Wave-induced Setup Research Articles

Pressure-gradient-driven nearshore circulation on a beach influenced by a large inlet-tidal shoal system

[1] The nearshore circulation induced by a focused pattern of surface gravity waves is studied at a beach adjacent to a major inlet with a large ebb tidal shoal. Using a coupled wave and wave-averaged nearshore circulation model, it is found that the nearshore circulation is significantly affected by the heterogeneous wave patterns caused by wave refraction over the ebb tidal shoal. The model is used to predict waves and currents during field experiments conducted near the mouth of San Francisco Bay and nearby Ocean Beach. The field measurements indicate strong spatial variations in current magnitude and direction and in wave height and direction along Ocean Beach and across the ebb tidal shoal. Numerical simulations suggest that wave refraction over the ebb tidal shoal causes wave focusing toward a narrow region at Ocean Beach. Due to the resulting spatial variation in nearshore wave height, wave-induced setup exhibits a strong alongshore nonuniformity, resulting in a dramatic change in the pressure field compared to a simulation with only tidal forcing. The analysis of momentum balances inside the surf zone shows that, under wave conditions with intensive wave focusing, the alongshore pressure gradient associated with alongshore nonuniform wave setup can be a dominant force driving circulation, inducing heterogeneous alongshore currents. Pressure-gradient-forced alongshore currents can exhibit flow reversals and flow convergence or divergence, in contrast to the uniform alongshore currents typically caused by tides or homogeneous waves.

Wave-induced setup of the mean surface over a sloping beach

A new theoretical approach for the wave-induced setup over a sloping beach is presented that takes into consideration the explicit variations of the surface waves due to bottom slope and viscosity. In this way, the wave forcing of the mean Lagrangian volume fluxes is calculated without assuming that the local depth is constant. The analysis is valid in the region outside the surf zone and is based on the shallow-water assumption. A novel approach for separating the viscous damping of the waves from the frictional damping of the mean flow is introduced, where the mean Eulerian velocity is applied in the bottom stress for the mean fluxes. In the case where the onshore Lagrangian mean transport is zero, a new formula is derived for the Eulerian mean free surface slope, in which the effects of bottom slope, viscous wave damping and frictional bottom drag on the mean flow are clearly identified. The analysis suggests that viscous damping of the waves and frictional dissipation of the Eulerian near-bed return flow could lead to setup outside the surf zone.

A modeling-based analysis of processes driving wave-dominated inlets

Among the different types of tidal inlets, wave-dominated inlets have been subjected to few quantitative studies, so that the physical processes controlling their dynamics are not fully understood. This study presents the application of a coastal area morphodynamic modeling system to a wave-dominated inlet (Óbidos Inlet, western coast of Portugal), in order to investigate the physical processes responsible for channel development during fair weather conditions and shoaling during periods of larger waves. The modeling system was able to reproduce reasonably well morphological changes at the Óbidos Inlet and subsequent tidal amplitude evolutions inside the lagoon over a period which includes 3 months of fair weather conditions, followed by 2 months representative of winter conditions. The inlet development during fair weather conditions was attributed to the strong ebb-dominance of the main channel without waves, enhanced by the combination of shallow channels and a meso-tidal range. The inlet infilling during the maritime winter was attributed to three main wave-induced mechanisms: (1) the onshore component of wave radiation stresse gradients, which is not fully compensated by the wave-induced setup in front of the inlet; (2) the acceleration and convergence of longshore transport toward the inlet, due to the presence of a strong lateral gradient in free surface elevation on both sides of the inlet, and, to a smaller extent, to wave refraction around the ebb-delta; and (3) the increase in mean water level inside the lagoon, which reduces tidal asymmetry and subsequent ebb-dominance.

Wave-adjusted boundary condition for longshore current in finite-volume circulation models

Numerical modeling of coastal circulation encompassing the nearshore requires forcing by tide, surface gravity waves, and possibly other factors. In the nearshore, the wave-induced longshore current and setup are dominant hydrodynamic processes, and lateral boundary conditions representing tide and oceanic forcing typically do not include surface-wave contributions. Without proper boundary conditions, significant gradients in current and water level can occur that contaminate the solution in the internal domain. A standard strategy is to place the boundaries far from the site of interest, but this strategy greatly increases computational demands, and it may not be appropriate for long-term simulations. This paper describes a wave-adjusted boundary condition that accounts for wave-induced water level and current acting in combination with tidal forcing. The wave-adjusted boundary condition is demonstrated for an idealized case of a parallel-contour beach and for an engineering application at Ocean City, MD.

