Physical and numerical modelling of tsunami generation by a moving obstacle at the bottom boundary

This paper presents a study of the waves generated by a solid block landslide moving along a horizontal boundary. The landslide was controlled using a mechanical system in a series of physical experiments, and laser-induced fluorescence measurements resolved both spatial and temporal variations in the free surface elevation. During its constant-velocity motion, the landslide transferred energy into ‘trapped’ offshore-propagating waves within a narrow frequency band. The wave trapping is demonstrated by investigating the wave dispersion characteristics using a two-dimensional Fourier Transform. The first of the trailing waves broke at Froude numbers greater than or equal to 0.625. The parametric dependence of the largest-amplitude waves and the potential energy within the wave field are discussed. The experimental results were compared to the predictions of an incompressible Navier–Stokes solver with and without turbulence models. The numerical model under-predicted the measured wave amplitudes, although it accurately predicted the measured wave phasing. The turbulent model more accurately predicted the shapes of the trailing waves. Both experimental and numerical results confirmed that investigations into wave generation by submerged objects moving at constant velocity should also consider the initial acceleration of the object, as this affects the overall evolution of the wave field. The applicability of the horizontal-boundary results to more realistic field scenarios is discussed.     

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.     

Designing a multifunctional artificial reef: studies on the influence of parameters with most influence in the vertical plane

Multifunctional artificial reefs are submerged breakwaters that serve several purposes. As well as protecting the local coastline, they enhance surfing possibilities and/or increase the environmental value of the area where they are situated. Multifunctional artificial reefs (MFARs) have some promising new aspects, too: first, they provide an unimpaired visual amenity, and second, they can offer tourist and economic benefits by improving the surfing conditions. Regarding the functionality of an MFAR, much research has been carried out on surfability, i.e. whether a wave is good for surfers. However, no research has yet been done on the influence of the submergence and the length of the reef slope on the breaker type, even though this is important for the design of the reef in terms of surfability. A preliminary design was achieved step by step, making use of the theory and state of the art of multifunctional artificial reefs (Voorde et al. 2009a, 2009b). This reef geometry was then used as an initial design in physical and numerical tests. These were performed to ascertain the capacity of a multifunctional reef to serve as a submerged breakwater and so protect the local coastline of Leirosa, Portugal, and improve the local surfing possibilities. This paper describes the numerical study conducted to analyze the influences of the main relevant parameters in the vertical plane, namely: the height, the submergence, and the length and slope of the reef. The investigation was conducted using the COBRAS-UC numerical model in the vertical plane and the main results and conclusions are described and presented; a brief discussion and some recommendations for future work are also included.     

Risk assessment of coastal flood in a site of special scientific interest

The Canary Islands have a long coastline with varying levels of exposure to severe sea conditions. Frequent states of alert and emergency in some parts of their coastline are commonly related to the occurrence of extreme wave conditions. Among the phenomena directly driven by the waves when reaching the shore are the wave run-up and overtopping. Both the study of the flood level, including its variability, and the associated risks are key tools in the planning and management of coastal zones. The aim of this research is to examine the probability of occurrence of run-up events capable of exceeding different topographical levels, for estimating the risk level associated with flooding of the different areas in which the Boca Barranco Beach can be divided, in terms of their nature and use. This beach is located on the island of Gran Canaria, Spain, and is part of the site of scientific interest of Jinámar. A large wave dataset is used as input to a high-resolution numerical model for propagating offshore wave conditions to shallow waters in the study area. Furthermore, the morphology of the study area is reproduced by combining different bathymetric databases. Finally, the probability of occurrence of different levels of run-up and the corresponding levels of consequences are assigned, to assess the flood risk in the different areas of the beach, which are presented in a risk map of flooding in the study area.     

Numerical modeling of the 26th December 2004 India Ocean tsunami at Andaman and Nicobar Islands

A numerical simulation of the 26th December 2004 Indian Ocean tsunami for the Andaman and Nicobar Islands case study is presented. The simulation approach is based on a fully nonlinear Boussinesq tsunami propagation model and included an accurate computational domain and a robust coseismic source. The simulation is first confronted to available tide gauge and run-up observations. The agreement between observations and the predicted wave heights allowed a reasonable validation of the simulation. As a result a full picture of the tsunami impact is provided over the entire coastal zone of Andaman and Nicobar Islands. The processes responsible for coastal vulnerability are discussed.     

