Auteur/autrice : davidlannes

Field data-based evaluation of methods for recovering surface wave elevation from pressure measurements

20 mai 2019 / / 0 Comments

A. Mouragues, P. Bonneton, D. Lannes, B. Castelle, and V. Marieu, Coastal Engineering, 150:147 – 159, 2019 Download

We compare different methods to reconstruct the surface elevation of irregular waves propagating outside the surf zone from pressure measurements at the bottom. The traditional transfer function method (TFM), based on the linear wave theory, predicts reasonably well the significant wave height but cannot describe the highest frequencies of the wave spectrum. This is why the TFM cannot reproduce the skewed shape of nonlinear waves and strongly underestimates their crest elevation. The surface elevation reconstructed from the TFM is very sensitive to the value of the cutoff frequency. At the individual wave scale, high-frequency tail correction strategies associated with this method do not significantly improve the prediction of the highest waves. Unlike the TFM, the recently developed weakly-dispersive nonlinear reconstruction method correctly reproduces the wave energy over a large number of harmonics leading to an accurate estimation of the peaked and skewed shape of the highest waves. This method is able to recover the most nonlinear waves within wave groups which some can be characterized as extreme waves. It is anticipated that using relevant reconstruction method will improve the description of individual wave transformation close to breaking.

Location map with the field site of La Salie indicated by the black circle. (b) Unmanned aerial vehicle photo of the field site at mid-tide during the experiment. A video system was installed on the pier shown in the lefthand side of the image. The yellow star and the red star show the location of the video system and the instrument, respectively, during the experiment.


Waves interacting with a partially immersed obstacle in the Boussinesq regime

13 février 2019 /

D. Bresch, D. Lannes, G. Métivier, to appear in Analysis & PDE, Analysis & PDE, 14 (2021), 1085-1124 Download

This paper is devoted to the derivation and mathematical analysis of a wave-structure interaction problem which can be reduced to a transmission problem for a Boussinesq system. Initial boundary value problems and transmission problems in dimension d= 1 for 2 x 2 hyperbolic systems are well understood. However, for many applications, and especially for the description of surface water waves, dispersive perturbations of hyperbolic systems must be considered. We consider here a conguration where the motion of the waves is governed by a Boussinesq system (a dispersive perturbation of the hyperbolic nonlinear shallow water equations), and in the presence of a fixed partially immersed obstacle. We shall insist on the differences and similarities with respect to the standard hyperbolic case, and focus our attention on a new phenomenon, namely, the apparition of a dispersive boundary layer. In order to obtain existence and uniform bounds on the solutions over the relevant time scale, a control of this dispersive boundary layer and of the oscillations in time it generates is necessary. This analysis leads to a new notion of compatibility condition that is shown to coincide with the standard hyperbolic compatibility conditions when the dispersive parameter is set to zero. To the authors’ knowledge, this is the rst time that these phenomena (likely to play a central role in the analysis of initial boundary value problems for dispersive perturbations of hyperbolic systems) are exhibited.


MathOcean du 25/03/2019

13 février 2019 /

(Bordeaux, salle 2 de l’IMB)

  • 14h00-15h00 Jean-François Filipot (France Energies Marines) : Le projet DiMe: vers une meilleure caractérisation du déferlement dans les états de mer de tempête pour le dimensionnement des machine EMR
  • 15h00-16h00 Damien Sous (Institut Méditerranéen d’Océanologie): Hydrodynamique d’un récif barrière corallien

Jean-François Filipot: Le projet DiMe: vers une meilleure caractérisation du déferlement dans les états de mer de tempête pour le dimensionnement des machine EMR. Dans le cadre du projet DiMe (Dimensionnement et Météocéan : caractérisation des états de mer extrêmes déferlants pour le dimensionnement des systèmes EMR), un consortium de 17 partenaires mènent des recherches dans l’objectif d’affiner la connaissance du déferlement et de ses statistiques en conditions extrêmes. Les travaux s’organisent autour de la définition de nouvelles paramétrisations du déferlement en eau profonde et peu profonde pour les modèles de vagues à phases moyennées et résolues. Ces efforts se nourrissent d’observations collectées depuis le phare de La Jument, un ouvrage mythique exposé à des états de mer exceptionnellement énergétiques. Cette expérience fait intervenir de manière couplée des observations des vagues et de leur déferlement par stéréo vidéo, radar bande X, houlographe, ADCP. Elles devraient permettre d’interpréter les mesures d’accélération et de pression s’exerçant sur le phare.