A simple new shoreline change model

A simple new shoreline change model has been developed and calibrated/evaluated with several sets of high quality field data. The model is based upon the general observation that the shoreline tends to approach an equilibrium position exponentially with time when subjected to constant forcing. The model represents the shoreline response to cross-shore processes only and is extremely efficient, requiring only readily obtainable wave and water-level data as input. Shoreline changes are forced by changes in the local water surface elevation due to a combination of local tide, storm surge and wave-induced setup. The model contains three adjustable parameters, representing a baseline condition from which equilibrium shoreline displacements are calculated, and two rate constants, all of which are evaluated by minimizing the error between model hindcasts and several historical shoreline data sets. Several possible forms for the rate parameters, incorporating local wave and sediment properties, were considered and evaluated. At most sites, the model has proven successful in predicting large-scale shoreline response to local water level and wave forcing. The combination of model accuracy and efficiency, along with the minimal data required to drive the model, make it a potentially useful tool in many coastal engineering applications. As more high-quality shoreline, wave and water-level data sets become available, significant improvements can be made in the determination of the rate parameter governing the time scale of the beach response.

On the modelling of wave breaking and set-up on coral reefs

An extended refraction–diffraction equation [Massel, S.R., 1993. Extended refraction–diffraction equation for surface waves. Coastal Eng. 19, 97–126] has been applied to predict wave transformation and breaking as well as wave-induced set-up on two-dimensional reef profiles of various shapes. A free empirical coefficient α in a formula for the average rate of energy dissipation 〈ϵ b 〉=(αρgω/8π)( gh /C)(H 3/h) in the modified periodic bore model was found to be a function of the dimensionless parameter F c0=( g 1.25 H 0 0.5 T 2.5)/ h r 1.75, proposed by Gourlay [Gourlay, M.R., 1994. Wave transformation on a coral reef. Coastal Eng. 23, 17–42]. The applicability of the developed model has been demonstrated for reefs of various shapes subjected to various incident wave conditions. Assuming proposed relationships of the coefficient α and F c0, the model provides results on wave height attenuation and set-up elevation which compare well with experimental data.

Intertidal beach profile estimation using video images

In this paper, we present a technique suitable for measurement of intertidal bathymetry over a broad range of length scales (10 1 to 10 3 m) and time scales (days to decades). A series of time-averaged images of the swash zone are used to map contour lines of the beach surface. In each image, contours are identified using bands of maximum brightness associated with breaking waves at the shoreline. By mapping the location of these bands in a sequence of images collected over one tidal cycle, contour maps of the intertidal bathymetry are generated. We expect this technique to work best (smallest absolute error) under waves which are nearly reflective at the shoreline, but break enough to be observed visually. This is typical of a barred beach since the wave height at the shoreline is limited by wave breaking over the bar crest. The ability of the measurements made with this technique to resolve actual beach elevation variation depends on the ratio of the measurement error variance to the true beach elevation variance. Thus, large measurement errors may be compensated by either large tidal ranges or large temporal changes of the beach itself. In a comparison to bathymetry surveyed using a Differential Global Positioning System (DGPS) during the Duck94 experiment, in Duck, N.C., the image-based elevation estimates were well correlated with the actual bathymetry. The deviations (imagebased vs. DGPS measurements) may be partially attributed to effects scaled by wave height at the shoreline, wave-induced setup, and wave height saturation over the sand bar. In particular, setup was important during dissipative conditions. The rms deviation (vertical) between the DGPS and image-based bathymetry was reduced from 0.24 m to 0.06 m by correcting for the systematic deviations due to variations in setup and wave height saturation. Further improvement of the elevation estimates resulted from parameterizing the actual bathymetry with a simple plane beach surface, which reduced random (or unresolvable) measurement errors. This led to estimates of the beach slope that were accurate to within 10% of the actual slope and estimates of the cross-shore location of the mean sea level line accurate to about 0.50 m.

One-dimensional modelling of individual waves and wave-induced longshore currents in the surf zone

A probabilistic model ( Wavis-model) was developed to describe the propagation and transformation of individual waves (wave by wave approach). The individual waves shoal until an empirical criterion for breaking is satisfied. Wave height decay after breaking is modelled by using an energy dissipation method. Wave-induced set-up and set-down and breaking-associated longshore currents are also modelled. Laboratory and field data were used to calibrate and verify the model. The model was calibrated by adjusting the wave breaking coefficient (as a function of local wave steepness and bottom slope) to obtain optimum agreement between measured and computed wave height. Four tests carried out in the large Delta flume of Delft Hydraulics were considered. Generally, the measured H 1 3 -wave heights are reasonably well represented by the model in all zones from deep water to the shallow surf zone. The fraction of breaking waves was reasonably well represented by the model in the upsloping zones of the bottom profile. Verification of the model results with respect to wave-induced longshore current velocities was not extensive, because of a lack of data. In case of a barred profile the measured longshore velocities showed a relatively uniform distribution in the (trough) zone between the bar crest and the shoreline, which could to some extent be modelled by including space-averaging of the radiation force gradient, horizontal mixing and longshore water surface gradients related to variations in set-up. In case of a monotonically upsloping profile the cross-shore distribution of the longshore current velocities is reasonably well represented.