Design parameters for coastal dikes

This paper presents results of the assessment of the design parameters leading to the definition of the crest level of a coastal dike along the German North Sea. Procedures to estimate the design water level have been proposed, distinguishing between comparative and single value procedures. The transformation of the wave characteristics from deep water towards the shallow foreshore was achieved through the application of a spectral wave model. To improve the wave parameter estimations, the existing model was nested to a grid with a higher resolution closer to the coast. The estimation of the wave run-up followed the Dutch procedure with some adjustments to the local wave characteristics and dike geometry. The computed maximum crest level of 8.4 m is below the crest height of the existing dike, which is 8.8 m. However a proposal for a more economical design should be carefully evaluated, paying attention to the uncertainties encountered in this research. The general recommendation is to enhance the reliability of the hindcasted wave parameters through calibration and validation of the wave model and to include in the design process an investigation of the effect of the medium term morphological developments.     

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.     

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.     

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.     

Enhancing submerged coastal constructions by incorporating multifunctional purposes

Surfing has becoming more and more attractive in the past few decades, constituting nowadays an important source of revenue for many countries with extensive coastlines. For this purpose and also for environmental reasons, the conventional ways of protecting a coastline appear to entail some disadvantages. An innovative and interesting way of improving surfing capacities and contributing to protect a local coastal zone is by means of multifunctional artificial reefs. A multifunctional artificial reef (MFAR) is a submerged structure that serves several purposes; in particular, it may enhance the surfing possibilities and the environmental value of the local area. This structure has some promising new aspects, too: first, it provides an unimpaired visual amenity; second, it offers tourist and economic benefits by improving the surfing conditions; third, it can enhance the environmental value of the area where it is built, and fourth, if designed properly, the down drift erosion can be minimal. An appropriate reef design in terms of ‘surfability’, i.e. the possibility to surf a wave, for the Leirosa beach, located to the south of Figueira da Foz, midway along Portugal’s West Atlantic coast, has been investigated. In order to achieve the best design several steps were conducted. First, the performance of the Boussinesq-type COULWAVE model is tested with experimental data. Next, this numerical model is used to define the best values for three design parameters: reef angle; geometry of the reef (without or with a platform), and horizontal dimensions for the appropriate geometry. A preliminary design was achieved step by step, making use of the theory and of the state of the art of multifunctional reefs. This reef geometry is used in the numerical study. In terms of ‘surfability’ and for the conditions of the local coastline of Leirosa, the following values were found for the main parameters: a reef angle of 66°; a structure height of 3.20 m; a reef geometry composed of a delta without a platform; a reef submergence of 1.50 m, and a structure seaward slope of 1:10.     

Hydrodynamics and bed stability of open channel flows with submerged foliaged plants

In this work we investigate experimentally and numerically the flow structure around foliaged plants deployed in a channel with gravels on the bed under submerged and barely submerged conditions. Velocity and Reynolds stress were measured by using a NORTEK Vectrino profiler. Visual observation shows that the initial motion of gravels is easier to be triggered under the condition of flow with barely submerged vegetation. This is confirmed by the measured velocity, Reynolds stress and total kinetic energy (TKE) profiles. The velocity exhibits a speed up in the near-bed region, and the associated Reynolds stress and TKE increase there. A 3D numerical model is then verified against the experiments and used to investigate systematically the effect of degree of submergence of foliaged plants on the channel bed shear stress. The results show that the maximum bed shear stress occurs when the foliage is situated slightly below the water surface, which can enhance channel bed instability.     

