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International audience; We report on the development and validation of a new Numerical Wave Tank (NWT) solving fully nonlinear potential flow (FNPF) equations, as a more efficient variation of Grilli et al.'s NWT [Grilli et al., A fully nonlinear model for three-dimensional overturning waves over arbitrary bottom, International Journal for Numerical Methods in Fluids 35 (2001) 829-867], which was successful at modeling many wave phenomena, including landslide-generated tsunamis, rogue waves, and the initiation

Two manuscripts are presented which develop a numerical method for studying boundary layer flow and sediment transport on the seafloor. Inviscid flow, either through an analytic solution or a numerical wavetank (NWT) is used to force a previously developed three-dimensional Navier-Stokes model. The resulting hybrid model is able to simulate complex turbulent flows near the ocean bottom or around obstacles. The first manuscript reports on developments of a perturbation approach to large-eddy simulations (LES) of wave-induced boundary layers. In the present formulation, the total velocity and pressure fields are expressed as the sum of irrotational and near-field viscous perturbation, where the irrotational field is known a priori. The LES equations are formulated and solved for the perturbation fields only, which are forced by the known incident fields. Results are presented for laminar oscillatory boundary layers, as well as for laminar steady streaming induced by small-amplitude waves, which show convergence to known analytic solutions. To demonstrate potential applications, forcing from a two-dimensional NWT is applied, showing the steady streaming that exists in a laminar boundary layer under large-amplitude water waves. Results are also shown for turbulent oscillatory boundary layers, which agree well with published experimental data. The second manuscript presents LES results of sediment transport over vortex ripples. A conformal mapping is used to match the computational domain to an experimentally derived shape of vortex ripples formed in a large-scale oscillatory water tunnel. While the instantaneous velocity field and time-averaged velocity field agrees reasonably well with published experimental data, the timeand rippleaveraged velocity profile differs substantially. As well, the suspended sediment concentration above the ripple crest is substantially different than that observed experimentally. These effects, likely the result of insufficient resolved turbulent intensity in the LES, result in poor predictions of suspended sediment transport rates.

In this paper, we present a new source assessment of the La Palma collapse scenario previously described and studied in Abadie et al. (2012). Three scenarios (i.e., slide volumes of 20, 40 and 80 km3) are considered, from the initiation of the slide to the water waves generation, using THETIS, a 3D Navier–Stokes model. The slide is considered as a Newtonian fluid whose viscosity is adjusted to approximate a granular behavior. After 5 minutes of propagation with THETIS, the generated water wave is transferred into FUNWAVE-TVD for 15 minutes of Boussinesq model simulation. Then, four different depth-averaged codes are used to propagate the wave to the Guadeloupe area, Europe and French coasts. Finally, the wave impact in terms of run-up is evaluated through direct computations in specific areas or using theoretical formulas. Although the wave source appears reduced due to the rheology used compared to former works, the wave impact is still significant for the maximum slide volume considered on surrounding islands and coasts, as well as on remote most exposed coasts such as Guadeloupe. In Europe and in France, the wave impact is moderate (for specific areas in Spain and Portugal) to weak (Atlantic French coast). The comparison between the different wave models in overlapping computational regions shows an overall agreement in terms of first wave amplitude and time of arrival, but differences appear in the trailing waves.

International audience; This paper presents the development and validation of a three-dimensional numerical wave tank devoted to studying wave-structure interaction problems. It is based on the fully nonlinear potential flow theory, here solved by a boundary element approach and using unstructured triangular meshes of the domain's boundaries. Time updating is based on a second-order explicit Taylor series expansion. The method is parallelized using the Message Passing Interface (MPI) in order to take advantage of multi-processor systems. For radiation problems, with cylindrical bodies moving in prescribed motion, the free-surface is updated with a fully Lagrangian scheme, and is able to reproduce reference results for nonlinear forces exerted on the moving body. For diffraction problems, semi-Lagrangian time-updating is used, and reproduces nonlinear effects for diffraction on monopiles. Finally, we study the nonlinear wave loads on a fixed semi-submersible structure, thereby illustrating the possibility to apply the proposed numerical model for the design of offshore structures and floaters.

