Eric Barthélemy

Experimental study of interfacial solitary waves

A small-scale experiment was conducted (in a 3 m long flume) to study interfacial long-waves in a two-immiscible-fluid system (water and petrol were used). Experiments and nonlinear theories are compared in terms of wave profiles, phase velocity and mainly frequency–amplitude relationships. As expected, the KdV solitary waves match the experiments for small-amplitude waves for all layer thickness ratios. The characteristics of ‘large’-amplitude waves (that is when the crest is close to the critical level – approximately located at mid-depth) asymptotically tend to be predicted by a ‘KdV-mKdV’ equation containing both quadratic and cubic nonlinear terms. In addition a numerical solution of the complete Euler equations, based on Fourier series expansions, is devised to describe solitary waves of intermediate amplitude. In all cases, solitary interfacial waves in this numerical theory tally with the experimental data. When the layer thicknesses are almost equal (ratio of lower layer to total depth equal to 0.4 or 0.63) both the KdV-mKdV and the numerical solutions match the experimental points.

Wave-Breaking Model for Boussinesq-Type Equations Including Roller Effects in the Mass Conservation Equation

We investigate the ability of a 1D fully nonlinear Boussinesq model including breaking to reproduce surf zone waves in terms of wave height and nonlinear intraphase properties such as asymmetry and skewness. An alternative approach for wave-breaking parameterization including roller effects through diffusive-type terms on both, the mass conservation and momentum equations is developed and validated on regular wave and solitary wave experiments as an attempt to improve wave height and left-right asymmetry estimates. The new approach is able to reproduce wave height decay, and intraphase nonlinear properties within the entire surf zone of spilling breakers without requiring temporal evolution of model parameters.

Double-averaging analysis and local flow characterization of near-bed turbulence in gravel-bed channel flows

This investigation focuses on the characteristics of near-bed turbulence in fully rough gravel-bed open-channel flows. The analysis combines results obtained with the double-averaging methodology and local flow characterization, using velocity measurements provided by a high-resolution three-axis Acoustic Doppler Velocity Profiler (ADVP). As a result of the flow heterogeneity induced by the bed topography, the flow is not locally uniform in the near-bed region, and a double-averaging methodology is applied over a length scale much greater than the gravel size. In smooth- and rough-bed flow conditions, without macro-roughness bed elements, maximum turbulent kinetic energy (TKE) production occurs very close to z = 0, while in our case with fully rough flows with macro-roughness elements, maximum turbulence activity is found to occur at gravel crest levels z c ( z c / h = 0.1). Turbulent diffusion also reaches a maximum at this elevation. The characteristics of the spatially averaged TKE budget are in good agreement with those obtained in flows over canopies. The hydrodynamic double-averaged properties have strong similarities with mixing layers and reattached mixing layers in flows over backward facing steps. Local time-averaged velocity profiles can be split into three typical classes, namely log, S-shaped and accelerated. It appears that the S-shaped class profiles, located in the wakes of the macro-roughness elements, exhibit an inflectional profile typical of mixing layers. They are of major importance in the double-averaged TKE budget, as they provide a local high contribution to the double-averaged TKE flux, TKE production and dissipation compared to the log class profiles. Consequently, double-averaged TKE production is roughly 75% greater than the dissipation rate at the point of maximal TKE production. Moreover the macro-roughness bed elements imply mixing-layer-type hydrodynamics that play a dominant role in the overall structure of mean near-bed turbulence of gravel-bed channel flows.

Physical modeling of intermediate cross‐shore beach morphology: Transients and equilibrium states

Laboratory experiments on cross-shore beach morphodynamics are presented. A lightweight sediment (density rho(s) = 1.19 g cm(-3)) model is used in order to fulfill a Shields number and Rouse number scaling. This choice aims at correctly reproducing bed load transport as well as suspension dynamics. Terraces and barred beach profiles obtained in the experiments also present close similarities with profiles observed in the field. In order to question the concept of equilibrium beach profile, wave forcings conforming to a JONSWAP spectrum were imposed over long periods (up to more than a hundred hours). An average bottom evolution velocity is defined and used to determine when the profile reaches equilibrium. Usually, beach profiles are characterized according to the Wright and Short (1984) classification based on the Dean number W. This well-known classification is investigated and refined in the intermediate range, that is, for 1 = Omega 5. For W close to 1, a typical reflective profile is obtained. Terraces are obtained for the Omega = 2.5 cases. For Omega approximate to 3.7, the profiles exhibit two parts: a mild dissipative offshore slope producing low reflection and a steeper beach face with slightly higher reflection. The wave dissipation, velocity skewness, and acceleration skewness are computed from the free surface elevation time series. The dissipation and wave nonlinearities patterns are similar for similar equilibrium beach profiles, that is, with the same Dean number. Dissipation peaks coincide with bottom slope transitions as higher energy dissipation occurs with milder bottom slope sections. Besides, the uniformity of volumetric wave energy dissipation seems to concern only a limited zone of beaches with a widely developed surf zone.

