The mean wave overtopping rate is an essential parameter to design coastal protections. Estimating it with a high precision is primordial to find a balance between a satisfactory safety level and a limited impact on the environment and construction costs. A series of laboratory experiments was conducted in a wave flume to estimate the wave overtopping discharge over a rock-armored breakwater in bimodal sea state conditions (combining swell and wind waves). Both simulated swell and wind wave systems were long-crested and colinear. Preliminary tests were performed on a smooth breakwater to validate the experimental set-up. Some trends in the results with the smooth slope can be characterized by the representative wave steepness. These trends are confirmed and amplified in the presence of the armor rubble slope. In that case, the measured wave overtopping rate can be significantly overestimated by existing prediction formulas, especially for sea state conditions with a high representative wave steepness, corresponding to a high wind-wave proportion in the sea state energy. We suggest two methods to take into account the effect of sea-state bimodality via the representative wave steepness to improve the wave overtopping rate estimations for smooth and armored rubble breakwaters.

A weakly-compressible Smoothed Particle Hydrodynamics (SPH) model for the simulation of water seepage in a fixed and undeformable porous matrix is proposed in this paper. Within this model, the macroscopic governing equations of mass and momentum are expressed using an averaging process on an elementary volume of porous medium. A first set of particles is used for modelling the fluid, while a second one is employed for the porous structure to compute the volume fraction involved in the volume-averaged equations. The stabilization of the fluid model, based on a Riemann solver, is free of any diffusion parameter and results in regular and accurate pressure fields. Moreover, a Boundary Integral Method is chosen in this work to handle wall boundary conditions, with use of the so-called Espa & ntilde;ol and Revenga laplacian operator. To the authors' knowledge, both this stabilization and wall treatment technique have never been applied yet to this field of application. The validation of the present model on three test-cases demonstrates its strong reliability, showing good agreement with numerical and experimental results from the literature.

A new formulation for the head loss in an open channel with ice cover under steady flow is proposed. Based on a minimum principle, it gives the combined (bed+ice) Manning friction coefficient as a function of Manning coefficients and wetted perimeters of bed and ice cover. The model leads to numerical values close to a recent model but on simpler grounds.

In this study, we propose a modified version of section-averaged Boussinesq equations of Winckler-Liu. The model is reformulated in conservative variables, allowing a decoupling of the Shallow-Water equations and the dispersive problem. An appropriate hybrid finite volume and finite element discretisations are performed and verified with a solitary wave solution derived for the typical case of prismatic channels with a trapezoidal cross-section. For the finite volume step we compare upwind and energy conservative numerical fluxes. The impact of this choice on the long time dynamics for Favre waves is thoroughly investigated. The proposed model and numerical approximations can accurately reproduce the main features of the wave train's free surface. The impact of the numerical dissipation introduced by upwind fluxes is discussed, emphasising the need for precaution in their applications to evaluate quantities of engineering interest such as maximum wave amplitudes.

We consider a steady water flow in a channel where a vertical grid is clogged by a rectangular patch of aquatic vegetation. Laboratory experiments are conducted to observe the decrease in the water table within the patch, as well as the subsequent head loss, as a function of the patch length, the flowrate and the upstream water height. Various models of porous media are used to produce theoretical formulae describing the water surface profile within the patch, among which the Barree-Conway model proves to perform reasonably well. However, for large enough Froude numbers a seepage face or water chute appears past the vegetation patch while non-hydrostatic effects become important. Under the latter condition, the accuracy of our analytic solution is less satisfactory, while remaining accurate enough for practical purposes. As confirmed by numerical simulations, with the specific aquatic plants used in our experiments the porous flow is not Darcian, so that the seepage and head loss could not be explained by the exact Polubarinova-Kochina theory.

We present two mathematical models for weakly dispersive non-linear waves in prismatic channels of trapezoidal cross-sections. The first model, derived from a variational principle, is an extension of the well known Serre equations. The second one is a variation of Winckler and Liu’model (Winckler and Liu in J Fluid Mech 770:156–188, 2015 [1]), which belongs to the family of Boussinesq-type equations. Both are valid for arbitrary cross-sectional channels, but the very common case of constant, trapezoidal sections is investigated here in view of understanding and modelling Favre waves in such channels. The first model allows theoretical derivations in agreement with previous publications (including scale model measurements). The second model is well suited to numerical implementation and allows studying the dynamics of Favre waves. It is verified through an analytical solution and validated from published measured data.