For reasons of efficiency and accuracy, water wave propagation is often simulated with potential or inviscid models rather than Navier-Stokes solvers, but for wave-induced flows, such as wave-structure interaction, viscous effects are important under certain conditions. Alternatively, general purpose Navier-Stokes (CFD) models can have limitations when applied to such free-surface problems when dealing with large amplitude waves, run-up, or propagation over long distances. Here we present an Arbitrary Lagrangian-Eulerian (ALE) algorithm with special care to the time-stepping and boundary conditions used for the free-surfaces, integrated into Code_Saturne, and we test its capabilities for modeling a variety of water wave generation and propagation benchmarks, and finally consider interaction with a vertical cylinder. Two variants of the mesh displacement computation are proposed and tested against the discrete Geometric Conservation Law (GCL). The more robust variant, for highly curved or sawtoothed free-surfaces, uses a Compatible Discrete Operator scheme on the dual mesh for solving the mesh displacement, which makes the algorithm valid for any polyhedral mesh. Results for standard wave propagation benchmarks for both variants show that, when care is taken to avoid grids with excessive numerical dissipation, this approach is effective at reproducing wave profiles as well as forces on bodies.

To enable the development of floating offshore wind farms, it is important to have a clear understanding of the aerodyamic forces applied on a floating offshore wind turbine. The paper presents comparisons between a lifting line free vortex wake method and an actuator line method in the case of a wind turbine in surge with blade-resolved CFD data as a reference. Each model is compared to a quasi-steady estimation of the loads to understand the variations due to the surge movement. The near-wake flow field is investigated in order to give an insight into the flow features leading to the observed behavior. Both methods predict a higher axial velocity at the position of the rotor and one radius downstream of the rotor in surge conditions compared to the fixed case.

A previously unreported internal tidal bore, which evolves into solitary internal wave packets, was observed in Port Susan, Puget Sound, and the timing, speed, and amplitude of the waves were measured by CTD and visual observation. Acoustic Doppler current profiler (ADCP) measurements were attempted, but unsuccessful. The waves appear to be generated with the ebb flow along the tidal flats of the Stillaguamish River, and the speed and width of the resulting waves can be predicted from second-order KdV theory. Their eventual dissipation may contribute significantly to surface mixing locally, particularly in comparison with the local dissipation due to the tides. Visually the waves appear in fair weather as a strong foam front, which is less visible the farther they propagate.

In this work, we simulate the 2011 M9 Tohoku-Oki tsunami using new coseismic tsunami sources based on inverting onshore and offshore geodetic data, using 3D Finite Element Models (FEM). Such FEMs simulate elastic dislocations along the plate boundary interface separating the stiff subducting Pacific Plate from the relatively weak forearc and volcanic arc of the overriding Eurasian plate. Due in part to the simulated weak forearc materials, such sources produce significant shallow slip (several tens of meters) along the updip portion of the rupture near the trench. To assess the accuracy of the new approach, we compare observations and numerical simulations of the tsunami's far- and near-field coastal impact for: (i) one of the standard seismic inversion sources (UCSB; Shao et al. 2011); and (ii) the new FEM sources. Specifically, results of numerical simulations for both sources, performed using the fully nonlinear and dispersive Boussinesq wave model FUNWAVE-TVD, are compared to DART buoy, GPS tide gauge, and inundation/runup measurements. We use a series of nested model grids with varying resolution (down to 250 m nearshore) and size, and assess effects on model results of the latter and of model physics (such as when including dispersion or not). We also assess the effects of triggering the tsunami sources in the propagation model: (i) either at once as a hot start, or with the spatiotemporal sequence derived from seismic inversion; and (ii) as a specified surface elevation or as a more realistic time and space-varying bottom boundary condition (in the latter case, we compute the initial tsunami generation up to 300 s using the non-hydrostatic model NHWAVE). Although additional refinements are expected in the near future, results based on the current FEM sources better explain long wave near-field observations at DART and GPS buoys near Japan, and measured tsunami inundation, while they simulate observations at distant DART buoys as well or better than the UCSB source. None of the sources, however, are able to explain the largest runup and inundation measured between 39.5° and 40.25°N, which could be due to insufficient model resolution in this region (Sanriku/Ria) of complex bathymetry/topography, and/or to additional tsunami generation mechanisms not represented in the coseismic sources (e.g., splay faults, submarine mass failure). This will be the object of future work.

