional waves.     

Rip currents under obliquely incident wind waves and tidal longshore currents

A field experiment on the nature of rip currents was conducted on the Dutch coast, which differs from previous rip current study sites because it is a wind-sea dominated environment with mostly obliquely incident waves and tidally-driven longshore currents. During the experiment three distinct flow patterns, obtained with GPS tracked drifter instruments, were observed: (1) a locally governed circulation cell, (2) an offshore current that is deflected shore parallel outside the surf zone and (3) a meandering longshore current. The transition from rip currents (flow patterns 1 and 2) to meandering longshore currents (flow pattern 3) occurred gradually within the tidal cycle with longshore currents prevalent at mid to high tide. Rip currents at this site appeared at depressions in the surf zone bar and typically occurred when the water level fell below NAP (equivalent to MSL), even in the presence of obliquely incident waves and tidally driven longshore currents. Hindcast simulations of the drifter experiments were performed with the numerical model XBeach and showed good agreement with field observations. The model was subsequently used to investigate the influence of tidal water level fluctuations, longshore currents and obliquely incident waves on rip currents.Rip currents were initiated when the water level dropped below a specific threshold with the magnitude of the rip current associated with the water level. The strength of the tidal current and its orientation with respect to the incident waves governed the offshore extent and orientation of the rip current. In contrast to other studies that suggest that rip currents solely occur under shore normal (or slightly oblique waves), in this study both observations and numerical model simulations indicate that rip currents can exist under large angles of wave incidence, when the rip channel is sufficiently wide and the wave height is small.     

Wave-induced mean flows in vertical rubble mound structures

Waves impinging on rubble mound breakwaters and seawalls induce a mean flow within the breakwater, analogous to the so-called undertow within the surf zone. Here, using a plane wave approximation (kh<1.5), a second-order problem is solved for an idealized breakwater with a rectangular cross-section to show the origin and the nature of the mean flow within the porous structure. The mean flow is expressed in terms of a mean stream function analytically derived, obtained based on the mass flux balance between the incident, reflected and transmitted waves. Furthermore, the evolution of other second-order magnitudes such as mean water level and mass flux is analyzed under different incident wave conditions, structure geometry and porous material characteristics. Results show that the evolution of the different mean quantities is controlled mainly by reflection and consequently depends highly on structure geometry and porous material characteristics. Furthermore, it is shown that the return flow is stronger with increasing mass flux decay. Some qualitative experiments to show the described mechanism are also presented.     

SWAN predictions of waves observed in shallow water onshore of complex bathymetry

SWAN model predictions, initialized with directional wave buoy observations in 550-m water depth offshore of a steep, submarine canyon, are compared with wave observations in 5.0-, 2.5-, and 1.0-m water depths. Although the model assumptions include small bottom slopes, the alongshore variations of the nearshore wave field caused by refraction over the steep canyon are predicted well over the 50 days of observations. For example, in 2.5-m water depth, the observed and predicted wave heights vary by up to a factor of 4 over about 1000 m alongshore, and wave directions vary by up to about 10°, sometimes changing from south to north of shore normal. Root-mean-square errors of the predicted wave heights, mean directions, periods, and radiation stresses (less than 0.13 m, 5°, 1 s, and 0.05 m³/s² respectively) are similar near and far from the canyon. Squared correlations between the observed and predicted wave heights usually are greater than 0.8 in all water depths. However, the correlations for mean directions and radiation stresses decrease with decreasing water depth as waves refract and become normally incident. Although mean wave properties observed in shallow water are predicted accurately, nonlinear energy transfers from near-resonant triads are not modeled well, and the observed and predicted wave energy spectra can differ significantly at frequencies greater than the spectral peak, especially for narrow-band swell.     

