Erosional equivalences of levees: Steady and intermittent wave overtopping

Present criteria for acceptable grass covered levee overtopping are based on average overtopping values but do not include the effect of overtopping duration. This paper applies experimental steady state results for acceptable overtopping to the case of intermittent wave overtopping. Laboratory results consisting of velocities and durations for acceptable land side levee erosion due to steady flows are examined to determine the physical basis for the erosion. Three bases are examined: (1) velocity above a threshold value, (2) shear stress above a threshold value, and (3) work above a threshold value. The work basis provides the best agreement with the data and a threshold work value and a work index representing the summation of the product of work above the threshold and time are developed. The governing equations for flow down the land side of a levee establish that the flows near the land side levee toe will be supercritical. Wave runup is considered to be Rayleigh distributed with the runup above the levee crest serving as a surrogate for overtopping. Two examples illustrating application of the methodology are presented. Example 1 considers three qualities of grass cover: good, average, and poor. The required levee elevations for these three covers differ by 1.8 m. The results for Example 1 are compared with the empirical criteria of 0.1 liters per second per meter (l/s per m), 1.0  l/s per m, and 10.0  l/s per m. It is found that the required crest elevation by the methodology recommended herein for the “poor” cover is only slightly lower than for the criterion for average overtopping of q=10.0  l/s per m but significantly lower than for the overtopping criterion of 1.0 and 0.1 m/s per m. Example 2 considers two durations of the peak surge with the result that the longer duration peak surge requires a levee that is higher by approximately 0.8 m.     

Reconstruction of Hurricane Katrina's wind fields for storm surge and wave hindcasting

As the most costly US natural disaster in history, Hurricane Katrina fostered the IPET forensic study to better understand the event. All available observations from several hundred space-, land-, sea-, and aircraft-based measurement platforms were gathered and processed to a common framework for height, exposure, and averaging time, to produce a series of wind field snapshots at 3 h intervals to depict the wind structure of Katrina when in the Gulf of Mexico. The stepped-frequency microwave radiometer was calibrated against GPS sondes to establish the upper range of the instrument and then used to determine the wind field in the storm's core region in concert with airborne Doppler radar winds adjusted to the surface from near the top of the PBL (500 m). The SFMR data were used to develop a method to estimate surface winds from 3 km level reconnaissance aircraft observations, taking into consideration the observed azimuthal variation of the reduction factor. The “SFMR method” was used to adjust reconnaissance flight-level measurements to the surface in the core region when SFMR and Doppler winds were not available. A variety of coastal and inland mesonet data were employed, including portable towers deployed by Texas Tech University, University of Louisiana at Monroe, and the Florida Coastal Monitoring Program, as well as fixed mesonet stations from Louisiana State Universities Marine Consortium, University of Southern Mississippi, and Agricultural Networks from Louisiana, Mississippi, and Alabama, and the Coastal Estuarine Network of Alabama and Mississippi. Also included were land- (WSR-88D VAD and GBVTD, ASOS, Metar, LLWAS, HANDAR), space- (QuikScat, GOES cloud drift winds, WindSat), and marine- (GPS sondes, Buoys, C-MAN, ships) platforms. The wind fields serve as an analysis of record and were used to provide forcing for wave and storm surge models to produce hindcasts of water levels in the vicinity of flood control structures.     

Numerical analysis of wave overtopping of rubble mound breakwaters

The paper describes the results of a two-dimensional (2-D) numerical modelling investigation of the functionality of rubble mound breakwaters with special attention focused on wave overtopping processes. The model, COBRAS-UC, is a new version of the COBRAS (Cornell Breaking Waves and Structures) based on the Volume Averaged Reynolds Average Navier–Stokes (VARANS) equations and uses a Volume of Fluid Technique (VOF) method to capture the free surface. The nature of the model equations and solving technique provides a means to simulate wave reflection, run-up, wave breaking on the slope, transmission through rubble mounds, overtopping and agitation at the protected side due to the combined effect of wave transmission and overtopping. Also, two-dimensional experimental studies are carried out to investigate the performance of the model. The computations of the free surface and pressure time series and spectra under regular and irregular waves, are compared with the experimental data reaching a very good agreement. The model is also used to reproduce instantaneous and average wave overtopping discharge. Comparisons with existing semi-empirical formulae and experimental data show a very good performance. The present model is expected to become in the near future an excellent tool for practical applications.     

