Radiation Stress Gradients Research Articles

The wave-current interaction in the coastal area

In our investigation of the effect of wind-waves on barotropic mean flow in coastal areas, we compare two methods for calculating wave-induced force. The wave field is simulated by the nearshore spectral wave model SWAN. The wave-induced force (calculated using the radiation stress gradient and dissipation methods) and the Stokes drift are integrated in the COHERENS circulation model in the depth-averaged mode. The coupled set is validated using well-known academic test cases of planar beach and single-barred beach. Finally, in a two-dimensional test case based on Belgian coastal waters we compare simulations of mean flow using the two methods of calculating waveinduced force against field data.<br/> We show clearly that the two methods for calculation of wave-induced force yield very different results even in depth-averaged mode, depending on the angle of incident wave. Simulation of waveinduced circulation using the wave dissipation approach gives better results than using the radiation stress gradient approach. This is clearly visible for strong wave conditions in which the wind is blowing almost parallel to the shore. Under these conditions, the white-capping type of wave breaking is the dominant dissipation mechanism; in the radiation stress gradient, the dissipation signal is not visible, because the energy loss in the spectrum is compensated by wind input.

TIME-VARYING WAVE EFFECTS ON FLOWS AND DYNAMICS AT AN UNSTRATIFIED INLET

Surface gravity waves alter discharge and circulation near and within coastal inlets, affecting the exchange and transport of water masses, nutrients, sediments, and pollutants between inland waters and the ocean. Field observations and numerical simulations suggest that, during storms, wave forcing (radiation-stress gradients) owing to wave dissipation across the ebb shoal can enhance fluxes into the inlet (Bertin et al. 2009; Wargula et al. 2014). As a result, water levels may increase inside the bay (Olabarrieta et al. 2011; Dodet et al. 2013), creating an offshore-directed pressure gradient that may balance onshore fluxes during energetic waves, and may enhance offshore fluxes after the waves decrease. Spatial and tidal variability in water depths on the ebb shoal lead to complex wave breaking patterns that drive spatially and tidally asymmetric flows. Here, field observations and numerical simulations are used to evaluate the effects of waves on discharge and circulation, and the relative importance of wave radiation-stress and pressure gradients at an unstratified inlet during and following energetic waves.

The impact of wave energy converter arrays on wave-induced forcing in the surf zone

An alternative metric for assessing nearshore hydrodynamic impact due to Wave Energy Converter (WEC) arrays is presented that is based on the modeled changes in alongshore radiation stress gradients in the lee of the array. The metric is developed using a previously observed relationship between measured radiation stresses and alongshore current magnitudes. Next, a parametric study is conducted using the spectral model SWAN to analyze the nearshore impact of different WEC array designs. A realistic range of array configurations, locations, and incident wave conditions are examined and conditions that generate alongshore radiation stress gradients exceeding a chosen impact threshold on a uniform beach are identified. Finally, the methodology is applied to two permitted WEC test sites to assess the applicability of the results to sites with more realistic bathymetries. For these sites, the overall trends seen in the changes in wave height, direction, and radiation stress gradients in the lee of the array are similar to those seen in the parametric study. However, interactions between the wave field and real bathymetry induce additional alongshore variability in wave-induced forcing. Results indicate that array-induced changes can exceed the natural variability up to 15% of the time with certain array designs and locations.

Forecasting Storm Surge and Inundation: Model Validation

Abstract Coastal regions are increasingly vulnerable to damage from storm surge and inundation. Delft3D is used by the Naval Oceanographic Office to model the ocean dynamics in the near shore. In this study, the performance of Delft3D in predicting the surge and inundation during Hurricane Ike, which impacted the northern Gulf of Mexico in September 2008, is examined. Wave height, water level, and high-water mark comparisons with a number of observations confirm that the model does well in predicting the surge and inundation during extreme events. The impact of using forecast winds based on the best-track data as opposed to hindcast winds is also investigated, and it is found that the extent of inundation is represented reasonably well with the forecast winds. In Delft3D, waves can be coupled to the hydrodynamic component using the radiation stress gradient method or the dissipation method. Comparing the results of using the two shows that for low-resolution grids such as that needed for a forecast model the dissipation method works better at reproducing the water levels and inundation.

