Tsunami generation by submarine landslides: comparison of physical and numerical models

An idealised two-dimensional laboratory model of tsunamis generated by submarine landslides is described. The experimental configuration corresponds to the benchmark configuration suggested by other researchers in the international tsunami community. It comprises a semi-elliptical rigid landslide with a height to length ratio of 0.052 sliding down a 15° slope. The initial landslide submergence and specific gravity are varied, the second of which primarily determines the initial landslide acceleration. In these experiments the landslide motion is generally well approximated as consisting of two periods of constant acceleration. The first phase of positive acceleration finishes as the landslide reaches the base of the slope, while the second period of a slower deceleration continues until the landslide comes to rest along the horizontal base of the tank. A novel experimental technique, which utilises laser-induced fluorescence (LIF), is employed to measure the free surface displacement over the entire space and time domains. This enables the wave potential energy field to be computed directly and provides a vivid picture of the wave generation and development process. Particle tracking velocimetry provides detailed information on the landslide motion and also some data on the sub-surface velocity field. Experimental runs require multiple repeats (typically 35–50) of the same setup in order to capture the entire wave field with the desired resolution. Thus high level experimental repeatability is required, and this is demonstrated. A range of parameters relevant to hazard management are presented and discussed. Maximum crest and trough amplitudes of the offshore propagating waves are shown to be approximately proportional to the initial landslide acceleration and somewhat less strongly dependent on the initial landslide submergence. The maximum wave run-up experienced at the shoreline is shown to depend almost linearly on the magnitude of a high deceleration that occurs for a short period when the landslide nears the toe of the slope. The initial submergence and initial acceleration do not directly determine the maximum wave run-up, although for these experiments they impact indirectly on the magnitude of the deceleration. The efficiency of the energy transfer from the landslide potential energy to the wave field potential energy reaches values of up to 6% and is found to be strongly dependent on the initial submergence. However because of the link between the landslide mass and its acceleration, this efficiency is almost completely independent of the initial acceleration. The results from a numerical model based on linear, inviscid and irrotational wave theory, and solved with the boundary element method, are compared with the data from the experimental program. The numerical model accurately produces the generated sequence of wave crests and troughs, but slightly overpredicts their phase speed by between 2 and 4%. For all other parameters the numerical model predictions are within 25% of the experimental values, although this includes both under- and overprediction for the range of independent parameters covered.     

Quantifying the effect of wind on internal wave resonance in Lake Villarrica,Chile

Lake Villarrica, located in south central Chile, has a maximum depth of 167 m and a maximum fetch of about 20 km. The lake is monomictic, with a seasonal thermocline located at a depth of approximately 20 m. Field data show the presence of basin-scale internal waves that are forced by daily winds and affected by Coriolis acceleration. A modal linear and non-linear analysis of internal waves has been used, assuming a two-layer system. The numerical simulations show good agreement with the internal wave field observations. The obtained modes were used to study the energy dissipation within the system, which is necessary to control the amplitude growth. Field data and numerical simulations identify (1) the occurrence of a horizontal mode 1 Kelvin wave, with a period of about a day that coincides with the frequency of daily winds, suggesting that this mode of the Kelvin waves is in a resonant state (subject to damping and controlled by frictional effects in the field) and (2) the presence of higher-frequency internal waves, which are excited by non-linear interactions between basin-scale internal waves. The non-linear simulation indicates that only 10 % of the dissipation rate of the Kelvin wave is because of bottom friction, while the rest 90 % represents the energy that is radiated from the Kelvin wave to other modes. Also, this study shows that modes with periods between 5 and 8 h are excited by non-linear interactions between the fundamental Kelvin wave and horizontal Poincaré-type waves. A laboratory study of the resonant interaction between a periodic forcing and the internal wave field response has also been performed, confirming the resonance for the horizontal mode 1 Kelvin wave.     

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.     