The anatomy of a disaster, an overview of Hurricane Katrina and New Orleans

Hurricane Katrina created the one of the worst natural disaster in the history of the United States, resulting in over 1600 fatalities and $30B in direct economic losses in southern Louisiana. The Louisiana and Mississippi coastlines experienced the highest surge level recorded in North America and Katrina-generated waves in the Gulf of Mexico that equaled the highest previously measured by NOAA buoys. What happened in New Orleans epitomizes the risk of living below sea level in a coastal city, depending on structures that were the result of considerable compromise and piecemeal funding and construction. The Interagency Performance Evaluation Task Force was established to examine the performance of the New Orleans and southeast Louisiana hurricane protection system and provide real-time input to the repairs and rebuilding of the system. In addition to this atypical just-in-time forensic analysis, the task force examined the risk of living in New Orleans prior to and following the repairs to the hurricane protection system. Much of the forensic analysis depended on modeling and simulation of hurricane surge and waves. With virtually all measurement instruments swept away by Katrina, only models and high-water marks were available to recreate the conditions that the structures experienced during the storm. Because of the complexities of the region and the processes involved, simulation of hurricane surge and waves required many fresh ideas and new approaches and these topics, along with new concepts for future planning and design, are the focus of this special issue. Yet, the need to influence the repair and rebuilding of the damaged structures prior to the next hurricane season (roughly 9 months) dictated using existing computational tools that were ready to go. The same modeling and simulation approach was put to work to define the surge and wave hazard New Orleans faces for the future. To put this important body of work in context, this paper provides a broad overview of the entire scope of work of the task force and summarizes its principal findings.     

Physical model study of wave and current conditions at 17th Street Canal breach due to Hurricane Katrina

A 1:50 scale physical model was constructed for the 17th Street Canal region, New Orleans, on the southern coast of Lake Pontchartrain, as part of the Interagency Performance Evaluation Task Force (IPET) study of Hurricane Katrina. The purpose of the 1350 m² physical model that represented about 3.4 km² of the local area was to aid in defining wave and water velocity conditions in the 17th Street Canal during the time period leading up to the breaching of the floodwall within the Canal. In the immediate period following this disaster, there were many hypothesis of failure put forth in the media. Some of these hypothesis indicated wave action may have been the underlying cause of the failure of the 17th Street Canal floodwall. Some performed numerical work with inappropriate boundary conditions, which indicated strong wave-generated currents may have caused erosion along the floodwalls. This physical model study indicated a number of wave-attenuating processes occurring as waves approached the location of the breach. Wave height reduction resulted due to: (1) refraction of wave energy over the shallower submerged land areas surrounding the harbor away from the canal; (2) reflection of energy off vertical walls in the region between the entrance to the canal near the Coast Guard Harbor and the bridge; and (3) interaction of the wave with the Hammond Highway bridge, including reflection and transmission loss. Wave heights near the lakeside of the bridge were 0.3-0.9 m in height, reduced from 1.8 to 2.7 m wave heights in the open lake. Waves on the south side of the bridge, near the breach, were further reduced to heights below 0.3 m. These results supported the conclusion that waves were not a significant factor for the 17th Street Canal floodwall failure. Other IPET investigations determined floodwall failure was of a geotechnical nature due to the high surge water level. The physical model also provided calibration information for numerical wave models. The effects of debris on flow and waves after the breach was formed were also investigated.     

