Derivation of asymptotic two-dimensional time-dependent equations for ocean wave propagation

A general method for the derivation of asymptotic nonlinear shallow water and deep water models is presented. Starting from a general dimensionless version of the water-wave equations, we reduce the problem to a system of two equations on the surface elevation and the velocity potential at the free surface. These equations involve a Dirichlet-Neumann operator and we show that all the asymptotic models can be recovered by a simple asymptotic expansion of this operator, in function of the shallowness parameter (shallow water limit) or the steepness parameter (deep water limit). Based on this method, a new two-dimensional fully dispersive model for small wave steepness is also derived, which extends to uneven bottom the approach developed by Matsuno \cite{matsuno3} and Choi \cite{choi}. This model is still valid in shallow water but with less precision than what can be achieved with Green-Naghdi model, when fully nonlinear waves are considered. The combination, or the coupling, of the new fully dispersive equations with the fully nonlinear shallow water Green-Naghdi equations represents a relevant model for describing ocean wave propagation from deep to shallow waters

Upwind Stabilized Finite Element Modelling of Non-hydrostatic Wave Breaking and Run-up

In the following report a new methodology is presented to model the propagation, wave breaking and run-up of waves in coastal zones. We represent the different coastal phenomena through the coupling of non-linear shallow water equations with the extended Boussinesq equations of Madsen and Sørensen. Each of the involved equations has a major role in describing a particular physical behaviour of the wave: the latter equations permit to model the propagation, while the non-linear shallow water ones lead waves to locally converge into discontinuities. We start from the third-order stabilized finite element scheme for the Boussinesq equations, developed in a previous scientific work (Ricchiuto and Filippini, J.Comput.Phys. 2014) and develop a non-linear variant, and detach the dispersive from the shallow water terms. A shock-capturing technique based on local non-linear mass lumping that permits in the shallow water regions to degrade locally the scheme to a first-order one across bores (shocks) and dry fronts is proposed. As for the detection of the breaking fronts, the shallow water areas, this involves physics based breaking criteria. We present different definitions of the breaking criterion, including a local implementation of the convective criterion of (Bjørkavåg and H. Kalisch, Phys.Letters A 2011), and the hybrid models of (Kazolea et. al, J.Comput.Phys. 2014), and (Tonelli and Petti, J.Hydr.Res. 2011). The behavior of different breaking criteria is investigated on several cases for which experimental data are available.On décrit une approche pour la simulation de la propagation et déferlement des vagues en proche cote basée sur la couplage entre les équations de Boussinesq améliorées de Madsen and Sorensen, pour la propagation, et les équations Shallow Water, pour le déferlement et le runup. La contruction de ce modele hybride passe d'abord la proposition une variante non-linéaire du schéma élément finis stabilisé de (Ricchiuto and Filippini, J.Comput.Phys. 2014) capable de résoudre les chocs de maniere monotone. Cela est obtenu par un operateur locale de condensation de la matrice de masse qui réduit le schéma de (Ricchiuto and Filippini, J.Comput.Phys. 2014) au schéma de Roe classique. Le couplage entre le modèle Boussinesq et Shallow Water est en suite étudié. On considere différents critères physiques de détection de fronts déferlants. En particulier, on présente une implémentation numérique locale du critère convectif de (Bjorkavag and H. Kalisch, Phys.Letters A, 2011), qui est comparée au critères proposés dans (Kazolea et. al, J.Comput.Phys., 2014) et (Tonelli and Petti, J.Hydr.Res. 2011). Le modèle obtenu est validé sur des nombreux benchmarks avec données expérimentales

A fourth-order compact finite volume scheme for fully nonlinear and weakly dispersive Boussinesq-type equations. Part I: Model development and analysis