Equilibrium slopes and cross-shore velocity asymmetries in a storm-dominated, barred nearshore system

The near-bed (0.10 m elevation), horizontal velocities were measured across a two-barred, lacustrine shoreface during a storm and reveal a spatially coherent but temporally variable pattern in the low-order moments of the velocity field. Large cross-shore velocity asymmetries indicated: 1. (1) Spatially extensive and temporally persistent offshore mean flows (up to 0.18 m s −1 across the landward slope of the linear outer bar) reflecting an undertow driven by a wave-induced setup. 2. (2) An onshore directed skewness opposing the mean flow, of wind wave origin and persistent under propagating bores in the inner bar system long after this asymmetry had disappeared from the outer bar. Extensive sediment reactivation with near-zero net sediment flux over the whole of the upper shoreface indicated a sediment prism in a steady state (volumetrically) over the storm cycle. Uniform depths of sediment reactivation with zero bed elevation change over the storm cycle revealed local slopes in a steady state in the outer linear bar. However, time integration of the near-bed velocity field at this location indicated an offshore net flux of water, while sedimentary structures indicated bedform migration (and thus at least bedload) almost uniformly onshore when ripples and megaripples were present. The sediment transport giving rise to the local equilibrium cannot be explained therefore on the basis of the mean properties of the near-bed velocity vector, but requires knowledge of the time-varying, instantaneous sediment transport vector. Onshore migration of the inner bar correlated well with the large and persistent onshore skewness of the velocity distribution in the inner surf zone associated with translatory surf bores throughout the storm decay period. Low-frequency oscillations were only significant close to the shoreline, but may have influenced the development of a sinuous three-dimensional inner bar form as it migrated onshore.

Numerical modelling of wave-induced currents in the presence of coastal structures

The hydrodynamic aspects of the general methodology of calculation of nearshore processes by means of numerical models are described. The paper focuses on the method implemented for calculating combined wave refraction-diffraction and reflection due to coastal structures and the associated radiation stresses. Results of numerical modelling are compared with experimental data obtained by Gourlay in the case of a shore-connected breakwater with periodic waves. A good agreement is found between both methods of investigation as concerns the spatial distribution of wave height and mean water level (wave-induced set-up). A good similarity of the wave-induced eddies in the lee of the structure is observed. A less satisfactory agreement is obtained between the velocity distributions in several profiles normal to the shore, although the overall order of magnitude is the same. A critical review of several wave-breaking criteria and sensitivity tests of the numerical model lead to advocate the use of the CERC criterion, particularly with steep beach slopes.

Wave Setup and Design Water Level

During the winter of 1975-76 measurements were made by the Leichtweiss-Institut of the Technical University of Braunschweig at the west coast of the island of Sylt in the North Sea. The purpose of the field investigations was to determine the wave-induced setup in the surf zone and on the beach, defined as the height difference between the mean water level (MWL) and the still water level (SWL) and the influence of typical offshore parameters on this phenomenon. A new scheme was defined to determine the MWL as the mean value of the water surface variations measured at incremental time intervals over a certain time span. The maximum setup on the beach can reach values up to 30% of the incident significant wave height. The field investigations have shown that the rise of the mean water level due to wave setup is significant and should be taken in account in determining the design water level for coastal structures.

RIP CURRENTS AND THEIR CAUSES

"The outworn dogmas of science seem to be particularly concentrated in the discussions of the ocean in geology books". Beginning with this controversial statement, F. P. Shepard in 1936 tried to lay to rest the concept of the undertow, which had been debated in the pages of Science for over a decade. At the same time, he introduced the term, rip current, to describe the rapidly seaward-flowing currents, which were well-known to lifeguards at that time, as these currents were responsible for carrying swimmers offshore at frightening speeds. Subsequent studies by Shepard and his colleagues (Shepard, Emery and LaFond, 1941; Shepard and Inman, 1950a, 1950b) showed that rip currents (1) are caused by longshore variations in incident wave height, (2) are often periodic in both time and in the longshore direction and (3) increase in velocity with increasing wave height. The major reason put forth to explain the variation in wave height was the convergence or divergence of wave rays over offshore bottom topography (such as submarine canyons) or the forced wave height variability caused by coastal structures, such as jetties. McKenzie (1958) and Cooke (1970) in their studies corroborated the findings of the Scripps Institution of Oceanography researchers and also pointed out the persistence of rip currents (once high energy waves in a storm had caused rip channels to be cut into the bottom) after the storm had abated. In fact it appears that on coastlines which are affected by major storms which build offshore bars, that the nearshore circulation may be dominated by the storm-1-induced bottom topography for long afterwards. The researchers up to the late 1960's who attempted to theoretically model rip currents knew the importance of longshore wave height variability and the wave-induced set-up in the formation of rip currents, but it was not until Longuet-Higgins and Stewart (e.g., 1964) codified the wave momentum flux tensor that great strides were made in providing models for rip currents. This paper is intended to categorize and review the more recent theories for rip current generation and to discuss a simple model for rip currents on barred coastlines.

Wave set-up on coral reefs

Momentum flux considerations give reasonably good predictions on the amount of wave-induced set-up to be expected on coral reefs. It is possible that water levels on the outer edge of sea-level reefs may be raised as much as 20% of the incident wave height above the mean water level just seaward of the reef. Such wave set-up can significantly affect circulation and sediment behavior in the coral reef environment.