One-dimensional numerical modelling of dam-break waves over movable beds: application to experimental and field cases

This paper reports a numerical study on dam-break waves over movable beds. A one-dimensional (1-D) model is built upon the Saint-Venant equations for shallow water waves, the Exner equation of sediment mass conservation and a spatial lag equation for non-equilibrium sediment transport. The set of governing equations is solved using an explicit finite difference scheme. The model is tested in various idealized experimental cases, with fairly good agreement between the numerical predictions and measurements. Discrepancies are observed at the earlier stage of the dam-break wave and around the dam location due to no vertical velocity component being taken into account. Sensitivity tests confirm that the friction coefficient is an important parameter for the evaluation of sediment transport processes operating during a dam-break wave. The influence of the non-equilibrium adaptation length (or the lag distance) is negligible on the wavefront celerity and weak on the free surface and bed profiles, which indicates that one may ignore the spatial lag effect in dam-break wave studies. Finally, the simulation of the Lake Ha!Ha! dyke-break flood event shows that the model can provide relevant results if a convenient formula for computing the sediment transport capacity and an appropriate median grain diameter of riverbed material are selected.     

Two and three-dimensional shoreline behaviour at a MESO-MACROTIDAL barred beach

The present work investigates cross-shore shoreline migration as well as its alongshore variability (with deformation) on timescales of days to years using 6 years of time-averaged video images. The variability of the shoreline is estimated through empirical statistical methods with comprehensive reference to three scales of variability. At the meso-to macro-tidal barred Biscarrosse beach, shoreline responds in decreasing order at seasonal (winter/summer cycles, 52%), event (storms, 28%) and inter-annual scales. Whereas seasonal evolution is dominated by wave climate modulation, short-term evolution is influenced by tidal range and surf-zone sandbar characteristics. The influence of tide range and sandbars increases when timescale decreases. This is even more the case for the alongshore deformation of the shoreline which is dominated by short-term evolution. An EOF analysis reveals that the first mode of shoreline change time series is associated with cross-shore migration and explains 58% of the shoreline variability. The rest of the modes are associated to deformation which explain 42% of shoreline variability.     

Adoption of recent formulae for sediment transport calculations applied on the Egyptian Nile delta coastal area

This study is considered as a completion for the carried out previous research on the Egyptian northern coast near Port Said. An evaluation was carried out for the purpose of analyzing satellite measured wave data, or carrying out preliminary evaluations for the study area, in the Nile delta coast near Damitta. The available offshore historical significant wave heights from altimeter measurements are used in this research for the period from 2005 to 2008. In this study waves were transformed from the offshore area to nearshore, sediment transport volumes were evaluated by applying and adjusting some of the practical formulae, which are considered reasonable for this area. The study domain dimensions are 50 km long offshore and 15 km wide alongshore. Wave nearshore transformation is carried out by using the mathematical Simulating WAves Nearshore model (SWAN) based on seasonal/directional bases. Two seasons are considered in the analysis, which are both winter and summer, to represent the mean seasons of the year. The three formulae, which are CERC, van Rijn and Boer and Galvin for sediment transport evaluation are applied in the study area. The reference values were applied for comparison were checked. The obtained rough evaluations were considered acceptable and can be roughly applied for both research and engineering purposes.     

Mid-depth oil concentration due to vertical oil dispersion in a regular wave field

An experimental program is organized to investigate the vertical oil dispersion of surface oil spills in a regular wave field. Various waves characteristics and different volumes of oil spills are tested to assess the oil concentration variations at two sampling stations. It is found that the oil concentration due to vertical oil dispersion follows an ascending diagram to reach a maximum and then decreases while oil slick passes the location. The maximum mid-depth oil concentration (C_max) at the farther sampling station is 30–50 % less than the concentration at the closer sampling station to the spill location. A 50 % increase in oil spill volume causes 30–60 % growth in oil concentrations. The relations between oil concentration and important parameters such as wave characteristics, amount of spilled oil and the distance of sampling stations from the spill location are indicated and also oil concentration variations are quantified. Two equations are derived through statistical analysis of the obtained experimental data, which estimate the magnitude and time of maximum oil concentration.     