Boussinesq水波方程新型数值解法

为建立高效的Boussinesq类水波数值模型,提出了一种新型的、基于有限差分和有限体积方法的混合数值格式。针对守恒形式的一维控制方程,在等间距矩形控制体内对其进行积分并离散,采用有限体积方法计算界面数值通量,剩余源项采用有限差分方法计算。其中,采用MUSTA格式并结合高精度状态插值方法计算控制体界面数值通量。时间积分则采用具有TVD性质的三阶龙格-库塔多步积分法进行。除验证模型外,重点对MUSTA格式和广泛使用的HLL格式进行了比较。结果表明,MUSTA格式可用于Boussinesq类水波方程数值求解,综合考虑数值精度、计算效率、程序编制和实际应用这几个方面,其较HLL格式更具有优势。     

Numerical study for vegetation effects on coastal wave propagation by using nonlinear Boussinesq model

The vegetation has important impacts on coastal wave propagation. In the paper, the sensitivities of coastal wave attenuation due to vegetation to incident wave height, wave period and water depth, as well as vegetation configurations are numerically studied by using the fully nonlinear Boussinesq model. The model is based on the implementation of drag resistances due to vegetation in the fully nonlinear Boussinesq equation where the drag resistance is provided by the Morison’s formulation for rigid structure induced drag stresses. The model is firstly validated by comparing with the experimental results for wave propagation in vegetation zones. Subsequently, the model is used to simulate waves with different height, period propagating on vegetation zones with different water depth and vegetation configurations. The sensitivities of wave attenuation to incident wave height, wave period, water depth, as well as vegetation configurations are investigated based on the numerical results. The numerical results indicate that wave height attenuation due to vegetation is sensitive to incident wave height, wave period, water depth, as well as vegetation configurations, and attenuation ratio of wave height is increased monotonically with increases of incident wave height and decreases of water depth, while it is complex for wave period. Moreover, more vegetation segments can strengthen the interaction of vegetation and wave in a certain range.     

Spatial distribution of wave overtopping water behind coastal structures

Spatial distribution of random wave overtopping water behind coastal structures was investigated using a numerical model based on Reynolds-Averaged Navier-Stokes solver (RANS) and Volume of Fluid (VOF) surface capturing scheme (RANS-VOF). The computed spatial distributions of wave overtopping water behind the structure agree well with the measurements by Pullen et al (2008) for a vertical wall and Lykke Andersen and Burcharth (2006) for a 1:2 sea dike. A semi-analytical model was derived to relate spatial distribution of wave overtopping water behind coastal structures to landward ground level, velocity and layer thickness on the crest. This semi-analytical model agrees reasonably well with both numerical model results and measurements close to coastal structures. Our numerical model results suggest that the proportion of wave overtopping water passing a landward location increases with a seaward slope when it is less than 1:3 and decreases with a seaward slope when it gets steeper. The proportion of wave overtopping water passing a landward location increases with landward ground level and overtopping discharge. It also increases with the product of incident wave height and wavelength, but decreases with increasing relative structure freeboard and crest width. We also found that the extent of hazard area due to wave overtopping is significantly reduced by using a permeable structure crown. Findings in this study will enable engineers to establish the extent of hazard zones due to wave overtopping behind coastal structures.     

An application of Boussinesq equations to Bragg reflection of irregular waves

A numerical model based on the second-order fully nonlinear Boussinesq equations of Wei et al. [1995. Journal of Waterway, Port, Coastal and Ocean Engineering 121 (5), 251-263] is developed to simulate the Bragg reflection of both regular and irregular surface waves scattered by submerged bars. Particularly for incident regular waves, the computed results are observed to agree very well with the existing experimental data as presented by Davies and Heathershaw [1984. Journal of Fluid Mechanics 144, 419-446] and Kirby and Anton [1990. Proceedings of the 22nd International Conference on Coastal Engineering, ASCE, New York, pp. 757–768). In the case of incident irregular waves, the simulated results reveal that the distribution of Bragg reflection from irregular waves becomes more flat than that of regular waves. Due to lack of experimental data, the numerical results for incident irregular waves are compared with those of the evolution equation of the mild-slope equation [Hsu et al., 2002 Proceedings of the 24th Ocean Engineering Conference in Taiwan, pp. 70–77 (in Chinese)]. In addition, several parameters such as the number of bars, the relative height of bars and the spacing of bars affecting Bragg reflection are also discussed.     