Assessing storm surge hazard and impact of sea level rise in the Lesser Antilles case study of Martinique

Abstract. In the Lesser Antilles, coastal inundations from hurricane-induced storm surges pose a great threat to lives, properties and ecosystems. Assessing current and future storm surge hazards with sufficient spatial resolution is of primary interest to help coastal planners and decision makers develop mitigation and adaptation measures. Here, we use wave–current numerical models and statistical methods to investigate worst case scenarios and 100-year surge levels for the case study of Martinique under present climate or considering a potential sea level rise. Results confirm that the wave setup plays a major role in the Lesser Antilles, where the narrow island shelf impedes the piling-up of large amounts of wind-driven water on the shoreline during extreme events. The radiation stress gradients thus contribute significantly to the total surge – up to 100 % in some cases. The nonlinear interactions of sea level rise (SLR) with bathymetry and topography are generally found to be relatively small in Martinique but can reach several tens of centimeters in low-lying areas where the inundation extent is strongly enhanced compared to present conditions. These findings further emphasize the importance of waves for developing operational storm surge warning systems in the Lesser Antilles and encourage caution when using static methods to assess the impact of sea level rise on storm surge hazard.

Effects of wave-current interaction on storm surge in the Taiwan Strait: Insights from Typhoon Morakot

The effects of wave-current interaction on storm surge are investigated by a two-dimensional wave-current coupling model through simulations of Typhoon Morakot in the Taiwan Strait. The results show that wind wave and slope of sea floor govern wave setup modulations within the nearshore surf zone. Wave setup during Morakot can contribute up to 24% of the total storm surge with a maximum value of 0.28m. The large wave setup commonly coincides with enhanced radiation stress gradient, which is itself associated with transfer of wave momentum flux. Water levels are to leading order in modulating significant wave height inside the estuary. High water levels due to tidal change and storm surge stabilize the wind wave and decay wave breaking. Outside of the estuary, waves are mainly affected by the current-induced modification of wind energy input to the wave generation. By comparing the observed significant wave height and water level with the results from uncoupled and coupled simulations, the latter shows a better agreement with the observations. It suggests that wave-current interaction plays an important role in determining the extreme storm surge and wave height in the study area and should not be neglected in a typhoon forecast.

Assessing the performance of formulations for nonlinear feedback of surface gravity waves on ocean currents over coastal waters

This study presents applications of a two-way coupled wave-circulation modelling system over coastal waters, with a special emphasis of performance assessments of two different methods for nonlinear feedback of ocean surface gravity waves on three-dimensional (3D) ocean currents. These two methods are the vortex force (VF) formulation suggested by Bennis et al. (2011) and the latest version of radiation stress (RS) formulation suggested by Mellor (2015). The coupled modelling system is first applied to two idealized test cases of surf-zone scales to validate implementations of these two methods in the coupled wave-circulation system. Model results show that the latest version of RS has difficulties in producing the undertow over the surf zone. The coupled system is then applied to Lunenburg Bay (LB) of Nova Scotia during Hurricane Juan in 2003. The coupled system using both the VF and RS formulations generates much stronger and more realistic 3D circulation in the Bay during Hurricane Juan than the circulation-only model, demonstrating the importance of surface wave forces to the 3D ocean circulation over coastal waters. However, the RS formulation generates some weak unphysical currents outside the wave breaking zone due to a less reasonable representation for the vertical distribution of the RS gradients over a slopping bottom. These weak unphysical currents are significantly magnified in a two-way coupled system when interacting with large surface waves, degrading the model performance in simulating currents at one observation site. Our results demonstrate that the VF formulation with an appropriate parameterization of wave breaking effects is able to produce reasonable results for applications over coastal waters during extreme weather events. The RS formulation requires a complex wave theory rather than the linear wave theory for the approximation of a vertical RS term to improve its performance under both breaking and non-breaking wave conditions.