In their pioneering work, Ward and Day suggested that a large scale flank collapse of the Cumbre Vieja Volcano (CVV) on La Palma (Canary Islands) could trigger a mega-tsunami throughout the North Atlantic Ocean basin, causing major coastal impact in the far-field. While more recent studies indicate that near-field waves from such a collapse would be more moderate than originally predicted by Ward and Day [Lovholt et al. (J Geophy Res 113:C09026, 2008); Abadie et al. (J Geophy Res 117:C05030, 2012)], these would still be formidable and devastate the Canary Island, while causing major impact in the far-field at many locations along the western European, African, and the US east coasts. Abadie et al. (J Geophy Res 117:C05030, 2012) simulated tsunami generation and near-field tsunami impact from a few CVV subaerial slide scenarios, with volumes ranging from 20 to 450 km $$^3$$ ; the latter representing the most extreme scenario proposed by Ward and Day. They modeled tsunami generation, i.e., the tsunami source, using THETIS, a 3D Navier-Stokes (NS) multi-fluid VOF model, in which slide material was considered as a nearly inviscid heavy fluid. Near-field tsunami impact was then simulated for each source using FUNWAVE-TVD, a dispersive and fully nonlinear long wave Boussinesq model [Shi et al. (Ocean Modell 43–44:36–51, 2012); Kirby et al. (Ocean Modeling, 62:39–55, 2013)]. Here, using FUNWAVE-TVD for a series of nested grids of increasingly fine resolution, we model and analyze far-field tsunami impact from two of Abadie et al.’s extreme CVV flank collapse scenarios: (i) that deemed the most “credible worst case scenario” based on a slope stability analysis, with a 80 km $$^3$$ volume; and (ii) the most extreme scenario, similar to Ward and Day’s, with a 450 km $$^3$$ volume. Simulations are performed using a one-way coupling scheme in between two given levels of nested grids. Based on the simulation results, the overall tsunami impact is first assessed in terms of maximum surface elevation computed along the western European and African, and US east coasts (USEC). Strong wave elevation decay is predicted over the wide USEC shelf, which is shown to be essentially due to bottom friction effects. We then show more detailed results for the USEC, which is the object of high-resolution tsunami inundation mapping under the auspices of the US National Tsunami Hazard Mitigation Program. In this context, we compare the maximum surface elevation predicted along the coastline for each CVV scenario and show that, besides the initial directionality of the sources, coastal impact is mostly controlled by focusing/defocusing effects resulting from the shelf bathymetric features. A simplified ray-tracing analysis confirms this controlling effect of the wide USEC shelf for incident long waves. Finally, we perform high-resolution (10 m) inundation mapping for the most extreme CVV scenario and show results at one of the most vulnerable and exposed communities in the mid-Atlantic US states, in and around Ocean City, Maryland. Such maps are being generated for all exposed areas of the USEC, to be used in tsunami hazard assessment and mitigation work.

With support from the US National Tsunami Hazard Mitigation Program (NTHMP), the authors have been developing tsunami inundation maps for the upper US East Coast (USEC), using high-resolution numerical modeling. These maps are envelopes of maximum elevations, velocity, or momentum flux, caused by the probable maximum tsunamis identified in the Atlantic oceanic basin, including from far-field coseismic or volcanic sources, and near-field Submarine mass failures (SMFs); the latter are the object of this work. Despite clear field evidence of past large-scale SMFs within our area of interest, such as the Currituck slide complex, their magnitude, pre-failed geometry, volume, and mode of rupture are poorly known. A screening analysis based on the Monte Carlo simulations (MCS) identified areas for possible tsunamigenic SMF sources along the USEC, indicating an increased level of tsunami hazard north of Virginia, potentially surpassing the inundation generated by a typical 100-year hurricane storm surge in the region, as well as that from the most extreme far-field coseismic sources in the Atlantic; to the south, the MCS indicated that SMF tsunami hazard significantly decreased. Subsequent geotechnical and geological analyses delimited four high-risk areas along the upper USEC where the potential for large tsunamigenic SMFs, identified in the MCS, was realistic on the basis of field data (i.e., sediment nature and volume/availability). In the absence of accurate site-specific field data, following NTHMP’s recommendation, for the purpose of simulating tsunami hazard from SMF PMTs, we parameterized an extreme SMF source in each of the four areas as a so-called Currituck proxy, i.e., a SMF having the same volume, dimensions, and geometry as the historical SMF. In this paper, after briefly describing our state-of-the-art SMF tsunami modeling methodology, in a second part, we parameterize and model the historical Currituck event, including: (1) a new reconstruction of the SMF geometry and kinematics; (2) the simulation of the resulting tsunami source generation; and (3) the propagation of the tsunami source over the shelf to the coastline, in a series of nested grids. A sensitivity analysis to model and grid parameters is performed on this case, to ensure convergence and accuracy of tsunami simulation results. Then, we model in greater detail and discuss the impact of the historical Currituck tsunami event along the nearest coastline where its energy was focused, off of Virginia Beach and Norfolk, as well as near the mouth of the Chesapeake Bay; our results are in qualitative agreement with an earlier modeling study. In a third part, following the same methodology, we model tsunami generation and propagation for SMF Currituck proxy sources sited in the four identified areas of the USEC. Finally, as an illustration of our SMF tsunami hazard assessment work, we present detailed tsunami inundation maps, as well as some other products, for one of the most impacted and vulnerable areas, near and around Ocean City, MD. We find that coastal inundation from near-field SMF tsunamis may be comparable to that caused by the largest far-field sources. Because of their short propagation time and, hence, warning times, SMF tsunamis may pose one of the highest coastal hazards for many highly populated and vulnerable communities along the upper USEC, certainly comparable to that from extreme hurricanes.