Experimental study on mechanism of sea-dike failure due to wave overtopping

This work, which was largely a fruit of China's national marine hazard mitigation service, explicitly reveals the major mechanism of sea-dike failure during wave overtopping. A large group of wave-flume experiments were conducted for sea dikes with varying geometric characteristics and pavement types. The erosion and slide of the landward slope due to the combined effect of normal hit and great shear from overtopping flows was identified the major trigger of the destabilization of sea dikes. Once the intermittent hydrodynamic load and swash caused any deformation (bump or dent) of the pavement layer, pavement fractions (slabs or rubble) on the slope started to be initiated and removed by the water. The erosion of the landward slope was then gradually aggravated followed by entire failure within a couple of minutes. Hence, the competent velocity would be helpful evaluate the failure risk if as well accounted in standards or criteria. However, the dike top was measured experiencing the largest hydrodynamic pressure with a certain cap while the force on the wall increased rapidly as the overtopping intensity approached the dike-failure threshold. The faster increase of the force on the wall than on the landward slope yielded the sequencing of loads reaching hypothetic limits before failure as: dike top – top-mounted wall – landward slope. Therefore, beside the slide failure, the fatigue damage due to the instantaneous hydrodynamic impact might be another mechanism of the dike failure, which did not appear in the experiment but should be kept in mind. Instead of the widely adopted tolerable overtopping rate, a 0.117–0.424 m³/(m s) range of overtopping discharge and a 10 m/s overtopping velocity for the failure risk of typical sea dikes along China's coastlines were suggested, which enables the possible failure risk prediction through empirical calculations. The failure overtopping rate was identified strongly dependent on the pavement material, the landward slope and the dike-mounted wall but showed little variation with the width of the dike top. The flat concrete pavement and gentle landward slopes are suggested for the dike design and construction. For given configurations and hydrodynamic conditions in the experiment, the dike without the wall experienced less overtopping volume than those with the 1-m top-mounted wall. Meanwhile, the remove of the wall increased the failure overtopping rate, which means a certain increase of the failure criterion. Thus, care must be taken to conclude that the dike-mounted wall seems not an entirely appropriate reinforcement for the stability and safety of coastal protections. This should be further checked and discussed by researchers and engineers in the future.     

Development of storm surge which led to flooding in St. Bernard Polder during Hurricane Katrina

Hurricane Katrina caused devastating flooding in St. Bernard Parish, Louisiana. Storm surge surrounded the polder that comprises heavily populated sections of the Parish in addition to the Lower 9th Ward section of Orleans Parish. Surge propagated along several pathways to reach levees and walls around the polder's periphery. Extreme water levels led to breaches in the levee/wall system which, along with wave overtopping and steady overflow, led to considerable flood water entering the polder. Generation and evolution of the storm surge as it propagated into the region is examined using results from the SL15 regional application of the ADCIRC storm surge model. Fluxes of water into the region through navigation channels are compared to fluxes which entered through Lake Borgne and over inundated wetlands surrounding the lake. Fluxes through Lake Borgne and adjacent wetlands were found to be the predominant source of water reaching the region. Various sources of flood water along the polder periphery are examined. Flood water primarily entered through the east and west sides of the polder. Different peak surges and hydrograph shapes were experienced along the polder boundaries, and reasons for the spatial variability in surge conditions are discussed.     