Contributions to the wave-mean momentum balance in the surf zone

Mean (wave-averaged) cross-shore flow in the surfzone has a strong vertical variation. Good understanding and prediction of this mean velocity profile is of crucial importance, as it determines the advective transport of constituents, such as sediment, and consequently the coastal morphological evolution. Most modeling systems for coastal hydrodynamics and morphodynamics do no resolve the wave motion, and wave-current coupling is a challenging topic. This paper investigates stresses and forces that control mean surfzone hydrodynamics based on detailed wave flume velocity measurements above a fixed sloping bed including two breaker bars. The data show that the vertical distribution of normal stress below the wave trough level is fairly uniform. At the same time, the data suggest that a significant part is concentrated between the wave trough and crest level. Furthermore, it is concluded that the horizontal radiation stress gradients and the vertical shear stress gradients can be of the same order of magnitude in the vicinity of the breaker bar. Although usually ignored in 3D mean flow modeling systems, the wave Reynolds stress makes an important contribution to the mean shear stress. The normal stress below the wave trough level could be reasonably well predicted using the classical [16] expression, accounting for the contribution between wave crest and trough. The model of [39] reproduces the main trends in the wave Reynolds stresses above the bottom boundary layer.

Tide-surge and wave interaction in the Gulf of Maine during an extratropical storm

The fully coupled spectral wave and circulation model SWAN + ADCIRC was applied to investigate tide-surge and wave interaction in the Gulf of Maine during the extratropical storm on Patriot’s Day of 2007. Significant tide-surge and wave interaction was found over Georges Bank and in the coastal areas. Over Georges Bank, the wave-induced current reached 0.2 m/s at the storm peak, accounting for 17 % of the total depth-averaged current. In Saco Bay, the current was dominated by wave-induced current with a magnitude up to 1.0 m/s during the storm. Two clockwise circulation gyres were found to form and sustain over a period of 26 hours during the storm in the bay. They were driven by spatial variations of wave height, direction and the resulting wave radiation stress gradient. Wave setup reached 0.2 m at the storm peak along the coast of Saco Bay. In Saco Bay, wave energy dissipation was reduced and wave height increased due to the increased water depth at high tide and surge. Therefore, wave height was modulated by tide and surge accordingly along the coast. As a result, wave setup and wave-induced current in the bay were also modulated by tide and surge. During the tidal cycle at the storm peak, wave setup increased with tidal level and the maximum wave setup coincided with high tide.

Wave Setup over a Fringing Reef with Large Bottom Roughness

AbstractThe effect of bottom roughness on setup dynamics was investigated using high-resolution observations across a laboratory fringing reef profile with roughness elements scaled to mimic the frictional wave dissipation of a coral reef. Results with roughness were compared with smooth bottom runs across 16 offshore wave and still water level conditions. The time-averaged and depth-integrated force balance was evaluated from observations collected at 17 locations along the flume and consisted of cross-shore pressure and radiation stress gradients whose sum was balanced by quadratic mean bottom stresses. The introduction of roughness had two primary effects. First, for runs with roughness, frictional wave dissipation occurred on the reef slope offshore of the breakpoint, reducing wave heights prior to wave breaking. Second, offshore-directed mean bottom stresses were generated by the interaction of the combined wave–current velocity field with the roughness elements. These two mechanisms acted counter to one another. Frictional wave dissipation resulted in radiation stress gradients that were predicted to generate 18% (on average) less setup on the reef flat for rough runs than for smooth runs when neglecting mean bottom stresses. However, mean bottom stresses increased the predicted setup by 16% on average for runs with roughness. As a result, setup on the reef flat was comparable (7% mean difference) between corresponding rough and smooth runs. These findings are used to assess prior results from numerical modeling studies of reefs and also to discuss the broader implications for how large roughness influences setup dynamics in the nearshore zone.

