Galerkin-type coupled Boundary Element Method for Time domain simulations on Discontinuous surfaces

In the context of this abstract, we present the 2D and linearized Galerkin-type coupled BEM (cBEM) that solves for the mixed boundary value problem (BVP) containing the discontinuous free surface and body surface. The incorporation of the high order spectral (HOS) method, introduced by West et al. (1987) and Dommermuth & Yue (1987), allows the monolithic coupling of wave and body dynamics. In the presented application, small amplitude motions of a surface piercing body around its equilibrium position are considered. High-order basis functions are used to approximate the solution function space composed of the velocity potential $\phi$ and its normal derivative $\frac{\partial \phi}{\partial n}$, and the geometry of the body. We discuss the verification of cBEM with an analytic reference solution and demonstrate the validity of the solver for hydrodynamic problems with experimental and numerical data

The stellar occultations by the largest satellite of the dwarf planet Haumea, Hi'iaka

Two stellar occultations by the largest satellite of the dwarf planet Haumea, Hi'iaka, were predicted to happen on April, 6th and 16th, 2021. Additional high accuracy astrometric analysis was carried out in order to refine the prediction for April 6th, using several telescopes in the 1.2-m to 2-m range, with the final shadow path crossing North Africa. We successfully detected the first event from TRAPPIST-North telescope at Oukaïmeden Observatory (Morocco). Although it was recorded from only one site, this first detection allowed us to improve the prediction for the second that crossed North America from East to West. We had a good success recording six positive detections and several negative detections that constrain the shape and size of the body. The light curves obtained from the different observatories provide the time at which the star disappears and reappears, which are translated into chords (the projected lines on the sky-plane as observed from each location). Additionally, we carried out a campaign to study Hi'iaka's rotational light-curve, studying the residuals of Haumea's rotational light-curve to a four-order Fourier fit. We obtained the rotational phases at the times of the occultations, which is critical for the analysis of the occultations, given that Hi'iaka is clearly non-spherical. Our preliminary results show that Hi'iaka indeed has a triaxial shape with a larger effective diameter than what has been published so far. The preliminary results and their implications will be discussed in this talk

Physical properties of the trans-Neptunian binary 2000 YW₁₃₄

The study of trans-Neptunian binaries (TNBs) remains one of the most active areas of progress in understanding the solar system beyond Neptune. TNBs have been found in every dynamical population of the trans-Neptunian region (Noll et al. 2020), with proportions ranging from 29 % in the cold classical population to 5.5 % for the remaining classes combined (Brunini 2020). The formation of the contact TNB Arrokoth is one of the challenges that formation models face nowadays. The current angular momentum of Arrokoth is too low and the current binary formation scenarios, by either rotational fission or streaming instability (Nesvorný et al. 2019), require also loss of angular momentum (McKinnon et al. 2020). Additionally, formation mechanisms of close binaries may be distinct from those for the wider pairs. As the angular momentum of a system approaches that of an object spinning near its critical rotation period, rotational fission is the most likely explanation for their formation (Descamps et al. 2008), which is thought to be the case for the proposed satellites of Varuna and 2002 TC302 systems (Fernández-Valenzuela et al. 2019; Ortiz et al. 2020). If close TNBs turn out to be common for objects rotating close to the breakup limit, that could reveal important clues about angular momentum evolution during accretion for TNOs (Petit et al. 2011). However, characterizing binary systems at such distances is challenging. From the ~120 known TNBs, only around 40 have their mutual orbit fully determined, let alone physical characterization. 2000 YW134 is a TNB in a 3:8 resonance with an orbital semi-major axis of 57.4 au (a rare occurrence). On February 23rd, 2022, it occulted the Gaia EDR3 star 627356458358636544 (V = 17.1 mag). The stellar occultation was initially predicted using the JPL orbit solution #24, and updated using data from the 1.5-m and 1.23-m telescopes at Sierra Nevada and Calar Alto Observatories, using the same methodology as explained in Ortiz et al (2020). From the 17 observatories involved, seven reported positive chords, with five of them corresponding to the main body and the other two chords corresponding to its satellite. We are currently working on the analysis of these data in order to obtain the physical properties that characterize the system. Preliminary results show that the lower limit for the equivalent projected diameter of the satellite is twice the previously estimated size from HST observations (Stephens et al. 2006). We will also compare our results with the area-equivalent diameter and albedo obtained using thermal data from Herschel and Spitzer observations (Farkas-Takács et al. 2020)