Damien Sous: Hydrodynamique d’un récif barrière corallien. Les vagues jouent un rôle déterminant dans les processus côtiers: érosion, submersion, circulation et transport des masses d’eaux, sédiments, contaminants et nutriments. Un point clé de la transformation de la houle à l’approche du rivage est la prise en compte des terrains complexes, type rocheux ou récifaux qui s’écartent souvent des hypothèses posées pour les plages sableuses ouvertes. En particulier, les fortes pentes et la complexité géométrique des fonds ont une forte influence sur les processus de réflexion, déferlement et dissipation des vagues et ondes longues associées. Le travail de recherche présenté ici vise à comprendre le fonctionnement hydrodynamique des récifs barrières, où les interactions entre vagues, niveaux moyens et courants sont largement controlés par la bathymétrie. La compréhension de ces processus complexes nécessite la combinaison de mesures sur le terrain et de simulations numériques. Le site atelier choisi est le récif barrière de Ouano en Nouvelle Calédonie. L’exposé présentera les méthodes utilisées et leur limitations, les résultats obtenus ainsi que les travaux encore en cours sur les questions en suspens.

Generating boundary conditions for a Boussinesq system

3 février 2019 /

D. Lannes, L. Weynans, Nonlinearity 33 (2020), 6868 Download

We present a new method for the numerical implementation of generating boundary conditions for a one dimensional Boussinesq system. This method is based on a reformulation of the equations and a resolution of the dispersive boundary layer that is created at the boundary when the boundary conditions are non homogeneous. This method is implemented for a simple first order finite volume scheme and validated by several numerical simulations. Contrary to the other techniques that can be found in the literature, our approach does not cause any increase in computational time with respect to periodic boundary conditions


Hyperbolic free boundary problems and applications to wave-structure interactions

31 janvier 2019 /

T. Iguchi, D. Lannes, to appear in Indiana University Journal of Mathematics, Download

Motivated by a new kind of initial boundary value problem (IBVP) with a free boundary arising in wave-structure interaction, we propose here a general approach to one dimensional IBVP as well as transmission problems. For general strictly hyperbolic N xN
quasilinear hyperbolic systems, we derive new sharp linear estimates with refi ned dependence on the source term and control on the traces of the solution at the boundary. These new estimates are used to obtain sharp results for quasilinear IBVP and transmission problems, and we also use them to propose a general approach to 2 x2 quasilinear IBVP and transmission problems with a moving or possibly free boundary. In the latter case, two kinds of evolution equations for the boundary are considered. The fi rst one is of « kinematic type » in the sense that the velocity of the interface has the same regularity as the trace of the solution. Several applications that fall into this category are considered: the interaction of waves with a lateral piston, and a new version of the well-known stability of shocks (classical and undercompressive) that improves the results of the general theory by taking advantage of the specifi cities of the one-dimensional case. We also consider « fully nonlinear » evolution equations characterized by the fact that the velocity of the interface is one derivative more singular than the trace of the solution. This confi guration is the most challenging; it is motivated by a free boundary problem arising in wave-structure interaction, namely, the evolution of the contact line between a floating object and the water. This problem is solved as an application of the general theory developed here.

An example of free boundary with kinematic boundary condition: the piston problem
An example of free boundary with fully nonlinear boundary condition : the floating structure


The shoreline problem for the one-dimensional shallow water and Green- Naghdi equations

16 janvier 2019 /

D. Lannes, G. Métivier, J. Ec. Polytech. Math. 5 (2018), 455–518. Download

The Green-Naghdi equations are a nonlinear dispersive perturbation of the nonlinear shallow water equations, more precise by one order of approximation. These equations are commonly used for the simulation of coastal flows, and in particular in regions where the water depth vanishes (the shoreline). The local well-posedness of the Green-Naghdi equations (and their justification as an asymptotic model for the water waves equations) has been extensively studied, but always under the assumption that the water depth is bounded from below by a positive constant. The aim of this article is to remove this assumption. The problem then becomes a free-boundary problem since the position of the shoreline is unknown and driven by the solution itself. For the (hyperbolic) nonlinear shallow water equation, this problem is very related to the vacuum problem for a compressible gas. The Green-Naghdi equation include additional nonlinear, dispersive and topography terms with a complex degenerate structure at the boundary. In particular, the degeneracy of the topography terms makes the problem loose its quasilinear structure and become fully nonlinear. Dispersive smoothing also degenerates and its behavior at the boundary can be described by an ODE with regular singularity. These issues require the development of new tools, some of which of independent interest such as the study of the mixed initial boundary value problem for dispersive perturbations of characteristic hyperbolic systems, elliptic regularization with respect to conormal derivatives, or general Hardy-type inequalities.


