Modelling storm surge wave overtopping of seawalls with negative freeboard

A Reynolds-averaged Navier-Stokes based wave model (RANS) is used to simulate storm surge wave overtopping of embankments. The model uses a wave generating boundary condition that accepts a wave time history as an input and reproduces the time history in the model. This allows a direct wave by wave simulation of recorded data. To investigate the success of the model at reproducing the wave generation, transformation and overtopping processes the model is compared with experimental laboratory data. A wave-by-wave comparison is performed for overtopping parameters such as discharge, depth and velocity. Finally the overtopping discharge predicted by the model is compared against design formulae.</jats:p

An investigation of surge wave profiles in open channel flow

When a sudden increase in the discharge occurs in an open channel, a surge wave is formed. This body of water appears to move along the initial surface. Depending on the discharge this surge can be undular, breaking undular, or steep fronted as the discharge increases.A theoretical expression has been derived for the undular form, but no allowances have been made in the theory for the effect of forces that cause the waves to break. To simplify matters the surge was assumed to have been arrested, by superimposing on it a velocity equal and opposite to that of the mean velocity of the head of the surge. Then it appears as an undular hydraulic jump, with moving boundaries. The expression for the profile is derived for permanent flow,^if solved alone, with no allowance for friction gives a solitary wave profile. Hence two further expressions have been derived for the changes in energy and momentum. After simplifying and assuming that the channel bed is horizontal and the channel cross section is rectangular, the resulting non dimensional equations are:-1/6 (dY/dX)² = EY² - Y/2³ +1/2 - $Y (41)dY/dX is the slope of the water surface. E refers to energy,$ to momentum, and Y to depth (y = ycY. yc - critical depth).d$/dX = g/E²[1/Y₀ - 1/Y]²[1 + 2y/l] (71) C - coefficient of friction. Suffix ₀ - initial conditions. l - width of channel. y - depth of water.dE/dX = g/YC²[1/Y₀ - 1/Y]²[1 + 2y/l] (72)With the small channel used in the experiments, allowances had to be made for wall friction (1 + 2Y/l).Benjamin and Lighthill show that this undular form of surge is not possible unless losses in energy and momentum occur.The waves are termed 'cnoidal' waves because the profile can be represented, to a very close approximation by, the graph of the square of the Jacobean elliptic function cn x. The term 'cnoidal' was coined by Korteweg and de Vries.The Equations 41, 71 and 72 were then obtained in a form suitable for computation, and a number of numerical examples were solved. The resulting profiles were checked by experiment, and the agreement between the results was considered to be good.It is believed that if the calculations were made for greater initial depths then those possible in the model channel, that there would be greater agreement with recorded values. This is because of the uncertainty of the determination of the value of the coefficient of friction at low Reynolds numbers. At high values of R the friction coefficient can be determined more accurately. It is thought that probably the values derived from the Bazin, Manning, or Gauckler-Strickler formulae would then be suitable.A considerable number of experimental determinations of wave profiles were made, and the results listed in graphical and tabular form. The curves show that until breaking occurs there is a definite dependence between wave length and amplitude of the waves.Probably the most significant result of this study of the undular surge, is the realisation of the importance of the effect of friction on the shape of the waves constituting the surge. In a rough-sided channel for a given Y₀, the crest height is greater and increases more rapidly from wave to wave, and the wave length is shorter than in a channel with a smoother surface

Positive Surge Propagation in Sloping Channels

A simplified model for the upstream propagation of a positive surge in a sloping, rectangular channel is presented. The model is based on the assumptions of a flat water surface and negligible energy dissipation downstream of the surge, which is generated by the instantaneous closure of a downstream gate. Under these hypotheses, a set of equations that depends only on time accurately describes the surge wave propagation. When the Froude number of the incoming flow is relatively small, an approximate analytical solution is also proposed. The predictive ability of the model is validated by comparing the model results with the results of an experimental investigation and with the results of a numerical model that solves the full shallow water equations