Quantification of changes in current intensities induced by wave overtopping around low-crested structures

The phenomenon of overtopping is traditionally studied for well-emerged harbour structures and often focuses on safety and stability. In this paper laboratory tests are presented and analysed to sharpen the hypothesis that overtopping is capable of changing the horizontal circulation pattern around low-crested structures. A unique data set from laboratory experiments was acquired in the wave basin at Delft University of Technology. The experiments were performed using an emerged impermeable low-crested structure (three freeboards and three different wave conditions for each freeboard) and yielded nine different combinations of set-up and overtopping driving forces. Using this information it was possible to quantify the changes in cross-shore and longshore velocity induced by the overtopping and the set-up changes under the different freeboard and wave conditions described. It is found that overtopping enhances the outgoing flows (longshore velocities parallel to the structure) away from the lee side of the structure and dampens the water level gradient driven flow towards the structure.     

A review of the climatological characteristics of landfalling Gulf hurricanes for wind, wave, and surge hazard estimation

The climatological characteristics of landfalling Gulf of Mexico hurricanes are presented, focusing on the basic parameters needed for accurately determining the structure and intensity of hurricanes for ocean response models. These include the maximum sustained wind, radius of maximum winds, the Holland-B parameter, the peripheral or far-field pressure, the surface roughness and coefficient of drag, and the central pressure for historical hurricanes in the Gulf.Despite evidence of a slight increase in the annual number of named storms over the past 50 years, presently there is no statistically significant trend in tropical storms, hurricanes, or major hurricanes in the Gulf of Mexico. In addition, the long-term variability of tropical cyclones in the Gulf reflects the observed variability in the Atlantic basin as a whole. Analyses of hurricane winds from multiple sources suggest the presence of a bias toward overestimating the strength of winds in the HURDAT dataset from 7% to 15%. Results presented comparing HURDAT with other sources also show an overestimation of intensity at landfall, with an estimated bias of ~10%.Finally, a review of recent studies has shown that hurricane frequencies and intensities appear to vary on a much more localized scale than previously believed. This exacerbates the sampling problem for accurate characterization of hurricane parameters for design and operational applications.     

Analysis of the coastal Mississippi storm surge hazard

Following the extreme flooding caused by Hurricane Katrina, the Federal Emergency Management Agency (FEMA) commissioned a study to update the Mississippi coastal flood hazard maps. The project included development and application of new methods incorporating the most recent advances in numerical modeling of storms and coastal hydrodynamics, analysis of the storm climatology, and flood hazard evaluation. This paper discusses the methods that were used and how they were applied to the coast of the State of Mississippi.     

A numerical model of wave overtopping on seadikes

This paper describes the development of a numerical model for wave overtopping on seadikes. The model is based on the flux-conservative form of the nonlinear shallow water equations (NLSW) solved with a high order total variation diminishing (TVD), Roe-type scheme. The goal is to reliably predict the hydrodynamics of wave overtopping on the dike crest and along the inner slope, necessary for the breach modelling of seadikes. Besides the mean overtopping rate, the capability of simulating individual overtopping events is also required. It is shown theoretically that the effect of wave breaking through the drastic motion of surface rollers in the surfzone is not sufficiently described by the conventional nonlinear shallow water equations, neglecting wave setup from the mean water level and thus markedly reducing the model predictive capacity for wave overtopping. This is significantly improved by including an additional source term associated with the roller energy dissipation in the depth-averaged momentum equation. The developed model has been validated against four existing laboratory datasets of wave overtopping on dikes. The first two sets are to validate the roller term performance in improving the model prediction of wave overtopping of breaking waves. The last two sets are to test the model performance under more complex but realistic hydraulic and slope geometric conditions. The results confirm the merit of the supplemented roller term and also demonstrate that the model is robust and reliable for the prediction of wave overtopping on seadikes.     