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Laboratory experiments were conducted on the breaching of homogeneous non-cohesive sandy fluvial dikes induced by flow overtopping. Tests were conducted using a main channel, an erodible lateral dike and a floodplain. The main channel width and Froude number prior to overtopping were systematically varied. Breach discharge was deduced from water level measurements and mass conservation. High-resolution 3D reconstructions of the evolving breach geometry were obtained using a non-intrusive laser profilometry technique. The main channel width and Froude number show significant influence on the breach expansion and hydrograph. Breach hydrographs are divided into three types, depending on the Froude number and a non-dimensional main channel width. An adapted fluvial dike breaching model based on the concept of "effective breach width" is proposed. Using the laboratory data, the computed breach discharge is found extremely satisfactory, although the breach downstream expansion is not accurately reproduced by the model.

A downshift of the wind wave peak frequency was observed in a wind wave tunnel when irregular long paddle-waves (i.e. generated mechanically with a plane wave-maker) are added in the sea state. The 3rd generation spectral wave model, TOMAWAC, is used to assess the extent at which this peak frequency downshift can take place at prototype scale in bimodal sea-state conditions involving swell and wind wave systems. Several parameterizations of the modeled physical processes are selected to numerically reproduce the laboratory experiments in the first place. Then, the model performances are further inquired in reproducing coastal observations during a specific event combining a wind wave and a swell system. Overall, a good agreement is obtained between the simulations and the observations both at laboratory and coastal scale. In particular, a set of parameterizations combining one of the latest developments in spectral wave models for the whitecapping dissipation and the nonlinear 4-wave interactions reveals high performances in reproducing the observations. Lastly, based on the performances of this latter set of parameterizations, a generic numerical domain with typical coastal scale dimensions is created to inquire the occurrence of the downshift at prototype scale. This last study reveals a wind wave peak period shift from 5 s without swell to more than 6.5 s with a 2 m high swell.

A variational approach was used to derive a set of Serre equations for fully nonlinear, dispersive waves in channels of arbitrary cross section. A family of travelling waves was found, as well as the relation between amplitude and celerity of solitary waves. An upper bound is proposed for the solitary wave amplitude as a function of the Froude number in trapezoidal cross-sectional canals, and it showed good agreement with existing theory. For waves of moderate amplitude, cnoidal waves result with a soliton limit; these waves and their properties (celerity and wave number) are written as functions of the channel bank slope and channel bank curvature. The theoretical findings are in agreement with well-established results in the literature, in particular with more-recent Boussinesq-type theories. A validation is proposed against existing experimental data.

The so-called 'Favre waves' can occur in a canal upstream of a dam when the gates are closed rapidly. The Favre waves belong to 'Dispersive Shock Waves' (DSW). The theory of DSW was initiated after the pioneering work of Whitham (1965) who showed how non-linear, dispersive waves can be described following a modulation theory. In his seminal paper, Whitham applied his theory to the Korteweg-de Vries equation (KdV), among others. Later on, Gurevich and Pitaevskii (1973, 1987) proposed two analytical models to described DSW from the KdV equation following Whitham's modulation theory. In the present work, we show that Gurevich and Pitaevskii's models (GP) can well predict Favre waves. We propose a quantitative comparison of both GP models with the experimental data by Soares- Frazao and Zech (2002). The 1987 GP model, which includes energy dissipation, is proved to predict better the laboratory data.

This work uses the smoothed particle hydrodynamics (SPH) meshless numerical method in order to investigate the behaviour of a water sheet falling under gravity by reproducing the experimental results of a laboratory chute of 9.5 m height. This kind of flow occurs typically over dam ogee-type spillways. The focus is on the trajectory and velocity of the water sheet as well as on the pressure upon impact. Simulations using a combination of adaptive particle refinement, surface tension model and air friction model were tested. The SPH simulations with refinement show good agreement with the experimental pressure results for all comparisons, while using air friction allows correct modelling of the falling velocity distribution.