Analyzing wave breaking in a barred beach using wavelet

In this paper, a cross-shore profile evolution model, Uniform Beach Sediment Transport-Time-Averaged Cross-Shore (UNIBEST-TC), is used. The model was developed at WL/Delft hydraulic laboratory in the Netherlands. The model is used to predict wave height in a barred beach (Egmond site, The Netherlands) and the results show that there is a good agreement between the measured and predicted values by the model. In the present study, Morlet wavelet is used to distinguish the breaking waves; it is integrated over frequency to provide the temporal variation of localized total energy. The study shows that the local peaks of the energy densities correspond to the events of wave breaking in the predicted–wave time series. Furthermore, the wave energy distribution shows a tendency to decrease in the off-shore direction of the inner bar.     

Idealized study on cohesive sediment flux by tidal asymmetry

The flux of cohesive sediment in an estuary is determined by many factors, including tidal asymmetry, wave effect, fluvial influence, phase difference between tidal velocity and tidal level fluctuations, sediment properties, flocculation, bed erodibility, bathymetry effect and other nonlocal effects. Our capability in predicting sediment fluxes in tide-dominant environments is critical to the morphodynamics and water quality of estuaries. Due to the difficulties in carrying out detailed measurement of sediment flux with high spatial and temporal resolutions, an one-dimensional-vertical (1DV) numerical model for cohesive sediment transport, previously verified and calibrated with field measured cohesive sediment concentration data, is utilized here to study some of the aforementioned factors in affecting tidal-driven sediment fluxes in idealized condition. Tidal-averaged sediment flux is shown to be correlated with tidal velocity skewness with a linear relationship. This linear relationship is different from that of non-cohesive sediment and it is demonstrated here to be mainly due to variable critical shear stress implemented for the mud bed in order to parameterize consolidation. The reason that tidal velocity skewness causes tidal-averaged residual sediment transport is shown to be due to nonlinear intra-tidal interactions between flow velocity and sediment concentration. Moreover, the effects of nonlinear intra-tidal interaction between tidal velocity and tidal level fluctuations is shown to mainly cause seaward transport, which is the most significant under progressive wave system (phase difference 90°) and almost negligible for standing wave system (phase difference 0°).     

Longshore sediment transport in the surf zone based on different formulae: a case study along the central west coast of India

Understanding longshore sediment transport (LST) is a prerequisite for designing an effective coastal zone management strategy. The present study estimates the LST along the central west coast of India based on four bulk LST formulae: (1) the Coastal Engineering Research Center (CERC) formula, (2) the Walton and Bruno formula, (3) the Kamphuis formula and (4) the Komar formula. The Delft3D–wave module is used for estimating nearshore waves with measured directional wave data at a water depth of 9 m as the input parameter. Wave data for the validation of the nearshore wave transformation model is measured using the InterOcean S4DW wave gauge. The model results show that waves approach from the south 90 % of the time in a year and that they generate predominantly northerly longshore currents. Upon comparison with the measured data, the findings show that the estimates based on the Kamphuis formula agree with the field data. A high ratio (~1) of the monthly net and gross transport rates indicates that the LST is dominating in one direction in all months except February and July. The study shows that a slight change in the angle of the wave approach during the Asian summer monsoon period (JJAS) can significantly alter the direction and magnitude of the LST. Inter-annual variations in the LST based on the data for 2009 and 2011 show that the variations in the annual net and gross LST rates in different years are less than 7 %.     

Wave Enhancement of Diffusivities within Surficial Sediments

The enhancement of solute diffusivities within coastal surficial sediments as a result of wave action is examined. Fluctuating pressure gradients associated with passing waves cause interstitial water motions leading to enhanced diffusivities through the mechanism of shear dispersion. Wave amplification of diffusivities is likely to be greatest for waves of period 10 s, in shallow water, over a bottom of coarse grain. Diffusivity enhancement of hundreds of times molecular diffusivity is achievable. The mechanism is distinct from, but complements, the mechanism of rotational dispersion which has been previously described. Other mechanisms that enhance solute transport within surficial sediments rely on the interaction between wave-driven or steady flow over bottom obstructions such as biogenic structures or sand ripples. It is suggested that while the resulting advective flows may dominate solute transport within the top few 10 s of centimeters of the sediment column, shear dispersion may be more important deeper within the sediment. In any event, in contrast to these other mechanisms, shear dispersion is operative even when the seabed is flat. Application of the theory to sediments of the South Atlantic Bight would suggest that shear dispersion is capable of explaining a major part of the interstitial transport inferred from measurements.     