Remote sensing of breaking wave phase speeds with application to non-linear depth inversions

A number of existing models for surface wave phase speeds (linear and non-linear, breaking and non-breaking waves) are reviewed and tested against phase speed data from a large-scale laboratory experiment. The results of these tests are utilized in the context of assessing the potential improvement gained by incorporating wave non-linearity in phase speed based depth inversions. The analysis is focused on the surf zone, where depth inversion accuracies are known to degrade significantly. The collected data includes very high-resolution remote sensing video and surface elevation records from fixed, in-situ wave gages. Wave phase speeds are extracted from the remote sensing data using a feature tracking technique, and local wave amplitudes are determined from the wave gage records and used for comparisons to non-linear phase speed models and for non-linear depth inversions. A series of five different regular wave conditions with a range of non-linearity and dispersion characteristics are analyzed and results show that a composite dispersion relation, which includes both non-linearity and dispersion effects, best matches the observed phase speeds across the domain and hence, improves surf zone depth estimation via depth inversions. Incorporating non-linearity into the phase speed model reduces errors to O(10%), which is a level previously found for depth inversions with small amplitude waves in intermediate water depths using linear dispersion. Considering the controlled conditions and extensive ground truth, this appears to be a practical limit for phase speed-based depth inversions. Finally, a phase speed sensitivity analysis is performed that indicates that typical nearshore sand bars should be resolvable using phase speed depth inversions. However, increasing wave steepness degrades the sensitivity of this inversion method.     

Virtual wave gauges based upon stereo imaging for measuring surface wave characteristics

A virtual wave gauge (VWG) technique based on stereo imaging is developed to remotely measure water wave height, period, and direction. VWG minimizes computational costs by directly tracking the elevation of the water surface at selected points of interest using a Eulerian based dynamic searching algorithm. Results show that the VWG technique developed in this paper dramatically improves efficiency by two orders of magnitude compared to the traditional Lagrangian–Eulerian based point cloud method of stereo image processing. VWG is tested against traditional wave wire gauges to within 98% accuracy for significant wave height. Furthermore, the flexibility of the VWG is demonstrated in two field applications. First in an offshore breaking wave case, an array of VWGs is used to efficiently measure wave directionality. Second to investigate the reflection coefficient of a rock-mounted structure interacting with nearshore waves, linear and spatial VWG arrays are designed and implemented based on a priori information of the wave field from a preliminary VWG measurement. Overall, we demonstrate that the flexible and computational efficient VWG technique has the potential to make real-time remote stereo imaging wave measurements a reality.     

Uptake of petroleum hydrocarbons by the Blue Mussel (Mytilus edulis L.) after Experimental Oiling and High Pressure, Hot Water Shore cleaning

High pressure, hot water shore cleaning after an oil spill will release high concentrations of petroleum hydrocarbons to ambient marine ecosystems. The immediate increase of hydrocarbons observed in blue mussels, Mytilus edulis, went from background concentrations of 40 μg/g to 657 μg/g and 533 μg/g at a distance of 3 and 8m respectively from the shore. After two weeks the accumulated oil had decreased by 20–45 %. In comparison natural surf and ice cleaning of shores will only produce a small increase in hydrocarbon concentrations. We recommend that high pressure, hot water cleaning is not used in areas where no special bird or wild life protection is needed.     

Fully nonlinear analysis of near-trapping phenomenon around an array of cylinders

The wave diffraction around an array of fixed vertical circular cylinders is simulated in a numerical wave tank by using a fully nonlinear model in the time domain. The emphasis of the paper lies in the insightful investigation of the nonlinear properties of the near-trapping phenomenon associated with the multiple cylinders. The numerical model is validated by analytical solutions as well as experimental data for waves propagating past two and four vertical cylinders in certain arrangements. An array of four identical circular cylinders at the corners of a square with an incident wave along the diagonal of the square is the main focus here for investigating the near-trapping phenomenon. When near-trapping occurs, the present study shows that an extremely high wave elevation near the cylinders can be observed. At the same time, the hydrodynamic forces on different cylinders are found to be either in phase or out of phase, leading to some characteristic force patterns acting on the whole structure. Due to the nature of the numerical model adopted, nonlinearity at different orders can be captured using a harmonic analysis. In addition to first- and second-order near-trapping, the third-order (triple-frequency) nonlinear component is presented for the first time. For the configuration selected, it is found that at one specific incident wave frequency and direction one trapped mode is excited by second-order effects, while a different trapped mode (having similar symmetries) is excited by the third harmonic of the incident wave frequency.     