Alongshore momentum transfer to the nearshore zone from energetic ocean waves generated by passing hurricanes

AbstractWave and current measurements from a cross‐shore array of nearshore sensors in Duck, NC, are used to elucidate the balance of alongshore momentum under energetic wave conditions with wide surf zones, generated by passing hurricanes that are close to and far from to the coast. The observations indicate that a distant storm (Hurricane Bill, 2009) with large waves has low variability in directional wave characteristics resulting in alongshore currents that are driven mainly by the changes in wave energy. A storm close to the coast (Hurricane Earl, 2010), with strong local wind stress and combined sea and swell components in wave energy spectra, has high variability in wave direction and wave period that influence wave breaking and nearshore circulation as the storm passes. During both large wave events, the horizontal current shear is strong and radiation stress gradients, bottom stress, wind stress, horizontal mixing, and cross‐shore advection contribute to alongshore momentum at different spatial locations across the nearshore region. Horizontal mixing during Hurricane Earl, estimated from rotational velocities, was particularly strong suggesting that intense eddies were generated by the high horizontal shear from opposing wind‐driven and wave‐driven currents. The results provide insight into the cross‐shore distribution of the alongshore current and the connection between flows inside and outside the surf zone during major storms, indicating that the current shear and mixing at the interface between the surf zone and shallow inner shelf is strongly dependent on the distance from the storm center to the coast.

Numerical study of wave–current–vegetation interaction in coastal waters

Research on interactions among wave, current, and vegetation has received increasing attention. An explicit depth-averaged hydrodynamic model coupled with a wave spectral model (CMS-wave) was proposed in this study in order to simulate the wave and wave-induced current in coastal waters. The hydrodynamic model was based on the finite volume method while the intercell flux was computed by employing the Harten–Lax–van Leer approximate Riemann solver to investigate the dry-to-wet interface, and the drag force of vegetation was modeled as the sink terms in the momentum equations. The CMS-wave model was used to investigate the non-breaking and the breaking random waves propagation in vegetation fields. Afterwards, an empirical wave energy dissipation term with plant effect was derived to represent the resistance induced by aquatic vegetation in the wave-action balance equation. The established model was calibrated and validated with both the experimental and field data. The results showed that the wave height decreased significantly along the wave propagation direction in the presence of vegetations. The sensitivity analysis for the plant density, the wave height, and the water depth were performed by comparing the numerical results for the wave height attenuation. In addition, wave and wave-induced current through a finite patch of vegetation in the surf zone were investigated as well. The strong radiation stress gradient could be produced due to the variation of the energy dissipation by vegetation effect in the nearshore zone, which impacted the direction and amplitude of the longshore current. The calculated results showed that the coupling model had good performance in predicting wave propagation and the current over vegetated water regions.

Application of SWAN+ADCIRC to tide-surge and wave simulation in Gulf of Maine during Patriot's Day storm

The southern coast of the Gulf of Maine in the United States is prone to flooding caused by nor'easters. A state-of-the-art fully-coupled model, the Simulating WAves Nearshore (SWAN) model with unstructured grids and the ADvanced CIRCulation (ADCIRC) model, was used to study the hydrodynamic response in the Gulf of Maine during the Patriot's Day storm of 2007, a notable example of nor'easters in this area. The model predictions agree well with the observed tide-surges and waves during this storm event. Waves and circulation in the Gulf of Maine were analyzed. The Georges Bank plays an important role in dissipating wave energy through the bottom friction when waves propagate over the bank from offshore to the inner gulf due to its shallow bathymetry. Wave energy dissipation results in decreasing significant wave height (SWH) in the cross-bank direction and wave radiation stress gradient, which in turn induces changes in currents. While the tidal currents are dominant over the Georges Bank and in the Bay of Fundy, the residual currents generated by the meteorological forcing and waves are significant over the Georges Bank and in the coastal area and can reach 0.3 m/s and 0.2 m/s, respectively. In the vicinity of the coast, the longshore current generated by the surface wind stress and wave radiation stress acting parallel to the coastline is inversely proportional to the water depth and will eventually be limited by the bottom friction. The storm surge level reaches 0.8 m along the western periphery of the Gulf of Maine while the wave set-up due to radiation stress variation reaches 0.2 m. Therefore, it is significant to coastal flooding.