Pore-scale modeling of fluid-particles interaction and emerging poromechanical effects

SUMMARY A micro-hydromechanical model for granular materials is presented. It combines the discrete element method for the modeling of the solid phase and a pore-scale finite volume formulation for the flow of an incompressible pore fluid. The coupling equations are derived and contrasted against the equations of conventional poroelasticity. An analogy is found between the discrete element method pore-scale finite volume coupling and Biots theory in the limit case of incompressible phases. The simulation of an oedometer test validates the coupling scheme and demonstrates the ability of the model to capture strong poromechanical effects. A detailed analysis of microscale strain and stress confirms the analogy with poroelasticity. An immersed deposition problem is finally simulated and shows the potential of the method to handle phase transitions. Copyright

Pore-Scale Modeling of Viscous Flow and Induced Forces in Dense Sphere Packings

We propose a method for effectively upscaling incompressible viscous flow in large random polydispersed sphere packings: the emphasis of this method is on the determination of the forces applied on the solid particles by the fluid. Pore bodies and their connections are defined locally through a regular Delaunay triangulation of the packings. Viscous flow equations are upscaled at the pore level, and approximated with a finite volume numerical scheme. We compare numerical simulations of the proposed method to detailed finite element simulations of the Stokes equations for assemblies of 8–200 spheres. A good agreement is found both in terms of forces exerted on the solid particles and effective permeability coefficients.

On the structure of shear stress and turbulent kinetic energy flux across the roughness layer of a gravel-bed channel flow

This study examines the structure of shear stress and turbulent kinetic energy (TKE) flux across the roughness layer of a uniform, fully rough gravel-bed channel flow ( k s + ≫ 100, δ/ k = 20) using high-resolution acoustic Doppler velocity profiler measurements. The studied gravel-bed roughness layer exhibits a complex random multi-scale roughness structure in strong contrast with conceptualized k - or d -type roughness in standard rough-wall flows. Within the roughness layer, strong spatial variability of all time-averaged flow quantities are observed affecting up to 40% of the boundary layer height. This variability is attributed to the presence of bed zones with emanating bed protuberances (or gravel clusters) acting as local flow obstacles and bed zones of more homogenous roughness of densely packed gravel elements. Considering the strong spatial mean flow variability across the roughness layer, a spatio-temporal averaging procedure, called double averaging (DA), has been applied to the analysed flow quantities. Three aspects have been addressed: ( a ) the DA shear stress and DA TKE flux in specific bed zones associated with three classes of velocity profiles as previously proposed in Mignot, Barthelemy & Hurther ( J. Fluid Mech. , vol. 618, 2009, p. 279), ( b ) the global and per class DA conditional statistics of shear stress and associated TKE flux and ( c ) the contribution of large-scale coherent shear stress structures (LC3S) to the TKE flux across the roughness layer. The mean Reynolds and dispersive shear structure show good agreement between the protuberance bed zones associated with the S-shape/accelerated classes and recent results obtained in standard k -type rough-wall flows (Djenidi et al ., Exp. Fluids , vol. 44, 2008, p. 37; Pokrajac, McEwan & Nikora, Exp. Fluids , vol. 45, 2008, p. 73). These gravel-bed protuberances act as local flow obstacles inducing a strong turbulent activity in their wake regions. The conditional statistics show that the Reynolds stress contribution is fairly well distributed between sweep and ejection events, with threshold values ranging from H = 0 to H = 8. However, the TKE flux across the roughness layer primarily results from the residual shear stress between ejection and sweep of very high magnitude ( H = 10–20) and of small turbulent scale. Although LC3S are seen to penetrated the interfacial roughness layer, their TKE flux contribution is found to be negligible compared to the very energetic small-scale sweep events. These sweeps are dominantly produced in the bed zones of local gravel protuberances where the velocity profiles are inflexional of S-shape type and the mean flow properties are of mixing-layer flow type as previously shown in Mignot et al . (2009).