The accurate modelling and prediction of bimodal sea states, combining swell and wind waves, is of upmost importance for many applications such as wave overtopping of coastal protections. Yet, the discrepancy in the field observations and the wave model limitations make the modeling of this common sea state condition rather complex. The question guiding this paper is: are wind waves generated the same way with and without pre-existing swell? The approach we chose starts with laboratory measurements in a wind-wave facility showing that wind-sea growth is modified in the presence of long waves (representing swell). To upscale this observation to open oceans, a numerical spectral wave model is firstly validated by comparison with laboratory results, and then at coastal scale using in situ bimodal sea-state observations collected during the SHOWEX campaign. By a separation of the physical processes involved in wind-wave generation, numerical simulations allow to assess the role each physical process plays in the wind-wave growth when a swell system is present.

The question of 'cosmogenic' tsunamis, i.e. tsunamis determined by the fall of an asteroid in the ocean, is difficult to address. It might sound odd to investigate such a question, but there is a need for probabilistic assessment of very rare extreme maritime and coastal events in some industrial contexts, such as in nuclear safety for the sake of power plants protection against coastal floods. A complete methodology for addressing this issue was proposed by Ward and Asphaug (2000). Here we use their methodology, along with more recent data regarding the asteroid rate of fall on the Earth, their falling velocity, etc., and make some simplifying assumptions to obtain analytical, simple formulae giving the return interval of a cosmogenic tsunami as a function of the maximum wave height of interest. We apply this method to the European Atlantic coasts and find that a wave of 1m would occur about every 100,000 years. As a comparison, such a return interval corresponds to a storm surge of about 3m on the same coasts, in average.

A series of experiments were conducted in a wind-wave tank facility in Marseilles (France) to study the effects of preexisting swell conditions (represented by long mechanically-generated waves) on wind-wave growth with fetch. Both monochromatic and irregular (JONSWAP-type) long wave conditions with different values of wave steepness have been generated in the presence of a constant wind forcing, for several wind velocities. A spectral analysis of temporal wave signals combined with airflow measurements allowed to study the evolution of both wave systems with the aim of identifying the interaction mechanisms transportable to prototype scale. In particular, a specific method is used to separate the two wave systems in the measured bimodal spectra. In fetch-limited conditions, pure wind-wave growth is in accordance with anterior experiments, but differs from the prototype scale in terms of energy and frequency variations with fetch. Monochromatic long waves are shown to reduce the energy of the wind-waves significantly, as it was observed in anterior laboratory experiments. The addition of JONSWAP-type long waves instead results in a downshift of the wind-wave peak frequency but no significant energy reduction. Overall, it is observed that the presence of long waves affects the wind-wave energy and frequency variations with fetch. Finally, in the presence of JONSWAP-type long waves, variations of wind-wave energy and peak frequency with fetch appear in close agreement with the wind-wave growth observed at prototype scale both in terms of variations and nondimensional magnitude.

The turbulent plunging jet of a nearly incompressible fluid into a stagnant fluid is of great importance in many practical applications, especially for the engineering of hydropower. As an example, the dynamic load exerted by the impact of turbulent high-velocity jets into a pool must be estimated to evaluate the potential destabilization of a rock bed or dam’s structure. Modelling plunging jets in the laboratory presents a challenge due to the complex two-phase environment, which requires models to be built at near-prototype scales. This paper deals with the application of a three-dimensional weakly compressible smoothed particle hydrodynamics (SPH) model to study a circular jet impinging into a water flat pool, at a near-prototype scale. To identify the level of reliability of the computed parameters, validation of the pool bottom pressures is carried out by comparison with existing experimental data. The self-similarity of the jet’s centreline velocity is correctly reproduced and the computed maximum dynamic pressures near the stagnation point are reasonably accurate. The differences observed are mainly attributed to the non-consideration of the air phase.

A multi-phase smoothed particle hydrodynamics (SPH) formulation in combination with a granular rheological model is applied to simulate the 2007 Chehalis Lake landslide and the subsequent tsunami. The model is implemented within the open-source 3D code GPUSPH. The lake geometry is built using the British Colombia Hydro (BCH) topography and bathymetry surveys, and the landslide initial geometry is reconstructed from pre- and post-failure geological profiles under the assumption of constant thickness across the entire width. The water and the landslide are treated as immiscible continua, discretized in two distinct sets of SPH particles with different mass and behaviour laws. The landslide material is modelled as a continuum whose shear stresses obey a friction law that takes its granular nature into consideration. A sensitive analysis for various physical parameters is carried out, and numerical results are checked by comparing run-up heights to BCH's surveys.