Le secteur de l’énergie houlomotrice s’appuie fortement sur la modélisation mathématique et la simulation d’expériences physiques mettant en jeu les interactions entre les ondes et les corps. Dans ce travail, nous avons développé un modèle d’interaction de fidélité moyenne vague-corps pour la simulation de structures tronquées flottantes fonctionnant en mouvement vertical. Ce travail concerne l’ingénierie de l’énergie marine, pour des applications telles que les convertisseurs d’énergie de vague (WEC) à absorption ponctuelle, même si ses applications peuvent aussi être utilisées en ingénierie maritime et navale. Les motivations de ce travail reposent sur les méthodes standard actuelles pour décrire l’interaction corps-vague. Cellesci sont basées sur des modèles résolvant le flux de potentiel linéaire (LPF), du fait de leur grande efficacité. Cependant, les modèles LPF sont basés sur l’hypothèse de faible amplitude et ne peuvent pas répresenter les effets hydrodynamiques non linéaires, importants pour le WEC opérant dans la région de résonance ou dans les régions proches du rivage. En effet, il a été démontré que les modèles LFP prédisent de manière excessive la production de puissance, sauf si des coefficients de traînée sont calibrés. Plus récemment, des simulations Reynolds Averaged Navier-Stokes (RANS) ont été utilisées pour les WEC. RANS est un modèle complet et précis, mais très coûteux en calcul. Il n’est ni adapté à l’optimisation d’appareils uniques ni aux parcs énergétiques. Nous avons donc proposé un modèle de fidélité moyenne basé sur des équations de type Boussinesq, afin d’améliorer le compromis entre précision et efficacité. Les équations de type Boussinesq sont des modèles d’ondes intégrées en profondeur et ont été un outil d’ingénierie standard pour la simulation numérique de la propagation d’ondes non linéaires dans les eaux peu profondes et les zones côtières. Grâce à l’élimination de la dimension verticale, le modèle résultant est très efficace et évite la description temporelle de la limite entre la surface libre et l’air. Jiang (2001) a proposé un modèle de Boussinesq unifié, décomposant le problème en deux domaines : surface libre et corps. Dans cette méthode, le domaine du corps est également modélisé par une approche intégrée en profondeur - d’où le terme unifié. Récemment, Lannes (2016) avait analysé de manière rigoureuse une configuration similaire dans une équation non linéaire en eaux peu profondes, en déduisant une solution exacte et semi-analitique pour des corps en mouvement. Suivant la même approche, Godlewski et al. (2018) a élaboré un modèle de flux d’eau peu profonde encombrée. [...] Dans cette thèse, nous développons les résultats présentés par Eskilsson et al. (2016) et Bosi et al. (2019). Le modèle est étendu à deux dimensions horizontales. Le modèle 1D est vérifié à l’aide de solutions fabriquées et validé par rapport aux résultats publiés sur l’interaction vague-corps en 1D pour les pontons fixes et corps en mouvement de soulèvement forcé et libre. Les résultats des preuves de concept de la simulation de plusieurs corps sont présentés. Nous validons et vérifions le modèle 2D en suivant des étapes similaires. Enfin, nous mettons en oeuvre la technique de verrouillage, une méthode de contrôle de mouvement du corps pour améliorer la réponse au mouvement des vagues. Il est démontré que le modèle possède une excellente précision, qu’il est pertinent pour les applications d’ondes en interaction avec des dispositifs à énergie houlomotrice et qu’il peut être étendu pour simuler des cas plus complexes. / The wave energy sector relies heavily on mathematical modelling and simulation of the interactions between waves and floating bodies. In this work, we have developed a medium-fidelity wave-body interaction model for the simulation of truncated surface piercing structures operating in heave motion, such as point absorbers wave energy converters (WECs). The motivation of the work lies in the present approach to wave-body interaction. The standard approach is to use models based on linear potential flow (LPF). LPF models are based on the small amplitude/ small motion assumption and, while highly computational efficient, cannot account for nonlinear hydrodynamic effects (except for Morison-type drag). Nonlinear effects are particularly important for WEC operating in resonance, or in nearshore regions where wave transformations are expected. More recently, Reynolds Averaged Navier-Stokes (RANS) simulations have been employed for modelling WECs. RANS is a complete and accurate model but computationally very costly. At present RANS models are therefore unsuited for the optimization of single devices, not to mention energy farms. Thus, we propose a numerical model based built on Boussinesq-type equations to include wave-wave interaction as well as finite body motion in a computationally efficient formulation. Boussinesq-type equations are depth-integrated wave models and are standard engineering tool for numerical simulation of propagation of nonlinear wave in shallow water and coastal areas. Thanks to the elimination of the vertical dimension and the avoidance of a time-dependent computational the resulting model is very computational efficient. Jiang (Jiang, 2001) proposed a unified Boussinesq model, decomposing the problem into free surface and body domains. Notably, in