International audienceA high‐order finite volume scheme is developed to numerically integrate a fully nonlinear and weakly dispersive set of Boussinesq‐type equations (the so‐called Serre equations) (J. Fluid Mech. 1987; 176:117–134; Surveys Geophys. 2004; 25(3–4):315–337). The choice of this discretization strategy is motivated by the fact that this particular set of equations is recasted in a convenient quasi‐conservative form. Cell face values are reconstructed using implicit compact schemes (J. Comput. Phys. 1999; 156:137–180; J. Comput. Phys. 2004; 198:535–566) and time integration is performed with the help of a four‐stage Runge–Kutta method. Numerical properties of the proposed scheme are investigated both, analytically using linear spectral analysis, and numerically for highly nonlinear cases. The numerical analysis indicates that the newly developed scheme has wider stability regions and better spectral resolution than most of the previously published numerical methods used to handle equivalent set of equations. Moreover, it was also noticed that the use of mixed‐order strategies to discretize convective and dispersive terms may result in an important overall reduction of the spectral resolution of the scheme. Additionally, there is some numerical evidence, which seems to indicate that the incorporation of a high‐order dispersion correction term as given by Madsen et al. (Coastal Eng. 1991; 15:371–388) may introduce instability in the syste

Un modèle d'équilibre d'ordre élevé pour les équations de Saint-Venant et extension au cas dispersif pour la propagation de la houle en milieu littoral

Nous rappelons ici brièvement les méthodes numériques introduites dans la cadre du modèle récent SURF_WB introduit par Marche et col. pour l'étude de la propagation des vagues en zone de surf. Une extension vers un schéma équilibre d'ordre élevé est ensuite présentée, en vue de l'étude des macro-structures de vorticité générée dans la zone de surf, suivie de validations simples. Enfin, nous proposons une extension vers un modèle de type Boussinesq afin d'être en mesure de simuler l'ensemble des processus concernant la propagation de la houle en milieu littoral

Structure verticale des courants associés à la propagation de la marée dans la Garonne-impact du mascaret

Les ressauts en translation tidaux (parfois dénommés mascarets) représentent un phénomène naturel non linéaire et non hydrostatique, pouvant avoir une forte intensité et ayant un fort impact sur les écosystèmes fluvio-estuariens. Nous présenterons des résultats expérimentaux issus de la première campagne de mesure de grande ampleur au niveau international, réalisée sur la Garonne. Nous analyserons en particulier les forts cisaillements de vitesse liés au passage du ressaut et des ondes secondaires associées, qui génèrent une forte remise en suspension des sédiments

Modélisation du festonnage des barres sableuses d'avant-côte : application à la côte aquitaine, France

Modeling of crescentic pattern development of nearshore bars: Aquitanian Coast, France. Nearshore crescentic bars play key role in nearshore morphodynamics. These bars are observed all along the Aquitanian Coast, with a mean wavelength of about 700 m. A non-linear stability analysis is undertaken to simulate the development of crescentic patterns. Results show that self-organization mechanism can lead alone to the development of these alongshore rhythmic features. Simulated wavelengths are in agreement with observations on the Aquitanian Coast

Hydrodynamique du plateau continental aquitain et influence sur les épisodes à Dinophysis dans le Bassin d'Arcachon

Des épisodes à Dinophysis affectent périodiquement l'exploitation des fruits de mer dans le Bassin d'Arcachon. Le réseau de surveillance interne au Bassin d'Arcachon montre que Dinophysis est advecté de l'océan ouvert. Le but de cette étude est de déterminer l'origine de Dinophysis. Des campagnes en mer sur le plateau continental Aquitain ont permis d'identifier une zone propice au développement de Dinophysis au large de Capbreton. Les épisodes à Dinophysis dans le bassin d'Arcachon se produisent suite à des vents d'Ouest qui induisent des courants vers le Sud d'après la littérature. L'étude des données hydrodynamiques acquises pendant les campagnes met en évidence un processus complexe et nouveau suite aux vents d'Ouest: de forts courants le long de la côte vers le Nord capables de transporter Dinophysis de Capbreton jusqu'au Bassin d'Arcachon. Un travail de modélisation a permis de reproduire ce courant et d'étudier son mécanisme particulier lié coin Sud-Est du Golfe de Gascogne.AbstractBORDEAUX1-Bib.electronique (335229901) / SudocSudocFranceF