Transport of Pollutant in Open Channel with Short Waves

This study examines the effect of short period water waves on the longitudinal mixing of pollutants in open channel flow. These waves create orbital motions and therefore increase the magnitude of the dispersion coefficient. Experiments are conducted for non-wavy and wavy flow. The values of the longitudinal dispersion coefficients are determined by applying the method of least squares to the measured solute concentrations at various time intervals. For non-wavy flow, the measured values of longitudinal dispersion coefficient match closely with those computed from the empirical equation given by Seo [1]. For wavy flow, a new factor called the wave parameter (a/TU _*, a=wave amplitude, T=wave period, U _*=shear velocity) is found important and a nonlinear multiple regression analysis is used to derive a new expression for the wave induced longitudinal dispersion coefficient (WILDC). An uncertainty analysis is conducted as per IS Code 5168 and the confidence interval is determined. Linear water wave theory is applied to modify the existing expression of the longitudinal dispersion coefficient of Seo [1] by including the effect of short waves. A mathematical model for WILDC is then developed. Comparative study between wavy and non-wavy flow cases has been conducted. The results clearly show an increase in the magnitude of longitudinal dispersion coefficient in the presence of waves.     

Estimation of total sediment load concentration obtained by experimental study using artificial neural networks

Estimation of sediment concentration in rivers is very important for water resources projects planning and managements. The sediment concentration is generally determined from the direct measurement of sediment concentration of river or from sediment transport equations. Direct measurement is very expensive and cannot be conducted for all river gauge stations. However, sediment transport equations do not agree with each other and require many detailed data on the flow and sediment characteristics. The main purpose of the study is to establish an effective model which includes nonlinear relations between dependent (total sediment load concentration) and independent (bed slope, flow discharge, and sediment particle size) variables. In the present study, by performing 60 experiments for various independent data, dependent variables were obtained, because of the complexity of the phenomena, as a soft computing method artificial neural networks (ANNs) which is the powerful tool for input–output mapping is used. However, ANN model was compared with total sediment transport equations. The results show that ANN model is found to be significantly superior to total sediment transport equations.     

Hierarchical modeling of the dilute transport of suspended sediment in open channels

We propose, discuss and validate a theoretical and numerical framework for sediment-laden, open-channel flows which is based on the two-fluid-model (TFM) equations of motion. The framework models involve mass and momentum equations for both phases (sediment and water) including the interactive forces of drag, lift, virtual mass and turbulent dispersion. The developed framework is composed by the complete two-fluid model (CTFM), a partial two-fluid model (PTFM), and a standard sediment-transport model (SSTM). Within the umbrella of the Reynolds-Averaged Navier-Stokes (RANS) equations, we apply K–ε type closures (standard and extended) to account for the turbulence in the carrier phase (water). We present the results of numerical computations undertaken by integrating the differential equations over control volumes. We address several issues of the theoretical models, especially those related to coupling between the two phases, interaction forces, turbulence closure and turbulent diffusivities. We compare simulation results with various recent experimental datasets for mean flow variables of the carrier as well as, for the first time, mean flow of the disperse phase and turbulence statistics. We show that most models analyzed in this paper predict the velocity of the carrier phase and that of the disperse phase within 10% of error. We also show that the PTFM provides better predictions of the distribution of sediment in the wall-normal direction as opposed to the standard Rousean profile, and that the CTFM is by no means superior to the PTFM for dilute mixtures. We additionally report and discuss the values of the Schmidt number found to improve the agreement between predictions of the distribution of suspended sediment and the experimental data.     

Numerical simulation of non-breaking solitary wave run-up using exponential basis functions

A meshless method based on exponential basis functions (EBFs) is developed to simulate the propagation of solitary waves and run-up on the slope. The presented method is a boundary-type meshless method applying the exponential basis functions with complex exponents. The solution of governing equations is considered as a series of these basis functions. Boundary conditions are satisfied through a point-wise collocation approach. Based on the presented EBF meshless method, a new formula is introduced for the maximum run-up height on different slopes, valuable for engineering applications. The results obtained through the numerical method in the prediction of solitary wave propagation and estimation of run-up are verified through the comparison with experimental data. The comparison with 159 experimental data indicates that this new formula is more accurate than the preceding formulas in predicting the maximum run-up of non-breaking solitary waves. Minimum calculation time and convenient performances are the other advantages of this method.     