Manifestation of an advanced fuzzy logic model coupled with Geo-information techniques to landslide susceptibility mapping and their comparison with logistic regression modelling

Landslides are very common natural problems in the Selangor area of Malaysia due to the improper use of landcover and tropical rainfall. There are many landslide susceptibility analyses such as statistical, bivariate and data mining approaches exist in the literature. This paper presents the use of fuzzy logic relations for landslide susceptibility mapping on part of Selangor area, Malaysia, using a Geographic Information System (GIS) and remote sensing data. At first, landslide locations were identified in the study area from the interpretation of aerial photographs and satellite images, supported by extensive field surveys. Topographic and geological data and satellite images were collected, processed, and constructed into a spatial database using GIS and image processing. Thirteen landslide conditioning factors such as slope gradient, slope exposure, plan curvature, altitude, stream power index, topographic wetness index, distance from drainage, distance from road, lithology, distance from faults, soil, landcover and normalized difference vegetation index (ndvi) were extracted from the spatial database. These factors were analyzed using fuzzy logic relations to produce the landslide susceptibility maps. Using the landslide conditioning factors and the identified landslides, the fuzzy membership values were calculated. Then fuzzy algebraic operators were applied to the fuzzy membership values for landslide susceptibility mapping. Finally, the ROC curves for all landslide susceptibility models were drawn and the area under curve values were calculated. Landslide locations were used to validate results of the landslide susceptibility maps and the validation results showed 94% accuracy for the fuzzy gamma operator employing all parameters produced in the present study as the landslide conditioning factors. Results showed that, among the fuzzy relations, in the case in which the gamma operator (λ =  0.975) showed the best accuracy (94.73%) while the case in which the fuzzy algebraic Or was applied showed the worst accuracy (84.76%). The landslide susceptibility maps produced by the fuzzy gamma operators shows similar trends as those obtained by applying logistic regression procedure by the same author and indicate that fuzzy relations results perform slightly better than the earlier method. Qualitatively, the model yields reasonable results which can be used for preliminary land-use planning purposes.     

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.     

Evaluating the influence of forest roads on shallow landsliding

This study investigates how subsurface flowpaths are altered by forest roads and how these changes influence shallow landsliding susceptibility in steep, forested landscape. A simple conceptual model of the effect of forest roads on hillslope subsurface flow is developed. The model is incorporated into a hydro-geomechanical, threshold-based model for slope instability. In the model, the occurrence of shallow landsliding is evaluated in terms of drainage areas, ground slope and soil properties (i.e., hydraulic conductivity, bulk density, and friction angle). Model results allow to quantify the influence of roads on shallow landsliding hazard across a landscape and to generate hypotheses about the broader geomorphic effect of roads.Modelling results are compared with field data collected in four sites located in north-eastern Italy. Observed landslide patterns are broadly consistent with model estimates, a finding that underscores the utility of this simple approach for predicting the geomorphic effects of forest roads constructed on steep slopes. The approach used in this study may be useful for defining criteria for road design that reduce the effects of roads on geomorphic processes.     

Where is the best site for wave energy exploitation? Case study along the coast of northern Latium (ITALY)

The present work proposes a siting process for the detection of a suitable site for wave energy exploitation. The choice of a suitable site is based on the good agreement between energy availability, environmental sustainability, and equipped facilities to exploit wave energy. The case study in the northern Latium coast is explicative because in this area there are several activities that affect marine ecosystems, and the introduction of renewable energies promote the reduction of anthropic pressures. The nearshore wave power is studied through the numerical wave model (CMS-Wave), and available wave buoys along the coast were used to compare numerical results. In correspondence with Civitavecchia harbour, the largest nearshore wave energy was found; the large depth in front of the breakwater allows to conserve a great part of offshore wave power, with an average dissipation rate of 10 % less than offshore, with mean annual available wave energy of 25.4 MWh/m and seasonal fluctuation of 5.4 MWh/m. This area appears to be an optimal site for nearshore and shoreline wave energy device tests and installations, for energy availability (intermediate level respect Mediterreanean Sea), low potential environmental impact, easier accessibility, and policy oriented towards a larger sustainability of harbour activities.     