Dynamics of Wave Setup over a Steeply Sloping Fringing Reef

AbstractHigh-resolution observations from a 55-m-long wave flume were used to investigate the dynamics of wave setup over a steeply sloping reef profile with a bathymetry representative of many fringing coral reefs. The 16 runs incorporating a wide range of offshore wave conditions and still water levels were conducted using a 1:36 scaled fringing reef, with a 1:5 slope reef leading to a wide and shallow reef flat. Wave setdown and setup observations measured at 17 locations across the fringing reef were compared with a theoretical balance between the local cross-shore pressure and wave radiation stress gradients. This study found that when radiation stress gradients were calculated from observations of the radiation stress derived from linear wave theory, both wave setdown and setup were underpredicted for the majority of wave and water level conditions tested. These underpredictions were most pronounced for cases with larger wave heights and lower still water levels (i.e., cases with the greatest setdown and setup). Inaccuracies in the predicted setdown and setup were improved by including a wave-roller model, which provides a correction to the kinetic energy predicted by linear wave theory for breaking waves and produces a spatial delay in the wave forcing that was consistent with the observations.

Radar Remote Sensing Estimates of Waves and Wave Forcing at a Tidal Inlet

AbstractThe time and space variability of wave transformation through a tidal inlet is investigated with radar remote sensing. The frequency of wave breaking and the net wave breaking dissipation at high spatial resolution is estimated using image sequences acquired with a land-based X-band marine radar. Using the radar intensity data, transformed to normalized radar cross section σ0, the temporal and spatial distributions of wave breaking are identified using a threshold developed via the data probability density function. In addition, the inlet bathymetry is determined via depth inversion of the radar-derived frequencies and wavenumbers of the surface waves using a preexisting algorithm (cBathy). Wave height transformation is calculated through the 1D cross-shore energy flux equation incorporating the radar-estimated breaking distribution and bathymetry. The accuracy of the methodology is tested by comparison with in situ wave height observations over a 9-day period, obtaining correlation values R = 0.68 to 0.96, and root-mean-square errors from 0.05 to 0.19 m. Predicted wave forcing, computed as the along-inlet gradient of the cross-shore radiation stress was onshore during high-wave conditions, in good agreement (R = 0.95) with observations.

Modeled alongshore circulation and force balances onshore of a submarine canyon

AbstractAlongshore force balances, including the role of nonlinear advection, in the shoaling and surf zones onshore of a submarine canyon are investigated using a numerical modeling system (Delft3D/SWAN). The model is calibrated with waves and alongshore flows recorded over a period of 1.5 months at 26 sites along the 1.0, 2.5, and 5.0 m depth contours spanning about 2 km of coast. Field observation‐based estimates of the alongshore pressure and radiation‐stress gradients are reproduced well by the model. Model simulations suggest that the alongshore momentum balance is between the sum of the pressure and radiation‐stress gradients and the sum of the nonlinear advective terms and bottom stress, with the remaining terms (e.g., wind stress and turbulent mixing) being negligible. The simulations also indicate that unexplained residuals in previous field‐based estimates of the momentum balance may be owing to the neglect of the nonlinear advective terms, which are similar in magnitude to the sum of the forcing (pressure and radiations stress gradients) and to the bottom stress.

The contribution of short-waves in storm surges: Two case studies in the Bay of Biscay

