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International audienceA large panel of instruments was deployed in the Eastern English Channel tomeasure the evolution of bedload fluxes during a tidal cycle for two different sites. The firstone was characterized by a sandy bed with a low dispersion in size while the other studysite implied graded sediments with grain sizes ranging from fine sands to granules. Thein situ results obtained were compared with predictions of total bedload fluxes by classicalmodels.Agoodagreementwasfoundforhomogeneoussedimentswiththeseformulas.Inthecase of size heterogeneous sediments, a fractionwise approach, involving a hiding-exposurecoefficientandahindrancefactor,providedbetterpredictionsofbedloadfluxes,butstillsomediscrepancies were noticed. Present results revealed that the consideration of particle shapein formulas through the circularity index enhanced the estimations of bedload transport rates.A new adjustment of Wu et al.’s (J Hydraul Res 38:427–434, 2000) formula was proposed and a very good agreement was obtained between the measured and predicted values

The propagation of focused wave groups in intermediate water depth and the shoaling zone is experimentally and numerically considered in this paper. The experiments are carried out in a two-dimensional wave flume and wave trains derived from Pierson-Moskowitz and JONSWAP spectrum are generated. The peak frequency does not change during the wave train propagation for Pierson-Moskowitz waves; however, a downshift of this peak is observed for JONSWAP waves. An energy partitioning is performed in order to track the spatial evolution of energy. Four energy regions are defined for each spectrum type. A nonlinear energy transfer between different spectral regions as the wave train propagates is demonstrated and quantified. Numerical simulations are conducted using a modified Boussinesq model for long waves in shallow waters of varying depth. Experimental results are in satisfactory agreement with numerical predictions, especially in the case of wave trains derived from JONSWAP spectrum.

We have investigated the spatiotemporal properties of solitons generated on the shallow water surface over a background of a large-scale mode in a hydrodynamic resonator when it is forced near the second frequency mode. We have used the space-time diagrams to highlight the spatiotemporal dynamics of nonlinear fields for two solitons colliding in a resonator and compared them to those of solitons occurring in an unbounded system. A state diagram of experimentally observed modes for different values of the excitation parameters has been obtained. In particular, we have evidenced period doubling and the multistability of nonlinear waves excited in the resonator. For a theoretical description of these experimental results, we have developed a phenomenological model, which leads to amplitude and phase equations of a soliton propagating over the background of a harmonic wave. To reproduce experimental results on the multistability, we have supplemented our analysis with a numerical simulation of a modified system of Boussinesq equations for shallow water, taking into account the dissipation effect

Laboratory-scale waves of two distinct types were generated in a twodimensional wave flume to model the spatial evolution of the frequency spectrum in the nearshore zone. The two generated types are Gaussian wave groups of different spectra widths and solitary waves. In the experiment, the time series of free surface elevation along the flume are obtained along a distance of 10m using wave gauges. For each Gaussian wave train, four regions were defined, namely peak, transfer, high frequency and low frequency region referred to as E1, E2, E3 and E4. The repartition was based on the maximum frequency spectrum situated in E1 at X=4m. Focusing is a complex process; this is mainly due to nonlinear energy transfer between different frequency ranges. It was concluded that the energy keeps stable in E1 and spreads toward E3 before breaking. The frequency spectrum in E2 has a decreasing trend during the wave train propagation and this is more appreciable for stronger wave breaking. After the breaking, the frequency spectrum in E2 stops decreasing. It was found also that frequency spectrum increases during the focusing process in E4. Concerning solitary waves, it was found that the frequency spectrum of the main solitary wave decreases as the wave approaches the breaking zone. Key words: Gaussian wave train/ frequency spectrum/ solitary wave/ peak frequency region/ Transfer region.Nomenclature E1, E2, E3 and E4: peak region, transfer region, high frequency region and low frequency region (Gaussian waves).Es: mains solitary wave frequency region situated between 0.7fp and 1.5fp, where fp being the peak frequency. X [m]: Distance along the flume. A' [m]: Solitary wave amplitude at the toe of the slope. A0 [m]: Solitary wave amplitude at X=4m from the wave maker. Ab [m]: local breaking height. As [m]: Solitary wave amplitude. C [m.s -1 ]: Solitary wave celerity. fc [Hz]: Center frequency.Physical modelling of extreme waves 3 fp [Hz]: Peak frequency. fs [Hz]: Characteristic frequency; Eq. 3. g [m.s -2 ]: Gravitational acceleration. h [m]: Water depth. hb [m]: local breaking depth. k [rad.m -1 ]: Wave number. S0: Global wave steepness (at X=4m from the wave maker). S(f): Frequency spectrum. Xb [m]: Breaking position. η (x, t) [m]: Free surface elevation. Δf [Hz]: Frequency stepping. φ [rad]: Phase at focusing.