The influence of sea state on formation speed of alongshore variability in surf zone sand bars

The formation time of alongshore morphological variability in surf zone sand bars has long been known to differ from one beach to the other and from one post-storm period to another. Here we investigate whether the type of sea state, i.e. distant swell waves or locally generated short period wind sea, affects the formation time of the emerging alongshore topographic variability.A numerical modeling approach is used to examine the emergence of alongshore variability under different shore-normal wave forcing. A research version of Delft3D, operating on the time-scale of wave groups, is applied to a schematised bathymetry with a single bar. The model is then used to investigate several wave scenarios, examining the impact of peak period, frequency spread and directional spread on the formation time of alongshore variability.Results show that an increase in wave period has a large effect, changing the formation time up to O (250%) in case the wave period is changed from a representative value for the Dutch coast (T_p ~ 5–6 s) to an Australian South East coast value (T_p ~ 10–12 s). In contrast, modifications in the directional and frequency spread of the wave field result only in a minor change in the formation time.Examination of hydrodynamics and potential sediment transport shows that the variations in formation time are primarily related to changes in the magnitude of the time-averaged flow conditions. Variations in the magnitude of very low frequency (f < 0.004 Hz) or infragravity (0.004 < f < 0.04 Hz) surf zone flow velocities do not affect the mean sediment transport capacity. Consequently the formation speed of patterns is primarily governed by positive feedback between mean flow and morphology, and low frequency flow fluctuations are of minor importance.These findings indicate that the development of alongshore topographic variability may be faster at swell dominated open coasts, primarily due to the occurrence of longer period swell. Also, at a given site, the arrival of a long wave period swell after a storm can accelerate the emergence of variability.     

Dynamics of surf-zone turbulence in a strong plunging breaker

The characteristics of turbulence created by a plunging breaker on a 1 on 35 plane slope have been studied experimentally in a two-dimensional wave tank. The experiments involved detailed measurements of fluid velocities below trough level and water surface elevations in the surf zone using a fibre-optic laser-Doppler anemometer and a capacitance wave gage. The dynamical role of turbulence is examined making use of the transport equation for turbulent kinetic energy (the k-equation). The results show that turbulence under a plunging breaker is dominated by large-scale motions and has certain unique features that are associated with its wave condition. It was found that the nature of turbulence transport in the inner surf zone depends on a particular wave condition and it is not similar for different types of breakers. Turbulent kinetic energy is transported landward under a plunging breaker and dissipated within one wave cycle. This is different from spilling breakers where turbulent kinetic energy is transported seaward and the dissipation rate is much slower. The analysis of the k-equation shows that advective and diffusive transport of turbulence play a major role in the distribution of turbulence under a plunging breaker, while production and dissipation are not in local equilibrium but are of the same order of magnitude. Based on certain approximate analytical approaches and experimental measurements it is shown that turbulence production and viscous dissipation below trough level amount to only a small portion of the wave energy loss caused by wave breaking. It is suggested that the onshore sediment transport produced by swell waves may be tied in a direct way to the unique characteristics of turbulent flows in these waves.     

Field intercomparison of nearshore directional wave sensors

Five measurement strategies (four in situ, one remote) for estimating directional wave spectra were intercompared in a 1980 experiment at the Coastal Engineering Research Center's Field Research Facility in Duck, NC. The systems included two pressure sensor/biaxial current meter combinations (different manufacturers), a triaxial acoustic current meter, an SXY gauge (square array of four pressure sensors), and a shore-based imaging radar. A detailed error analysis suggests sources for differences in estimated wave spectra from the different instruments; in general, they intercompare favorably. The major deviation among in situ gauges was associated with the triaxial acoustic current meter. Reliance on a vertical velocity measurement (instead of a direct pressure or sea-surface elevation measurement) can contribute additional uncertainty in directional spectral estimates. The imaging radar was successful in distinguishing multiple wave trains at the same frequency, which was not possible with the simple spectral estimation analysis applied to in situ data. However, the radar is not useful in providing accurate estimates of spectral density, nor in distinguishing multiple wave trains of different frequencies coming from the same direction. Selection of a measurement strategy for a particular need depends on the precise data requirements for that application. Although the five tested intercompared well, in practice not all are equally suitable for every application.     