Joint use of data and modeling in coastal wave transformation

In the framework of a research project entitled ??BRISA??BReaking waves and Induced SAnd transport??, a methodology was devised to characterize the waves joining together in-situ measurements and numerical wave propagation models. With this goal in mind, a number of in-situ measurements were made, for selected positions in front of Praia de Faro (South Portugal), during four days (25th to 28th March, 2009) by using different types of equipments (e.g., resistive wave gauges, pressure sensors, currentmeters and a new prototype pore pressure sensor using optical fibre). Wave records were obtained simultaneously offshore (at a water depth of 11.7?m below mean sea level, MSL) and at the surf and swash zones. The data processing and analysis were made by applying classical time domain techniques. Numerical simulations of the wave propagation between offshore and inshore for the measurement period were performed with two numerical models, a 1D model based on linear theory and a nonlinear Boussinesq-type model, COULWAVE, both forced by the measured offshore wave conditions of 27th March 2009. Comparisons between numerical results and field data for the pressure sensors placed in the surf and swash zones were made and discussed. This approach enables to evaluate the performance of those models to simulate those specific conditions, but also to validate the models by gaining confidence on their use in other conditions.     

Growth and damping of interfacial waves on a diffuse interface

The resonant interaction of surface and internal waves produces a nonlinear mechanism for energy transfer among wave components in oceans, lakes, and estuaries. In many field situations, the stratification may be well approximated by a two-layer fluid with a diffuse interface. The growth and damping rates of sub-harmonic interfacial waves generated by a surface wave through a three-wave resonant interaction are measured in the laboratory. These measurements are compared with theoretical predictions. A diffuse interface reduces the damping rate and increases the growth rate. The predicted growth rate provides excellent comparison with the laboratory measurements. The inclusion of the effects of a diffuse interface significantly improve the comparison.     

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.     

Impulsive waves caused by subaerial landslides

This paper presents the experimental results of impulsive waves caused by subaerial landslides. A wide range of effective parameters are considered and studied by performing 120 laboratory tests. Considered slide masses are both rigid and deformable. The effects of bed slope angle, water depth, slide impact velocity, geometry, shape and deformation on impulse wave characteristics have been inspected. The impulse wave features such as amplitude, period and also energy conversation are studied. The effects of slide Froude number and deformation on energy conversation from slide into wave are also investigated. Based on laboratory measured data an empirical equation for impulse wave amplitude and period have been presented and successfully verified using available data of previous laboratory works.     

城市化对北京夏季极端高温影响的数值研究

利用一个耦合了城市冠层模式（UCM）的区域数值模拟系统（WRF／NCAR）,引入由LandsatTM提取的京津冀区域30m分辨率下垫面GIS数据集代替美国USGS地表分类数据,对2009年6月24—25日出现在北京地区的一次超过40℃极端高温天气过程进行了高分辨率数值模拟,用以考察WRF／UCM系统对北京“城市热岛”及城市高温天气的模拟效果,并分析了城市化对北京地区城市高温和地表能量平衡的影响及其日变化特征。结果表明：采用精细化下垫面分类数据集后能更好地模拟出主要高温区的分布特征,并能较好再现夜间的“城市热岛”效应。城市化发展对近地层气温的影响主要表现在会促使城区及其下风向近郊区气温的升高,增幅可达0．5～2℃,这与城市热岛及其下游效应有关。城市下垫面的高粗糙度对近地层风速表现出明显的阻挡效应,表现在模拟的10m风场减弱明显。考虑了城市下垫面属性的敏感性试验更好地再现了城区温度的日变化,其模拟的日间最高温度与实际观测值更为接近,也较好地模拟出了城区具有较高最低温度的特征。通过城区与郊区能量平衡过程差异的分析表明,城市化可以显著改变能量平衡中各项所占的比重。地表对近地层大气热量输送过程的变化表明随着城市下垫面的日愈扩大,会显著增强白天地表对大气的向上感热输送,增大城区日间出现高温的可能。夜间,模式反映出地表能量收入来自土壤热通量的向上输送,同样由于城区的潜热通量小,收入的能量仍主要以感热形式加热大气,夜间城区具有较高的最低温度并表现出较强的热岛特征,主要与夜间感热加热的持续相关。     