Jiang’s methodology also the body domain is modeled by a depth-integrated approach –hence the term unified. As all models based on Boussinesq-type equations, the model is limited to shallow and intermediate depth regimes. We consider the Madsen and Sørensen model, an enhanced Boussinesq model, for the propagation of waves. We employ a spectral/hp finite element method (SEM) to discretize the governing equations. The continuous SEM is used inside each domain and flux-based coupling conditions are derived from the discontinuous Galerkin method. The use of SEM give support for the use of adaptive meshes for geometric flexibility and high-order accurate approximations makes the scheme computationally efficient. In this thesis, we present 1D results for the propagation and interaction of waves with floating structures. The 1D model is verified using manufactured solutions. The model is then validated against published results for wave-body interaction. The hydrostatic cases (forced motion and decay test) are compared to analytical and semi-analytical solutions (Lannes, 2017), while the non-hydrostatic tests (fixed pontoon and freely heaving bodies) are compared to RANS reference solutions. The model is easily extended to handle multiple bodies and a proof-of-concept result is presented. Finally, we implement the latching technique, a method to control the movement of the body such that the response to the wave movement is improved. The model is extended to two horizontal dimensions and verified and validated against manufactured solutions and RANS simulations. The model is found to have a good accuracy both in one and two dimensions and is relevant for applications of waves interacting with wave energy devices. The model can be extended to simulate more complex cases such as WEC farms/arrays or include power generation systems to the device.

Near-bottom current data was collected over a period of 8 years at the U.S. Army Corps of Engineers Field Research Facility in Duck, North Carolina. This data set consisted of currents measured up to three elevations above the bottom at deployment depths of 5 meters, 8 meters and 13 meters, as well as continuous real-time wind and wave data collected at the pier. The data was collated, quality checked and analyzed to define a climatology of near bottom currents along the study area using current moments. This data set had previously never been available for analysis due to the large amount of effort required to take old computer files and subject them to rigorous processing and quality control. The analyses conducted in this thesis represent the first ever attempt to analyze this type of data on this scale. An initial monthly investigation was conducted at the 8-meter site to determine driving forces of mean currents, and a more in depth seasonal investigation was subsequently completed to quantify the relationships between the cross-shore currents and different forcing mechanisms. Once seasonal trends were established relating mean current to incident wave height, wave steepness and wind speed, an examination of some significant historical events within the study was completed to help link cross-shore current behavior to storm events. Three separate nor’easter events and three significant hurricanes (Bonnie, Dennis and Floyd) were found to produce significant cross-shore currents at the study site. Similar to previous nearshore studies, it was found that the occurrence of onshore winds and wave heights greater than about 1.5 meters produce near-bottom mean currents moving in the offshore direction. Alternatively, when winds are blowing in the offshore direction, waves are still propagating onshore, but mean near-bottom currents tend to be directed in the onshore direction. The importance of vertical current structure within the water column was apparent, even though the instruments’ measurement elevations were all located within the bottom boundary layer. In contrast to the assumption of zero cross-shore velocity at near-coast sites implicit in two-dimensional depth averaged models used in most coastal engineering studies today, it was found that cross-shore near-bottom currents are rarely ever zero. Depth-averaged models inherently assume that currents move as a single block of water throughout the water column. The physical impacts of this misrepresentation of nearshore currents become very significant in predictions of many coastal phenomena, such as storm surge, sediment transport and wave conditions at the coast. When wave heights exceed 2 meters, mean currents tend to be between 0.2-0.5 meters per second in both the onshore and offshore direction, in the opposite direction of the primary forcing at the surface. In some instances, wave heights are low with strong mean currents while wind speeds are high, indicating the driving force in this situation is wind speed. However, there are cases where wave heights are large and mean current values are relatively low, which requires further investigation. Future work will include investigating phenomena that are related to higher-order odd moments of the current statistics, since they are expected to play a critical role in improved understanding of the physics within the nearshore and are very much needed for predictions of coastal evolution under future sea level rise and potential climate change.