Infragravity waves: From driving mechanisms to impacts

Infragravity (hereafter IG) waves are surface ocean waves with frequencies below those of wind-generated “short waves” (typically below 0.04 Hz). Here we focus on the most common type of IG waves, those induced by the presence of groups in incident short waves. Three related mechanisms explain their generation: (1) the development, shoaling and release of waves bound to the short-wave group envelopes (2) the modulation by these envelopes of the location where short waves break, and (3) the merging of bores (breaking wave front, resembling to a hydraulic jump) inside the surfzone. When reaching shallow water (O(1–10 m)), IG waves can transfer part of their energy back to higher frequencies, a process which is highly dependent on beach slope. On gently sloping beaches, IG waves can dissipate a substantial amount of energy through depth-limited breaking. When the bottom is very rough, such as in coral reef environments, a substantial amount of energy can be dissipated through bottom friction. IG wave energy that is not dissipated is reflected seaward, predominantly for the lowest IG frequencies and on steep bottom slopes. This reflection of the lowest IG frequencies can result in the development of standing (also known as stationary) waves. Reflected IG waves can be refractively trapped so that quasi-periodic along-shore patterns, also referred to as edge waves, can develop. IG waves have a large range of implications in the hydro-sedimentary dynamics of coastal zones. For example, they can modulate current velocities in rip channels and strongly influence cross-shore and longshore mixing. On sandy beaches, IG waves can strongly impact the water table and associated groundwater flows. On gently sloping beaches and especially under storm conditions, IG waves can dominate cross-shore sediment transport, generally promoting offshore transport inside the surfzone. Under storm conditions, IG waves can also induce overwash and eventually promote dune erosion and barrier breaching. In tidal inlets, IG waves can propagate into the back-barrier lagoon during the flood phase and induce large modulations of currents and sediment transport. Their effect appears to be smaller during the ebb phase, due to blocking by countercurrents, particularly in shallow systems. On coral and rocky reefs, IG waves can dominate over short-waves and control the hydro-sedimentary dynamics over the reef flat and in the lagoon. In harbors and semi-enclosed basins, free IG waves can be amplified by resonance and induce large seiches (resonant oscillations). Lastly, free IG waves that are generated in the nearshore can cross oceans and they can also explain the development of the Earth's “hum” (background free oscillations of the solid earth)

9-Genes Reinforce the Phylogeny of Holometabola and Yield Alternate Views on the Phylogenetic Placement of Strepsiptera

Background: The extraordinary morphology, reproductive and developmental biology, and behavioral ecology of twisted wing parasites (order Strepsiptera) have puzzled biologists for centuries. Even today, the phylogenetic position of these enigmatic “insects from outer space” [1] remains uncertain and contentious. Recent authors have argued for the placement of Strepsiptera within or as a close relative of beetles (order Coleoptera), as sister group of flies (order Diptera), or even outside of Holometabola.Methodology/Principal Findings Here, we combine data from several recent studies with new data (for a total of 9 nuclear genes and ∼13 kb of aligned data for 34 taxa), to help clarify the phylogenetic placement of Strepsiptera. Our results unequivocally support the monophyly of Neuropteroidea ( = Neuropterida + Coleoptera) + Strepsiptera, but recover Strepsiptera either derived from within polyphagan beetles (order Coleoptera), or in a position sister to Neuropterida. All other supra-ordinal- and ordinal-level relationships recovered with strong nodal support were consistent with most other recent studies. Conclusions/Significance: These results, coupled with the recent proposed placement of Strepsiptera sister to Coleoptera, suggest that while the phylogenetic neighborhood of Strepsiptera has been identified, unequivocal placement to a specific branch within Neuropteroidea will require additional study.Organismic and Evolutionary Biolog