Steady Shallow-Water Current and Solute Transport around a Semi-Conical Headland

Laboratory experiments have been carried out to investigate the effects of a sloping wall headland on the flow characteristics and the associated concentration distributions from a point source around the headland. A semi-conical headland with a slope of 1:2 was set up in a flow basin, 4.8 m long and 3.8 m wide. In this paper, the experimental results of a steady shallow-water current are reported. Three dimensional flow velocities in the basin were measured using Sontek-ADV instrument. The dye concentration levels in the basin were measured by two fluorometers. The experimental results showed a large-scale re-circulation region behind the semi-conical headland. The peak turbulence energy, at about 53% of the local kinetic flow energy, coincides with the region of high velocity gradient. Significant vertical flows were observed around the area near the downhill slope of the headland, with a maximum ratio of vertical to horizontal velocities being about 22%. Such relatively significant vertical scouring velocities, coupled with strong turbulence energy and high horizontal velocity gradients in the same region, could cause severe bed erosion. The experimental results have also been compared with the predicted results of a depth-averaged numerical model. The predicted eddy structure and the concentration distribution in the re-circulation area were found to compare favourably with the experimental results. However, the discrepancies in the flow velocities and the concentration levels near the headland were apparent. It was observed that the dye concentration continued to spread in the cross-stream direction after passing the headland, whereas only a limited extent of the lateral spreading was predicted by the numerical model further downstream of the headland.     

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.     

Characterization of storm wave asymmetries with functional data analysis

Functional data analysis (FDA) is a set of tools developed to perform statistical analysis on data having a functional form. In our case we consider the one-dimensional wave surface profiles registered during a North-Sea storm as functional data. The data is split into 20 min intervals within which an individual wave is defined as the profile between two consecutive downcrossings. After registration of these individual waves to the interval [0, 1], the mean wave profile for the entire 20 min interval is obtained along with the first two derivatives of this mean profile. We analyze the shape of these mean waves and their derivatives and show how they change as a function of the significant wave height, which is a measure of the severity of the sea for the corresponding time interval. We also look at the evolution of the energy, as represented by the phase diagram, as a function of significant wave height. The results show the asymmetry in vertical and horizontal scales for real data. Comparison with a Gaussian wave simulation model calculated from the actual wave spectra shows important differences in symmetry and shape of the average wave and seem to indicate that the greatest difference in the distribution of energy during the wave cycle lies in the second and fourth quarters of the wave period. FDA can be applied to derive information on the individual and average wave profiles and also provide an understanding of the variation in energy throughout the wave phase.     

Alternating skimming flow over a stepped spillway

The study of stepped spillways in laboratory scales has been essentially focused on two separated sub-regimes within skimming flow. In this paper we investigate the appearance of an unclassified alternating skimming flow regime in a 0.5 m wide stepped spillway which does not fit on these earlier definitions, and which does not occur in a 0.3 m wide spillway. Our aim is to explain the genesis of this unclassified flow which is visualised in the physical stepped spillway, by using 3D numerical modelling. Flow depths and velocities are measured using an ultrasonic sensor and Bubble Image Velocimetry in the wider flume (0.5 m). The numerical model is validated with the experimental data from the 0.5 m wide spillway. After validation, the channel width of the same numerical model is reduced to 0.3 m wide spillway in order to characterise (compare) the case without (with) alternating skimming flow. Both cases are solved using Reynolds-Averaged Navier–Stokes equations together with the Volume-of-Fluid technique and SST k-\(\omega\) turbulence model. The experimental results reveal that the alternating skimming flow regime is characterised by an evident seesaw pattern of flow properties over consecutive steps. In turn, the numerical modelling clarified that this seesaw pattern is due to the presence of a complex system of cross waves along the spillway. These cross waves are also responsible for a mass and momentum exchange in the transversal direction and for the formation of the alternating skimming flow in the spillway.     

A numerical model of wave- and current-driven nutrient uptake by coral reef communities

We developed a numerical model capable of simulating the spatial zonation of nutrient uptake in coral reef systems driven by hydrodynamic forcing (both from waves and currents). Relationships between nutrient uptake and bed stress derived from flume and field studies were added to a four-component biogeochemical model embedded within a three-dimensional (3-D) hydrodynamic ocean model coupled to a numerical wave model. The performance of the resulting coupled physical-biogeochemical model was first evaluated in an idealized one-dimensional (1-D) channel for both a pure current and a combined wave-current flow. Waves in the channel were represented by an oscillatory flow with constant amplitude and frequency. The simulated nutrient concentrations were in good agreement with the analytical solution for nutrient depletion along a uniform channel, as well as with existing observations of phosphate uptake across a real reef flat. We then applied this integrated model to investigate more complex two-dimensional (2-D) nutrient dynamics, firstly to an idealized coral reef-lagoon morphology, and secondly to a realistic section of Ningaloo Reef in Western Australia, where nutrients were advected into the domain via alongshore coastal currents. Both the idealized reef and Ningaloo Reef simulations showed similar patterns of maximum uptake rates on the shallow forereef and reef crest, and with nutrient concentration decreasing as water flowed over the reef flat. As a result of the cumulative outflow of nutrient-depleted water exiting the reef channels and then being advected down the coast by alongshore currents, both reef simulations exhibited substantial alongshore variation in nutrient concentrations. The coupled models successfully reproduced the observed spatial-variability in nitrate concentration across the Ningaloo Reef system.     