Many studies have modeled the Tohoku tsunami of March 11, 2011 as being due entirely to slip on an earthquake fault, but the following discrepancies suggest that further research is warranted. (1) Published models of tsunami propagation and coastal impact underpredict the observed runup heights of up to 40 m measured along the coast of the Sanriku district in the northeast part of Honshu Island. (2) Published models cannot reproduce the timing and high-frequency content of tsunami waves recorded at three nearshore buoys off Sanriku, nor the timing and dispersion properties of the waveforms at offshore DART buoy #21418. (3) The rupture centroids obtained by tsunami inversions are biased about 60 km NNE of that obtained by the Global CMT Project. Based on an analysis of seismic and geodetic data, together with recorded tsunami waveforms, we propose that, while the primary source of the tsunami was the vertical displacement of the seafloor due to the earthquake, an additional tsunami source is also required. We infer the location of the proposed additional source based on an analysis of the travel times of higher-frequency tsunami waves observed at nearshore buoys. We further propose that the most likely additional tsunami source was a submarine mass failure (SMF—i.e., a submarine landslide). A comparison of pre- and post-tsunami bathymetric surveys reveals tens of meters of vertical seafloor movement at the proposed SMF location, and a slope stability analysis confirms that the horizontal acceleration from the earthquake was sufficient to trigger an SMF. Forward modeling of the tsunami generated by a combination of the earthquake and the SMF reproduces the recorded on-, near- and offshore tsunami observations well, particularly the high-frequency component of the tsunami waves off Sanriku, which were not well simulated by previous models. The conclusion that a significant part of the 2011 Tohoku tsunami was generated by an SMF source has important implications for estimates of tsunami hazard in the Tohoku region as well as in other tectonically similar regions.

International audience; We present a comparison between two distinct numerical codes dedicated to the study of wave energy converters. Both are developed by the authors, using a boundary element method with linear triangular elements. One model applies fully nonlin-ear boundary conditions in a numerical wavetank environnment (and thus referred later as NWT), whereas the second relies on a weak-scatterer approach in open-domain and can be considered a weakly nonlinear potential code (referred later as WSC). For the purposes of comparison, we limit our study to the forces on a heaving submerged sphere. Additional results for more realistic problem geometries will be presented at the conference. INTRODUCTION Among the marine renewable energy sources, wave energy is a promising option. Despite the great number of technologies that have been proposed, currently no wave energy converter (WEC) has proven its superiority over others and become a technological solution. Usual numerical tools for modeling and designing WECs are based on boundary elements methods in linear potential theory [1-4]. However WECs efficiency relies on large amplitude motions [5], with a design of their resonance frequencies in the wave excitation. Linear potential theory is thus inadequate to study the behavior of WEC in such configuration.

Wave-induced boundary layer (BL) flows over sandy rippled bottoms are studied using a numerical model that applies a one-way coupling of a "far-field" inviscid flow model to a "near-field" large eddy simulation (LES) Navier–Stokes (NS) model. The incident inviscid velocity and pressure fields force the LES, in which near-field, wave-induced, turbulent bottom BL flows are simulated. A sediment suspension and transport model is embedded within the coupled flow model. The numerical implementation of the various models has been reported elsewhere, where we showed that the LES was able to accurately simulate both mean flow and turbulent statistics for oscillatory BL flows over a flat, rough bed. Here we show that the model accurately predicts the mean velocity fields and suspended sediment concentration for oscillatory flows over full-scale vortex ripples. Tests show that surface roughness has a significant effect on the results. Beyond increasing our insight into wave-induced oscillatory bottom BL physics, sophisticated coupled models of sediment transport such as that presented have the potential to make quantitative predictions of sediment transport and erosion/accretion around partly buried objects in the bottom, which is important for a vast array of bottom deployed instrumentation and other practical ocean engineering problems.