Secondary flow within a river bed and contaminant transport

We have developed a numerical method to simulate the transport of non-sorbing contaminants within the sediment layer of a stream and the leaching of these contaminants in the steam. Typical stream bottom surfaces are uneven with triangularly shaped undulation forms. The flow of the water above such triangular surfaces causes external pressure changes that result in a “pumping effect” and a secondary flow within the sediment. The latter causes a significant contaminant advection within the sediment layer. The flow field in the porous sediment layer is obtained by solving numerically Darcy’s equations. The unsteady mass transfer equation is solved by using a finite-difference method with an up-wind scheme. The effects of parameters, such as channel slope, hydraulic head and dispersion, are studied by quantitatively comparing the numerical results of the total mass flow rate from the contaminant source, the concentration front propagation, and the contaminant mass flow rate into the water column. The “pumping effect,” increases the flow in the vertical direction and, thus, enhances the vertical advective mass transport of the contaminant. This bedform-shape induced flow is largely responsible for the mass transfer of contaminants into the water column. The numerical results also show that the mechanical dispersion inside the sediment bed will significantly increase the contaminant mass flow rate from the source.     

Short- and long-term responses of nourishments: Barra-Vagueira coastal stretch,Portugal

Dredged material resulting from deepening and maintenance activities of the Aveiro Harbor inlet channel, northwestern coast of Portugal, has been used to mitigate the erosion trend recorded on nearby beaches (from Barra to Costa Nova Beach) through direct placement of sand by using standard dredge equipment. The disposal activities of dredged material have been undertaken at two main sites: between the south breakwater and the 1st groin of Costa Nova (dumping area 1, DA1) and between the 3rd and the 5th groin of Costa Nova (dumping area 2, DA2).The sand was placed in the nearshore, between the ?2 and ?7 m Chart Datum, CD, contours.In this study, short- and long-term coastal morphologic changes in the sea bottom, in response to several nourishment operations and to the incoming waves, within the dumping area boundaries are investigated based on a data set of hydrographic surveys collected annually, just before and after the nourishments, between 2009 and 2015. Preliminary results describing the main morphologic changes, evolution trends, sediment budget variations, and nourishments performance are discussed using mainly Geographic Information System techniques. Overall, the analysis demonstrates that the short-term losses in the dumping areas (one month of interval) can reach 50% of the nourished volume, revealing a significant movement of the fill material towards offshore. Seasonal variations promoting cross-shore material exchange can also prevail and misrepresent the sediment balances, if the monitoring area is not comprehensive. Furthermore, some bathymetric analysis suggested that longshore transport gradients have moved the fill material from Barra beach to downdrift areas. All the obtained results contribute to the ongoing discussion about the effectiveness of nearshore sand placements especially in context of an energetic environment.     

Prediction of mass and momentum transport in turbulent plane wall jets over smooth and transitionally rough surfaces

This paper is concerned with the prediction of mass and momentum transport in turbulent wall jets developing over smooth and transitionally rough plane walls. The ability to accurately predict the resulting wall shear stresses and vertical profiles of the Reynolds stresses in these flows is prerequisite to the accurate prediction of bed scour, sediment re-suspension and transport by turbulent diffusion. The computations were performed by solving the Reynolds-averaged forms of the equations describing conservation of mass, momentum and concentration. The unknown correlations that arise from the averaging process (the Reynolds stresses in the case of the momentum equation, and the turbulent mass fluxes in the case of concentration) were obtained from the solution of modeled differential equations that describe their conservation. Since these models are somewhat more complex than those typically used in practice, their benefits are demonstrated by comparisons with results obtained from simpler, eddy-viscosity based closures. Comparisons with experimental data show that results of acceptable accuracy can be obtained only by using the appropriate combination of models for the turbulent fluxes of mass and momentum that properly account for the reduction of the Reynolds stresses due to wall damping effects, and for the modification of the mass transfer rates due to interactions with the mean rates of strain.     