Wave hydrodynamics around a multi-functional artificial reef at Leirosa

This paper describes an application of the Boussinesq-type COULWAVE model to study the wave hydrodynamics in the vicinity of a multi-functional artificial reef (MFAR). This reef is under investigation and consists of a supplementary protection solution for the Leirosa sand dune system located at South of Figueira da Foz, on the Portuguese West coast. Such installation near the coastline is expected to contribute to enhance the surfing conditions in the area, protect the sand dune system in the surroundings of Leirosa beach, and increase its environmental value. Numerical calculations with the COULWAVE model were performed for four test cases, considering two reef geometries (differing in the reef angle) and two incident wave conditions (storm condition and a common wave condition). Comparisons between the results obtained, in terms of wave heights and breaking line positions allow us to assess the influence of the reef on the hydrodynamics near the beach and around the reef. Moreover, the reef performance was analysed in terms of surfability and coastal protection. The surfability parameters (breaker height, Iribarren number and peel angle) were calculated for each test case using the numerical wave heights, wave directions and wave breaking positions. Comparisons of parameters allow characterizing the most appropriate configuration of the reef to improve the surfing conditions in the study area. A methodology based on numerical free surface elevations and horizontal velocity components was developed to calculate wave directions, since this is not a direct output of the COULWAVE model. Concerning coastal protection, analyses of the mean currents around the reef were used together with observations of the velocity cells near the shoreline as an indication of the sediment transport.     

Effect of initial excess density and discharge on constant flux gravity currents propagating on a slope

The effect of the upstream conditions on propagation of gravity current over a slope is investigated using three-dimensional numerical simulations. The current produced by constant buoyancy flux, is simulated using a large eddy simulation solver. The dense saline solution used at the inlet is the driving force of the flow. Higher replenishment of the current is possible either by a high inflow discharge or high initial fractional density excess. In the simulations, it is observed that these two parameters affect the flow in different ways. Results show that the front speed of the descending current is proportional to the cube root of buoyancy flux, $(g_o^{\prime } Q)^{1/3}$ , which agrees with the previous experimental and numerical observations. The height of the tail of the current grows linearly in the streamwise direction. Formation of a strong shear layer at the boundary of mixed upper layer and dense lower layer is observed within the body and the tail of the current. Over the tail of the current far enough from the inlet, the vertical velocity and density profiles are compared to the ones from an experimental study. Distance from the bed to the point of maximum velocity increases with an increase in inflow discharge, while it remains practically unchanged with increasing initial fractional excess density in the simulations. Even though the velocity profiles are in good agreement, some discrepancies are observed in fractional excess density profiles among experimental and numerical results. Possible reasons for these discrepancies are discussed. Generally, gravity current type of flows could be expressed in layer-integrated formulation of governing equations. However, layer integration introduces several constants, commonly known as shape factors, to the equations of motion. The values of these shape factors are calculated based on simulation results and compared to the values from experiments and to the favorably used ‘top hat’ assumption.     

Experimental investigation of cross-shore sandbar volumes

Sandbars are critical to the cross-shore movement of sediment. Prediction of cross-shore sandbar volumes requires knowledge about the functional relationship of sediment transport rate conditions with waves, currents, base slope, sediment property and water depth. In this study, experiments on cross- shore sediment transport were carried out in a laboratory wave channel for initial base slopes of 1/8, 1/10 and 1/15. Using regular waves with different deep-water wave steepness generated by a pedal-type wave generator, bar volumes caused by cross-shore sediment transport are investigated for beach materials with the medium diameter of d₅₀?=?0.25, 0.32, 0.45, 0.62 and 0.80 mm. A non-dimensional equation for sandbar volume was obtained by using linear and non-linear regression methods through the experimental data and was compared with previously developed equations in the literature. The results have shown that the experimental data fitted well to the proposed equation with respect to the previously developed equations.     

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.     

Modelling the motion of an internal solitary wave over a bottom ridge in a stratified fluid

A series of laboratory experiments has been carried out to investigate the passage of an internal solitary wave of depression over a bottom ridge, in a two-layer fluid system for which the upper and lower layer is linearly-stratified and homogeneous respectively. Density, velocity and vorticity fields induced by the wave propagation over the ridge have been measured simultaneously at three locations, namely upstream, downstream and over the ridge crest, for a wide range of model parameters. Results are presented to show that wave breaking may occur for a sufficiently large wave amplitude and a strong ridge blockage factor, with accompanying mixing and overturning. Density field data are presented (i) to illustrate the overturning and mixing processes that accompany the wave breaking and (ii) to quantify the degree of mixing in terms of the wave and ridge parameters. For weak encounters, good agreement is obtained between the laboratory experimental results (velocity and vorticity fields induced by the wave propagation) and the predictions of a recently-developed fully nonlinear theory. Discrepancies between theory and experiment are discussed for cases in which breaking and mixing occur.