We derive fully nonlinear, weakly dispersive model equations for propagation of surface gravity waves in a shallow, homogeneous ocean of variable depth on the surface of a rotating sphere. A numerical model is developed for the weakly nonlinear version of the model based on a combined finite-volume and finite-difference method with a fourth-order MUSCL-TVD scheme in space and a third-order SSP Runge–Kutta scheme in time. In the context of tsunami generation and propagation over trans-oceanic distances, a scaling analysis reveals that the importance of frequency dispersion increases with a decrease of the source width, while the effect of the Coriolis force increases with an increase of the source width. A sensitivity analysis to dispersive and Coriolis effects is carried out using the numerical model in a series of numerical experiments in an idealized ocean using Gaussian and di-polar sources with different source sizes. A simulation of the Tohoku 2011 tsunami is used to illustrate the effects of dispersive and Coriolis effects at large distances from the source region.

[1] In this work, we study waves generated by the potential collapse of the west flank of the Cumbre Vieja Volcano (CVV; La Palma, Canary Island, Spain) through numerical simulations performed in two stages: (i) the initial slide motion and resulting free surface elevation are first calculated using a 3D Navier-Stokes model; (ii) generated waves are then input into a 2D (horizontal) Boussinesq model to further simulate propagation to the nearby islands. Unlike in earlier work on CVV, besides a similar extreme slide volume scenario of 450 km3, in our simulations: (i) we consider several slide scenarios featuring different volumes (i.e., 20, 40, 80 km3), which partly result from a geotechnical slope stability analysis; (ii) we use a more accurate bathymetry; and (iii) an incompressible version of a multiple-fluid/material Navier-Stokes model. We find wave trains for each scenario share common features in terms of wave directivity, frequency, and time evolution, but maximum elevations near CVV significantly differ, ranging from 600 to 1200 m (for increasing slide volume). Additionally, our computations show that significant energy transfer from slide to waves only lasts for a short duration (order 200 s), which justifies concentrating our best modeling efforts on the early slide motion phase. The anticipated consequences of such wave trains on La Palma and other Canary Islands are assessed in detail in the paper.

International audience

We present a high-order adaptive time-stepping TVD solver for the fully nonlinear Boussinesq model of Chen (2006), extended to include moving reference level as in Kennedy et al. (2001). The equations are reorganized in order to facilitate high-order Runge–Kutta time-stepping and a TVD type scheme with a Riemann solver. Wave breaking is modeled by locally switching to the nonlinear shallow water equations when the Froude number exceeds a certain threshold. The moving shoreline boundary condition is implemented using the wetting–drying algorithm with the adjusted wave speed of the Riemann solver. The code is parallelized using the Message Passing Interface (MPI) with non-blocking communication. Model validations show good performance in modeling wave shoaling, breaking, wave runup and waveaveraged nearshore circulation.

We report on further developments of a hybrid numerical model to simulate wave-induced sediment transport. A 2D numerical wavetank (NWT) based on fully nonlinear potential flow (FNPF) equations is used to simulate fully nonlinear wav e generation and propagation. A 3D Navier-Stokes model with large eddy simulation (LES) is coupled to the NWT to simulate complex turbulent flows near the ocean bottom or a round obstacles. Wave kinematics in the 2D-NWT thus forces flow simulations in the 3D-NS -LES model, and resulting sediment transport over the seabed and around a partially buried obstacle. The latter is calculated in a non-cohesive suspended load transport model simulating the (scalar) sediment concentration, using a constant settling velocity. The 2D NWT is based on a higher-order boundary element method (BEM), with explicit 2nd-order time stepping. The computational grid, thus, is the 2D-NWT boundary and the 3D-LES near-field domain. In the present new formulation, the total velocity and pressure fie lds are expressed as the sum of irrotational (incident/far-field) and near-field viscou s perturbations. The LES equations are formulated and solved for the perturbation fields only, w hich are forced by the incident fields computed in the NWT. The feasibility of coupling the mo dels in an efficient manner is demonstrated.

Recent observations of the coastal impact of large tsunamis (e.g., Indian Ocean 2004; Tohoku 2011) and related numerical and theoretical works have made it increasingly clear that tsunami waves arrive nearshore as a series of long waves (so-called N-waves) with, often, the superposition of undular bores around each crest. Such wave trains are much more complex and very much in contrast with the solitary wave paradigm which for a long time was the accepted idealization of tsunami waves in both experimental and numerical work. The dissipation associated with these breaking bores can be very large, particularly over a wide and shallow continental shelf such as along the east coast of North America, particularly for the shorter waves associated with tsunamis generated by Submarine Mass Failures (SMFs). In this paper, we perform numerical simulations of tsunami coastal impact in the context of both idealized laboratory experiments and several tsunami case studies. We attempt to clarify the key physical processes at play in such cases, and discuss the parameterization of long wave dissipation and implications for models of coastal tsunami hazard assessment.