Laboratory study of combined wave overtopping and storm surge overflow of a levee

Combined wave overtopping and storm surge overflow of a levee with a trapezoidal cross section was studied in a two-dimensional laboratory wave/flow flume at a nominal prototype-to-model length scale of 25-to-1. The goal of this study was to develop design guidance in the aftermath of Hurricane Katrina. Time series of water depth at two locations on the levee crown and flow thickness at five locations on the landward-side slope were measured along with horizontal velocity near the landward edge of the crown. New equations are presented for average overtopping discharge, distribution of instantaneous discharge, and distribution of individual wave volumes. Equations are also given for mean flow thickness, RMS wave height, mean velocity, and velocity of the wave front down the landward-side slope.     

一个改进的二阶Boussinesq方程模型在线性波浪反射问题中的适用性研究

基于改进型的二阶Boussinesq方程,在交错网络下建立数值模型.利用模型模拟波浪在常水深情况下的传播,波浪反射系数均低于2％.利用该模型模拟波浪在平斜坡前的反射,并将数值结果与解析解进行对比.结果表明,对于相对水深较大情况,坡度较陡时模拟结果明显偏大;对 于相对水深较小情况,坡度超过1:1时,数值结果仍与解析解有....     

Numerical modeling of wind waves generated by tropical cyclones using moving grids

A version of the WAVEWATCH III wave model featuring a continuously moving spatial grid is presented. The new model option/version is intended for research into wind waves generated by tropical cyclones in deep water away from the coast. The main advantage of such an approach is that the cyclones can be modeled with spatial grids that cover much smaller areas than conventional fixed grids, making model runs with high spatial resolution more economically feasible. The model modifications necessary are fairly trivial. Most complications occur due to the Garden Sprinkler effect (GSE) and methods used to mitigate it. The basic testing of the model is performed using idealized wind fields consisting of a Rankine vortex. The model is also applied to hurricane Lili in the Gulf of Mexico in October 2002. The latter application shows that the moving grid approach provides a natural way to deal with hurricane wind fields that have a high-resolution in space, but a low resolution in time. Although the new model version is originally intended for tropical cyclones, it is suitable for high-resolution modeling of waves due to any moving weather pattern.     

A note on linear dispersion and shoaling properties in extended Boussinesq equations

A set of optimum parameter α is obtained to evaluate the linear dispersion and shoaling properties in the extended Boussinesq equations of [Madsen and Sorensen, 1992 and Nwogu, 1993], and [Chen and Liu, 1995]. Optimum α values are determined to produce minimal errors in each wave property of phase velocity, group velocity, or shoaling coefficient relative to the analytical one given by the Stokes wave theory. Comparisons are made of the percent errors in phase velocity, group velocity, and shoaling coefficient produced by the Boussinesq equations with a different set of optimum α values. The case with a fixed value of α = −0.4 is also presented in the comparison. The comparisons reveal that the optimum α value tuned for a particular wave property gives in general poor results for other properties. Considering all the properties simultaneously, the fixed value of α = −0.4 may give overall accuracies in phase velocity and shoaling coefficient for all the types of Boussinesq equations selected in this study.     

Simulation of nonlinear wave run-up with a high-order Boussinesq model

This paper considers the numerical simulation of nonlinear wave run-up within a highly accurate Boussinesq-type model. Moving wet–dry boundary algorithms based on so-called extrapolating boundary techniques are utilized, and a new variant of this approach is proposed in two horizontal dimensions. As validation, computed results involving the nonlinear run-up of periodic as well as transient waves on a sloping beach are considered in a single horizontal dimension, demonstrating excellent agreement with analytical solutions for both the free surface and horizontal velocity. In two horizontal dimensions cases involving long wave resonance in a parabolic basin, solitary wave evolution in a triangular channel, and solitary wave run-up on a circular conical island are considered. In each case the computed results compare well against available analytical solutions or experimental measurements. The ability to accurately simulate a moving wet–dry boundary is of considerable practical importance within coastal engineering, and the extension described in this work significantly improves the nearshore versatility of the present high-order Boussinesq approach.