Unsteady flow in a channel with large scale bank roughness

Systematic investigations on positive and negative surge waves from upstream have been conducted in a 40 m long channel with a mean bed slope of 1.14? and non-prismatic bank geometries. The channel banks included macro-roughness elements, namely various cavities. In total, 41 different geometrical configurations have been investigated. The surge wave experiments confirmed the applicability of the elementary surge wave theory including secondary waves and wave breaking in the prismatic reference configuration. In geometries with channel bank macro-roughness, the absolute surge wave celerity Vw and the celerity surge wave celerity c are reduced. Among other reasons, the observed reduction of the absolute surge wave celerity is due to the increased flow resistance and lays between 5% and 30% for both, positive and negative waves from upstream. Due to the dispersive character, the positive and negative surges from upstream are characterized by a sudden change (front), followed by a progressive change (body) of the water level. Under the influence of bottom slope and friction, the height of the front of a surge wave is reduced exponentially along the channel. This reduction can be described by a simple mathematical model. Its calibration on the surge wave experiments pointed out the extra diffusion due to the macro-scale roughness

Energy harvesting, desalination and coastal protection by sscillating surge wave energy converter

As recognized by the United Nations, Food, Energy and Water (FEW) nexus is central to sustainable development, and the demand for all these three is increasing due to a rising global population, rapid urbanization, changing diets and economic growth. For the US, over 53% of the population lives within 50 miles of the coast (NOAA), the coastal zone is an interaction region between land and ocean and an interface of geosphere, hydrosphere, atmosphere, and biosphere, as well as greatly affected by human activities, the stability of coastal ecosystem is very weak. Oscillating surge wave energy converter can harvest energy from ocean waves to power saline water desalination and reduce the coastal erosion as physical barrier, and the desalinated fresh water can be used for saline-sodic-alkaline soil reclamation and make it suitable for plant growth and then act as a biological barrier. Power takeoff (PTO) is possibly the single most important element in wave energy technology, and underlines many (possibly most) of the failures to date (Falcão). The reason is that the wave energy is concentrated at low frequencies and oscillating velocities, which makes efficient conversion extremely difficult and limits the options for efficient power takeoff. A novel PTO, called mechanical motion rectifier (MMR), is proposed to convert bidirectional motion into unidirectional motion. Tank tests for small-scale prototypes have been down. Please click Additional Files below to see the full abstract

Design and Testing of a Foundation Raised Oscillating Surge Wave Energy Converter

Our oceans contain tremendous resource potential in the form of mechanical energy. With the ability to capture and convert the energy carried in surface waves into usable electricity, wave energy converters (WECs) have been a long-held aspiration in ocean renewable energy. One of the most popular wave energy design concepts is the Oscillating Surge Wave Energy Converter (OSWEC). True to their namesake, OSWECs extract energy from the surge force induced by incident waves. In their most basic form, OSWECs are analogous to a bottom-hinged paddle which pitches fore and aft in the direction of wave motion. Most commonly, OSWECs are designed for nearshore use in water depths of less than 20 m where they are mounted to the seafloor at their point of rotation. This work seeks to explore the response and design loads of foundation raised OSWECs for use in deeper waters, unlocking new and greater areas of wave energy resource. A foundation raised OSWEC was designed, built, and tested in a laboratory wave tank. The scale OSWEC was modeled using two methods and compared to data from the experiments. The first of these methods is a highly efficient, analytical approach which derives from the solution to the boundary value problem transformed into elliptical coordinates. Previous validation results demonstrate the analytical model is capable of reproducing results from higher fidelity numerical simulations with computation times on the order of seconds. The second approach combines hydrodynamic coefficients evaluated in WAMIT with the open-source time domain solver WEC-Sim. Two model configurations were observed: the scale OSWEC with no external attachments, and the OSWEC with external torsion springs, as to excite the model at its natural period. The pitch displacement, surge and heave forces, and pitch moment were recorded at the base of the model foundation in response to regular waves with periods ranging from 0.8 s to 2.8 s and heights from 1.5 mm to 14.3 mm. The experimental results show the surge force and pitch moment increase drastically across the observed period range from the addition of external springs. The increase is 20–30 times greater in the most extreme cases. Little to no change in heave forcing was observed between the configurations. The analytical and numerical models capture the natural period of the two configurations well, but the pitch displacement responses of both models fall short of the observations by as much as 60-80% at some periods. Excellent agreement in surge, heave, and pitch loading was obtained between the experimental data and both models. The models were used to simulate a simple power takeoff (PTO) system to approximate the additional PTO torque on the OSWEC. This torque was found to be substantial in magnitude relative to the pitch foundation moment over much of the observed period range