Morphodynamics of a bar-trough surf zone

A field study was made of the distinguishing morphodynamic processes operating in a surf zone which perennially exhibits accentuated bar-trough topography (the “longshore-bar-trough” and “rhytmic-bar-and-beach” states as described by Wright and Short, 1984). Characteristic features of the morphology include a shallow bar with a steep shoreward face, a deep trough, and a steep beach face. This morphology, which is favored by moderate breaker heights and small tidal ranges, strongly controls the coupled suite of hydrodynamic processes. In contrast to fully dissipative surf zones, the bar-trough surf zone is not at all saturated and oscillations at incident wave frequency remain dominant from the break point to the subaerial beach. The degree of incident wave groupiness does not change appreciably across the surf zone. Infragravity standing waves which, in dissipative surf zones, dominate the inshore energy, remain energetically secondary and occur at higher frequencies in the bar trough surf zone. Analyses of the field data combined with numerical simulations of leaky mode and edge wave nodal—antinodal positions over observed surf-zone profiles, indicate that the frequencies which prevail are favored by the resonant condition of antinodes over the bar and nodes in the trough. Standing waves which would have nodes over the bar are suppressed. Sediment resuspension in the surf zone appears to be largely attributable to the incident waves which are the main source of bed shear stress. In addition, the extra near-bottom eddy viscosity provided by the reformed, non-breaking waves traversing the trough significantly affects the vertical velocity profile of the longshore current. Whereas the bar is highly mobile in terms of onshore—offshore migration rates, the beach face and inner regions of the trough are remarkably stable over time.     

Bragg reflection of sinusoidal waves due to trapezoidal submerged breakwaters

Numerical and laboratory experiments are performed to investigate characteristics of the Bragg reflection due to multi-arrayed trapezoidal submerged breakwaters. The numerical model is based on the Reynolds averaged Navier–Stokes equations with the VOF method and the k–ε turbulence closure model. As expected, the reflection coefficients increase as the array of submerged breakwaters increases in both laboratory measurements and numerical results. The resonant periods provide similar relative wave numbers regardless of the permeability and the number of arrays. The reflection coefficients due to porous breakwaters are smaller than those due to non-porous breakwaters. The velocity contours for two and three arrays are also described.     

Cross-shore hydrodynamics within an unsaturated surf zone

This paper concerns the hydrodynamics induced by random waves incident on a steep beach. New experimental results are presented on surface elevation and kinematic probability density functions, cross-shore variation in wave heights, the fraction of broken waves and velocity moments. The surf zone is found to be unsaturated at incident wave frequencies, with a significant proportion of the incident wave energy remaining at the shoreline in the form of bores. Wave heights in both the outer and inner surf zones are best described by a full Rayleigh distribution [Thornton, E.B., Guza, R.T., 1983. Transformation of wave height distribution. J. Geophys. Res. 88, 5925–5938], rather than a truncated Rayleigh distribution as used by Battjes and Janssen (1978) [Battjes, J.A, Janssen, J.P., 1978. Energy loss and setup due to breaking of random waves. Proc. 16th Int. Conf. Coastal Eng. ASCE, New York, pp. 569–588]. A new parametric wave transformation model is outlined which provides explicit expressions for the fraction of broken waves and the energy dissipation rate within the surf zone. On steep beaches, the model appears to offer improved predictive capabilities over the original Battjes and Janssen model. Cross-shore variations in the velocity variance and velocity moments are best described using Linear Gaussian wave theory, with less than 20% of the velocity variance in the inner surf zone due to low frequency energy.     

Examination of drag coefficient with special reference to the windsea Reynolds number: Conditions with counter and mixed swell

The effect of swell on the drag coefficient, C _D, observed at the Hiratsuka Tower Station, presented by Suzuki et al. (1998, 2002), has been investigated. C _D increases sharply with the windsea Reynolds number, R _B, when there is a counter swell against the windsea direction, and only gradually when the swell comes from a mixture of directions. In cases where 2-D wave spectra were unavailable (1998, and others), swells showed a scattering effect compared with the pure windsea case on the C _D-R _B Diagram. R _B is a useful parameter for investigating the effect of swells and further systematic accumulation of appropriate data is needed.