Measurements of surf zone sand bed dynamics under irregular waves

Measurements of velocity profiles, sediment concentration, pore-pressure and sheet flow layer dynamics are analysed in order to better assess the relative importance of the processes that contribute to destabilise the bed of a sandy beach. These measurements were conducted in the surf zone of irregular waves, in a 30 m × 30 m wave tank. The effects of flow acceleration, excess pore-pressure vertical gradients across the bed and infiltration/exfiltration seepage flow are studied. The appearance of a sheet flow layer is apparently initiated by the strong accelerations in the wave fronts. These results are compared to field measurements at Truc-Vert beach (Atlantic coast of France). Probably due to the partial saturation of the bed made of finer sand in the wave tank experiments, the upwards-directed excess pore-pressure gradient could enhance the bed destabilisation compared to that observed in the field. Des mesures de profil de vitesses, de concentration en sédiment, de pressions intersticielles et de la dynamique de la couche de fond sont analysées afin de mieux juger de l’importance relative des processus susceptibles de déstabiliser le lit d’une plage. Ces mesures ont été réalisées en laboratoire, dans un bassin de 30 m × 30 m, dans la zone de déferlement de vagues irrégulières et sur la plage du Truc Vert (côte Aquitaine, France). Les effets d’accélération, du gradient vertical de pression à travers le lit et de l’écoulement d’infiltration/exfiltration sont étudiés. L’apparition d’une couche mobile et fortement concentrée semble initiée par les fortes accélérations précédant le passage de la crête des vagues. Probablement dû à un lit partiellement saturé et constitué de grains plus fins dans les expériences en bassin, la déstabilisation du lit par un gradient de pression interstitielle orienté vers le haut n’apparaît pas négligeable comme dans les mesures de terrain.

Short wave phase shifts by large free surface solitary waves. Experiments and models

In this paper, we compare experiments on short gravity wave phase shifting by surface solitary waves to a Wentzel–Kramers–Brillouin–Jeffreys (WKBJ) refraction theory. Both weak interactions (head-on interaction) and strong interactions (overtaking interaction) are examined. We derive a dispersion relation and wave action conservation relation which are similar to the ones obtained for short waves refraction on slowly varying media. The model requires an exact solitary wave solution. To this end, a steady wave solution is numerically computed using the algorithm devised by Byatt-Smith [Proc. R. Soc. London, Ser. A 315, 405 (1970)]. However, two other solitary wave solutions are incorporated in the model, namely the classical Korteweg and De Vries (KdV) [Phil. Mag. 39, 422 (1895)] solution (weakly nonlinear/small amplitude solitary wave) and the Rayleigh [Phil. Mag. 1, 257 (1876)] solution (strongly nonlinear/large amplitude solitary wave). Measurements of the short wave phase shift show better agreement with the theoretical predictions based on the Byatt-Smith numerical solution and the Rayleigh solution rather than the Korteweg and De Vries one for large amplitude solitary waves. Theoretical phase shifts predictions based on Rayleigh and Byatt-Smith numerical solutions agree with the experiments for A/h0⩽0.5. A new heuristic formula for the phase shift allowing for large amplitude solitary waves is proposed as a limiting case when the short wave wave number increases.

NONLINEAR SURF ZONE WAVE PROPERTIES AS ESTIMATED FROM BOUSSINESQ MODELLING: RANDOM WAVES AND COMPLEX BATHYMETRIES

The present work aims at investigating the ability of Boussinesq-type equations and breaking-wave parameterizations to reproduce nonlinear properties of surf zone waves. We compare results produced by two different breaking models : those proposed by Kennedy et al. (2000) and by Cienfuegos et al. (2005). Both breaking strategies are implemented in a fully nonlinear and weakly dispersive Boussinesq code (Cienfuegos et al., 2006a,b). In the first part we calibrate model parameters on the spilling regular wave experiment conducted by Ting and Kirby (1994). In the 2nd part, we apply the breaking Boussinesq models on a new laboratory experiment on random waves propagating over uneven bathymetries.