Mathocean du 21/01/19

10 janvier 2019 /

(Bordeaux, salle 2 de l’IMB)

  • 14h00-15h00 Nicolas Barral (Imperial College London) : Framework pour des simulations côtières avec adaptation de maillage anisotrope
  • 15h00-16h00 Kevin Martins (EPOC): Wave transformation in the surf zone: new insights from 2D LiDAR scanners

Nicolas Barral: Framework pour des simulations côtières avec adaptation de maillage  anisotrope. La plupart des simulations numériques pour l’ingénierie marine requièrent la modélisation de larges zones géographiques, alors que la quantité d’intérêt est très localisée (par exemple les systèmes de génération d’énergie marémotrice, ou l’étude de l’impact de tsunamis sur des zones habitées ou à risque). La taille des domaines considérés, combinée à la haute précision requise conduisent généralement à des simulations très coûteuses en temps de calcul.
L’adaptation de maillage a démontré depuis une vingtaine d’années son efficacité pour améliorer la précision numérique tout en réduisant le temps de calcul en permettant un contrôle fin de la répartition des degrés de liberté. En particulier, l’adaptation de maillage anisotrope tire parti de la flexibilité des maillages non structurés, et permet d’optimiser à la fois la taille et l’orientation des éléments du maillage. La génération de ces maillages adaptés est basée sur des champs de métriques Riemanniennes, eux-même dérivés d’un estimateur d’erreur, a priori ou a posteriori. La construction de cet estimateur d’erreur, propre au modèle étudié, est essentiel au processus d’adaptation. Dans cette présentation, on considère des métriques « multi-échelles » basée sur la Hessienne des champs de solution, qui sont capables de capturer les différentes échelles des dynamiques océaniques et des structures d’ingénierie étudiées.
L’efficacité de ces estimateurs d’erreur peut être considérablement améliorée en considérant des approches dites « goal oriented », qui sont en cours de développement dans notre framework: en considérant l’adjoint de la solution dans le modèle d’erreur, seuls les phénomènes physiques ayant une influence sur une certaine quantité cible sont maillées et résolues avec précision.
Dans cet exposé, je présenterai l’implémentation d’un framework permettant de réaliser de telles simulations adaptatives dans notre code de simulations côtières Thetis, s’appuyant sur son intégration sous-jacente avec PETSc. On considéra des applications pour la modélisation de la propagation de tsunamis, ainsi que la modélisation de structures de générations d’énergie marémotrice (barrages ou turbines).

Kevin Martins: Wave transformation in the surf zone: new insights from 2D LiDAR scanners: Over the last few decades, remote-sensing technology became an essential tool for improving our understanding of nearshore processes. Very recently, the application of lidar scanners (Light Detection And Ranging) to study swash zone hydrodynamics and morphodynamics was made possible thanks to the initiatives of few researchers. In this talk, I will present my PhD work, in which we explore the use of 2D lidar scanners to monitor the time-varying surface elevation of breaking waves in the surf zone. The surf zone constitutes one of the most challenging environments where to deploy instruments, due to the energetic wave conditions often found there. Hence, obtaining direct measurements of wave profiles at a high sampling rate represents a unique opportunity to better understand wave transformation in the surf zone.
In the first part, I will describe the working principles of 2D lidar scanners, and its potential applications to study nearshore hydro- and morphodynamics. In a second part, we use an innovative laboratory dataset to validate a CFD model of breaking wave in a wave flume at prototype scale (BARDEXII experiments). This numerical model is used to study and quantify the influence of wave reflection, generated at the inner surf/swash zone boundary, on surf zone hydrodynamics at various temporal scales. Then, the main field experiments performed during my PhD is presented. An array of three lidar scanners was deployed from a nearshore pier at Saltburn-by-the-Sea (UK) to monitor waves from the shoaling area and up to the runup limit. New insights on individual wave properties at breaking and on energy dissipation rates in the inner surf zone were obtained and will be presented. I will conclude by briefly describing my current work and how lidar data can be used to improve the parameterizations of physical processes in the surf zone.