Storm surge, wave, and inundation simulation in the bay of Bengal

Bangladesh's geographical and land characteristics along the coastal area has created the most disastrous country by tropical cyclones originating in the Bay of Bengal and associated with the storm surges. During the past 61 years (1950-2011), India Meteorology Department (IMD) was observed 902 events from deep depression (tropical\ud storm) up to super cyclonic storm (tropical cyclone category 5) with average 5 storms per year. This condition is strengthening storm surge and increasing sea level to the sudden inundation and flooding along the Bangladesh coast. Consequently, the storm surge and sea level rise are the key factor of coastal damage. Therefore, it is critical to estimate the future storm surges in a changing climate for vulnerability study and adaptation strategy. In this study, numerical simulations are performed to validate the storm surge induced by the 1991 Bangladesh cyclone, one of the deadliest cyclone in the Bay of Bengal using an atmosphere-waves-ocean integrated modelling system. Then, further numerical experiments are performed to estimate the future storm surges in 2050 and 2080 and inundation map for Bangladesh's disaster management strategy

Joint Probabilities of Storm Surge, Significant Wave Height and River Discharge Components of Coastal Flooding Events. Utilising statistical dependence methodologies & techniques.

In this Report, the possibility of utilizing joint probability methods in coastal flood hazard component calculations is investigated, since flood risk is rarely a function of just one source variable but usually more of two or three variables such as river discharge, storm surge, wave etc. Joint probability values provide the likelihood of source variables taking high values simultaneously and resulting to a situation where flooding may occur. This report focuses on data preparation, parameter selection and methodology application. The source variable-pairs presented here, which include enough information for calculations, are: (i) surge & wave, (ii) surge & discharge and (iii) wave & discharge. The analysis is focused over 32 river ending (RIEN) points that have been selected to cover a variety of coastal environments along European riverine and estuary areas. In the absence of coincident long-term measurements, the methodology of simulating data observations by modelling was adapted resulting to a set of hindcasts for the three source variables (surge, wave height and discharge). Storm surge hindcasts were performed by utilising the hydrodynamic model Delft3D-Flow that was forced by wind and pressure terms from ECMWF ERA-Interim reanalysis. In a similar way, wave hindcasts were generated by utilizing the latest version of ECMWF ECWAM wave (stand-alone) model, forced by neutral wind terms from ERA-Interim. For the construction of river discharge hindcasts the LISFLOOD model – developed by the floods group of the Natural Hazards Project of the Joint Research Centre (JRC) – was employed. Validation of hindcasts was made over the RIEN point of river Rhine (NL) where coincident observations were available. Considering the physical driver complexity behind interactions among surge, wave height and discharge variables, hindcasts were found to perform quite well, not only simulating observation values over the common interval of interest, but also in resolving the right type and strength of both correlations and statistical dependencies. Results are presented by means of analytical tables and detailed maps referring to both correlation and dependence (chi) values being estimated over RIEN points. In particular, dependencies coming from such analytical tables can be used in an easy way to calculate the joint return period for any combined event by inserting chi in a simple formula containing the individual return periods of source variables. It is then straightforward to estimate the joint probability value as the inverse of the joint return period. Overall, the highest values of (strong / very strong) correlations and dependencies were found between surges and waves mainly over North Sea and English Channel with (such combined) events to take place on the same day (zero-lag mode). Moderate to well category dependencies were found for most sea areas, also on a zero-lag mode. In the case of surge and river discharge, moderate to well category values were found in most cases but not in a zero-lag mode as in surge & wave case. It became clear that in order to achieve such (relatively high) values, a considerable lag time interval of a few days was required with surge clearly leading discharge values. For the case of wave and river discharge, well to strong category values were found but once more mostly in non-zero lag mode indicating the necessity of a considerable lag time interval for dependence to reach such (well / strong) values with wave distinctly leading discharge values.JRC.G.2-Global security and crisis managemen