Simulation-based optimization of in-stream structures design: rock vanes

We employ a three-dimensional coupled hydro-morphodynamic model, the Virtual Flow Simulator (VFS-Geophysics) in its Unsteady Reynolds Averaged Navier–Stokes mode closed with \(k-\omega\) model, to simulate the turbulent flow and sediment transport in large-scale sand and gravel bed waterways under prototype and live-bed conditions. The simulation results are used to carry out systematic numerical experiments to develop design guidelines for rock vane structures. The numerical model is based on the Curvilinear Immersed Boundary approach to simulate flow and sediment transport processes in arbitrarily complex rivers with embedded rock structures. Three validation test cases are conducted to examine the capability of the model in capturing turbulent flow and sediment transport in channels with mobile-bed. Transport of sediment materials is handled using the Exner equation coupled with a transport equation for suspended load. Two representative meandering rivers, with gravel and sand beds, respectively, are selected to serve as the virtual test-bed for developing design guidelines for rock vane structures. The characteristics of these rivers are selected based on available field data. Initially guided by existing design guidelines, we consider numerous arrangements of rock vane structures computationally to identify optimal structure design and placement characteristics for a given river system.     

The wave-induced solute flux from submerged sediment

The issue of the transport of dissolved nutrients and contaminants between the sediment in the bottom of a lake or reservoir and the body of water above it is an important one for many reasons. In particular the biological and chemical condition of the body of water is intricately linked to these mass transport processes. As the review by Boudreau (Rev Geophys 38(3):389–416, 2000) clearly demonstrates those transport processes are very complex involving mechanisms as diverse as the wave-induced flux between the sediment and the overlying water and the effect of burrowing animals on the transport within the sediment as well as basic diffusion mechanisms. The present paper focuses on one facet of these transport processes; we re-examine the balance of diffusion and wave-induced advection and demonstrate that the wave-induced flux of a solute from submerged sediment is not necessarily purely diffusive as suggested by Harrison et al. (J Geophys Res 88:7617–7622, 1983) but can be dominated by a mean or time-averaged flux induced by the advective fluid motion into and out of the sediment caused by the fluctuating pressure waves associated with wave motion. Indeed along the subtidal shoreline where the fluctuating bottom pressures are greatest, wave-induced advection will dominate the mean, time-averaged transport of solute into or out of the sediment as suggested in the work of Riedl et al. (Mar Biol 13:210–221, 1972). However, the present calculations also indicate that this advective flux decreases rapidly with increasing depth so that further away from the shoreline the advective flux becomes negligible relative to the diffusive flux and therefore the latter dominates in deeper water.     

Vertical oil dispersion profile under non-breaking regular waves

An experimental program was conducted to investigate vertical oil dispersion of surface oil spills under non-breaking regular waves. The variation in oil concentration caused by oil dispersion in a water column was studied to determine the vertical oil dispersion profile. The experiments were performed using different waves characteristics for different volumes of oil spill to evaluate the variation in oil concentration at three depths at two sampling stations. The correlations between oil concentration and the main parameters of wave characteristics, oil spill volume, sampling depth, and distance of sampling stations to spill location were assessed. The results revealed that the trend of variation in oil concentration versus wave steepness is linear. The results obtained from experimental measurements indicated that the oil concentrations at mid-depth were 44–77 % and the concentrations near the flume bed were 12–33 % of the concentration near the water surface.     

Experimental study on dynamic equilibrium of headland-bay beaches

A dynamic equilibrium bay (DEB) is an embayment with continuous sediment supply and its shoreline planform can remain stable over a long period of time without erosion or accretion. For coastal conservation of sandy headland-bay beaches (HBB), the concept of using a static equilibrium bay (SEB) is well known, but that for DEB has received little attention. Moreover, an empirical equation for the stability of a DEB is not yet available. Experiments on DEB shape that aim to derive new coefficients in the parabolic bay shape equation (PBSE) for DEB are now being conducted in the laboratory. The work commences from an initial artificial HBB in static equilibrium with sediment supply source from the lee of an upcoast headland. A final equilibrium planform is obtained for the condition with a specific wave obliquity and sediment supply rate until no further shoreline change is found. In order to fit the PBSE for a DEB, a new parameter called SSR (sediment supply ratio) that represents the ratio of sediment supply rate from the source and the potential longshore sediment transport rate is introduced to quantify the balance of sediment to the bay. Alternative C coefficients in the PBSE for DEB, which include wave obliquity and the SSR, are then calculated. These new coefficients for DEB can now be used to evaluate the influence of sediment supply from a riverine source on a DEB and to classify its equilibrium status for planning sediment management strategies in coastal conservation.