MathOcean du 10/12/18

10 décembre 2018 /

(Toulouse, 14h à l’IMT)

Eliane Becache (INRIA et ENSTA Paris Tech) : minicours sur les PML

Eliane Becache : La méthode des couches PMLs est très populaire pour borner le domaine de calcul dans les problèmes d’ondes et a été  appliquée  à de nombreux modèles  (acoustique, électromagnétisme, élasticité…)  transitoires et fréquentiels.
Cette présentation  commencera par rappeler la définition des  PMLs et leurs propriétés.  Nous nous intéresserons ensuite à leur analyse mathématique, en particulier à des questions de stabilité. Nous présenterons d’abord l’analyse pour des modèles d’ondes transitoires hyperboliques linéaires non-dispersifs  pour lesquels on peut exhiber une condition nécessaire de stabilité. Ces résultats permettent de comprendre pourquoi les PMLs peuvent devenir instables dans certains milieux anisotropes et donnent des pistes  pour construire des PMLs stabilisées. Nous aborderons ensuite des questions de convergence des PMLs pour des problèmes fréquentiels dans des guides d’ondes, qui mettent en évidence des différences étonnantes par rapport au cas transitoire. Nous finirons par des résultats  plus récents concernant des modèles linéaires dispersifs ainsi que par les problèmes qui restent ouverts.

MathOcean du 26/11/2018

26 novembre 2018 /

(Bordeaux, salle 2 de l’IMB)

  • 14h00-15h00 Anne Mangeney (Institut de Physique du Globe de Paris): Recovering ice mass loss in Greenland from seismic data and mechanical modelling.
  • 15h00-16h00 Lisl Weynans et David Lannes (IMB): Generating boundary conditions and floating objects in Boussinesq systems.

Anne Mangeney (Institut de Physique du Globe de Paris) Recovering ice mass loss in Greenland from seismic data and mechanical modelling (joint work with Amandine Sergeant, Pauline Bonnet, Vladislav Yastrebov, Olivier Castelnau, Eléonore Stutzmann, Jean-Paul Montagner, and Patrick Quetey). Quantification of ice mass loss is a key issue to better understand the impact of climate change and in particular to constrain regional and global circulation models. The Greenland ice sheet is losing mass as a result of both increased surface melting and runoff and increased ice discharge from marine-terminating outlet glaciers. Ice discharge at these glaciers includes submarine ice melting and iceberg production. Calving of icebergs generate glacial earthquakes of magnitudes up to 5 that can be recorded at 100’s of km from the source. These waves result from the forces applied by km-scale icebergs against the terminus face, as they slowly capsize. Long-period inversion of the recorded seismic signal makes it possible to calculate these forces. Former studies failed to recover iceberg volume from the earthquake magnitude or from the maximum force due to the complex physical processes involved. We recently showed that numerical modelling of the iceberg capsize taking into account the interplay between these processes help constraining seismic inversion, making it possible to recover icebergs volume. This coupled seismic and modelling approach allows to monitor ice-mass loss from iceberg capsize in Greenland over a 20-year period of recorded glacial seismicity and to investigate its relation to climate change, ocean temperature, or glacier dynamics.

Lisl Weynans et David Lannes: Generating boundary conditions and floating objects in Boussinesq systems. Boussinesq systems are dispersive perturbations of the (hyperbolic) nonlinear shallow water equations, and are widely used for applications in coastal oceanography and more recently for the description of wave-structure interactions (eg for marine renewable energies). We shall consider two different phenomenons in this talk, in which we exhibit a dispersive boundary layer that plays an important role:
– Generating boundary conditions: for numerical simulations, one quantity (eg the surface elevation) is known at the entrance of the domain, and one is let to solve an initial boundary value problem. The theory is known for hyperbolic systems but there is no general theory in the presence of dispersion. Several techniques have been proposed, which are often difficult to implement and/or time consuming. We present here a simple method based on the analysis of the dispersive boundary layer, and that can be implemented without extra computational cost.
– Nonlinear dispersive waves with a floating object (joint work with D. Bresch and G. Métivier). We consider here a the interaction of wave described by a Boussinesq system with a floating object. We show that the problem can be reduced to a simple transmission problem (and even to an ODE) and show how to solve it by analysing the dispersive boundary layer.