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.     

Spatial structure of internal Poincaré waves in Lake Michigan

In this paper we examine the characteristics of near-inertial internal Poincaré waves in Lake Michigan (USA) as discerned from field experiments and hydrodynamic simulations. The focus is on the determination of the lateral and vertical structure of the waves. Observations of near-inertial internal wave properties are presented from two field experiments in southern Lake Michigan conducted during the years 2009 and 2010 at Michigan City (IN, USA) and Muskegon (MI, USA), respectively. Spectra of thermocline displacements and baroclinic velocities show that kinetic and potential baroclinic energy is dominated by near-inertial internal Poincaré waves. Vertical structure discerned from empirical orthogonal function analysis shows that this energy is predominantly vertical mode 1. Idealized hydrodynamic simulations using stratifications from early summer (June), mid-summer (July) and fall (September) identify the basin-scale internal Poincaré wave structure as a combination of single- and two-basin cells, similar to those identified in Lake Erie by Schwab, with near-surface velocities largest in the center of the northern and southern basins. Near-inertial bottom kinetic energy is seen to have roughly constant magnitude over large swathes across the basin, with higher magnitude in the shallower areas like the Mid-lake Plateau, as compared with the deep northern and southern basins. The near-bottom near-inertial kinetic energy when mapped appears similar to the bottom topography map. The wave-induced vertical shear across thermocline is concentrated along the longitudinal axis of the lake basin, and both near-bottom velocities and thermocline shear are reasonably explained by a simple conceptual model of the expected transverse variability.     

Numerical study of coastal sandbar migration, by hydro-morphodynamical coupling

We present a numerical model based on the hydro-morphodynamical coupling to study coastal sandbar migration. In order to improve both nonlinear and dispersive wave processes in relatively shallow water, we developed a finite element model based on the Legendre polynomials and on the Extended Boussinesq model. This model reproduces the propagation of wave trains with a high degree of accuracy on a greater range of depths than the standard Boussinesq models. We also implemented the Total Variation Diminishing schemes to improve the quality of the computed hydrodynamic fields, especially in areas where sharp flow gradients occurred. The coupled morpho-hydrodynamical model is then used to simulate the migration of real sandbars observed at Rousty beach (Mediterranean French coast). For verification the model results are compared with field measurements obtained from a small-scale field campaign carried out over two years at Rousty beach, and the results of this comparison are thoroughly discussed and analyzed.     

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 %.     

Shoaling internal waves may reduce gravity current transport

Gravity currents descending along slopes have typically been studied in quiescent environments, despite the fact that in many geophysical settings there is significant externally driven motion. Here we investigate how the head of a gravity current is influenced by interfacial internal waves at the pycnocline of a two-layer ambient water column. Our experimental measurements show that larger amplitude internal waves, interacting with the gravity current, reduce both the mass transport by the gravity current and its thickness. These results suggest that the ambient internal wave field should be considered when estimating transport by gravity currents in geophysical settings with strong internal waves, such as lakes and the coastal ocean.     

Are breaking waves,bores, surges and jumps the same flow?

The flow structure in the aerated region of the roller generated by breaking waves remains a great challenge to study, with large quantities of entrained air and turbulence interactions making it very difficult to investigate in details. A number of analogies were proposed between breaking waves in deep or shallow water, tidal bores and hydraulic jumps. Many numerical models used to simulate waves in the surf zone do not implicitly simulate the breaking process of the waves, but are required to parameterise the wave-breaking effects, thus relying on experimental data. Analogies are also assumed to quantify the roller dynamics and the energy dissipation. The scope of this paper is to review the different analogies proposed in the literature and to discuss current practices. A thorough survey is offered and a discussion is developed an aimed at improving the use of possible breaking proxies. The most recent data are revisited and scrutinised for the use of most advanced numerical models to educe the surf zone hydrodynamics. In particular, the roller dynamics and geometrical characteristics are discussed. An open discussion is proposed to explore the actual practices and propose perspectives based on the most appropriate analogy, namely the tidal bore.