This study investigates the contributions of short waves in storm surges through the hindcast of two storms that hit the central part of the Bay of Biscay recently. Despite displaying comparable wind speed and directions in the study area, these two storms induced different storm surges and sea states. Xynthia (27–28th of February 2010) was characterized by large (up to 7m significant wave height Hs) and short-period waves and induced an exceptional storm surge, locally larger than 1.6m. The second storm, Joachim (15–16th of December 2011), was characterized by very large (up to Hs>10m) and long-period waves but only induced a storm surge almost two times lower. To investigate these differences, a new unstructured grid and fully coupled modeling system is applied, with a spatial resolution fine-enough to adequately represent the surf zones over most of the study area (25m). The analysis of the modeling results and the available field observations reveals firstly that the exceptional surge during Xynthia originated from young and steep waves, enhancing surface stress. This particular sea-state is explained by the abnormal track of Xynthia, which restricted the fetch to a few hundred km. The wave radiation stress gradient locally induced setup larger than 0.4m along the coastlines fully exposed to ocean waves, while wave setup in the range 0.1–0.2m was also shown to develop regionally and to propagate in sheltered harbors. Comparatively, wave-enhanced bottom stress appears to be a second-order process and has a more limited impact on storm surges.

Field observations of wave‐driven circulation over spur and groove formations on a coral reef

AbstractSpur and groove (SAG) formations are found on the forereefs of many coral reefs worldwide. Modeling results have shown that SAG formations together with shoaling waves induce a nearshore Lagrangian circulation pattern of counter‐rotating circulation cells, but these have never been observed in the field. We present results from two separate field studies of SAG formations on Palmyra Atoll which show their effect on waves to be small, but reveal a persistent order 1 cm/s depth‐averaged Lagrangian offshore flow over the spur and onshore flow over the grooves. This circulation was stronger for larger, directly incident waves and low alongshore flow conditions, consistent with predictions from modeling. Favorable forcing conditions must be maintained on the order of 1 h to accelerate and develop the SAG circulation cells. The primary cross and alongshore depth‐averaged momentum balances were between the pressure gradient, radiation stress gradient, and nonlinear convective terms, and the bottom drag was similar to values found on other reefs. The vertical structure of these circulation cells was previously unknown and the results show a complex horizontal offshore Lagrangian flow over the spurs near the surface driven by alongshore variability in radiation stress gradients. Vertical flow was downward over the spur and upward over the groove, likely driven by alongshore differences in bottom stress and not by vortex forcing.

Observations of surfzone alongshore pressure gradients onshore of an ebb-tidal delta

The relative importance of radiation stress gradients and alongshore pressure gradients to surfzone dynamics is investigated using observations of water levels, waves, and flows measured onshore of a large ebb-tidal delta. Incident wave heights measured along the ~11-m depth contour varied about 10% over a 1.2-km alongshore transect, resulting in alongshore wave setup differences on the order of 10cm over the 600-m extent of the surfzone instrument array in 1.5-m depth. Despite the moderate alongshore variability in wave heights, the southerly alongshore pressure gradient, associated with the alongshore variability of wave-driven set-up, was typically twice as large as the northerly radiation stress gradient forcing, consistent with the observed southerly currents during the week-long experiment. The magnitude of the alongshore forcing and resulting alongshore velocity is reproduced by the two-dimensional depth-averaged numerical model of Shi et al. (JGR-Oceans, 2011). These observations, together with the numerical results, indicate that moderate alongshore wave height gradients (O(10−4)) outside the surfzone owing to alongshore variations in the offshore bathymetry can result in alongshore pressure gradients that are larger than radiation stress gradients.

Numerical Simulation of Nearshore Hydrodynamics and Sediment Transport Downdrift of a Tidal Inlet

AbstractNearshore hydrodynamics and sediment transport patterns induced by waves and tide adjacent to a structured tidal inlet with complex bathymetry are investigated to determine the potential causes of downdrift beach erosion. A coupled wave and hydrodynamic model is used to simulate the nearshore hydrodynamics and morphodynamics. Near the inlet, the tidal-induced pressure gradient dominates the wave radiation stress gradient only in the first half of the flood duration. The nearshore hydrodynamic pattern for the rest of the tidal cycle is driven mainly by the wave-driven pressure gradient. The wave-driven pressure gradient results from alongshore variation of water surface elevation induced by nearshore wave focal points caused by wave refraction over irregular bathymetry (with ebb tidal shoals and nonparallel shoreline depth contours). The resulting alongshore sediment transport patterns suggest that the direction of the time-averaged alongshore sediment transport rate near the inlet and at the downd...