Real-time reconstruction and prediction of ocean wave fields from remote optical measurements

Les recherches présentées dans le cadre de cette thèse portent sur le traitement de mesures par télédétection optique de la surface océanique en vue de la prédiction de champs de vagues au voisinage d’une structure marine, information cruciale pour l’analyse et le contrôle d’une large gamme d’opérations en mer. Elles visent notamment à inclure, à moindre coût calcul, la modélisation de phénomènes nonlinéaires, conservant une représentation réaliste de la surface en cas d’état de mer sévère. Une approche Lagrangienne faiblement nonlinéaire (ICWM), dont les propriétéshydrodynamiques sont étudiées par intercomparaison avec des modèles de référence, est sélectionnée pour la description de la surface libre. Le problème de prédiction est formulé comme un problème inverse dont le but est de faire correspondre la solution décrite par le modèle de vagues à des observations, composées ici d’élévations de surface mesurées par un capteur lidar synthétique balayant la surface en incidence rasante. Les prédictions résultent de la propagation en temps/espace du modèle ainsi paramétré. L’applicabilité de la méthodologie est validée à l’aide d’observations de champs de vagues unidirectionnels et directionnels, acquises à des instants différents pour pallier à leur forte nonuniformité spatiale. La comparaison relative des performances de ICWM et de modèles d’ordre inférieur met en évidence les améliorations dues à la modélisation des non-linéarités, notamment celles issues de la correction de la relation dedispersion. Une démonstration de la pertinence de l’utilisation de ICWM est ensuite proposée au moyen d’une procédure entièrement validée expérimentalement en bassin de houle.Researches conducted in this thesis address the problem of deterministic prediction of ocean wave fields around a marine structure, a key parameter for the analysis and control of a vast range of offshore operations, on the basis ofdatasets acquired remotely by an optical sensor. Efforts focus on the inclusion, at low computational cost, of the modeling of nonlinear hydrodynamic phenomena, preserving the reliability the surface representation in case of severe sea state.A weakly nonlinear Lagrangian approach (ICWM), whose hydrodynamic properties are evaluated by inter-comparison with reference wave models, is selected for the description of the free surface. The prediction problem is then formulated as an inverse problem that aims at fitting the solution described by the wave model to observations, here composed of free surface elevation datasets generated by a synthetic, yet realistic, lidar sensor scanning the ocean surface at grazing angle. Predictions are then issued through the propagation in time and space of the parameterized wave model. The applicability of the methodology is validated using observations of both unidirectional and directional wave fields, obtained at differentinstants to compensate for their strong spatial non-uniformity. The relative performance comparison between ICWM and lower-order wave models highlights the improvements due to the modeling of wave nonlinearities, especially those pertaining to the correction of the dispersion relation. A demonstration of the usefulness of ICWM is then provided by meansof a procedure that is fully validated experimentally in a wave tank

Reconstruction et prédiction en temps réel de champs de vagues par télédétection optique

Researches conducted in this thesis address the problem of deterministic prediction of ocean wave fields around a marine structure, a key parameter for the analysis and control of a vast range of offshore operations, on the basis ofdatasets acquired remotely by an optical sensor. Efforts focus on the inclusion, at low computational cost, of the modeling of nonlinear hydrodynamic phenomena, preserving the reliability the surface representation in case of severe sea state.A weakly nonlinear Lagrangian approach (ICWM), whose hydrodynamic properties are evaluated by inter-comparison with reference wave models, is selected for the description of the free surface. The prediction problem is then formulated as an inverse problem that aims at fitting the solution described by the wave model to observations, here composed of free surface elevation datasets generated by a synthetic, yet realistic, lidar sensor scanning the ocean surface at grazing angle. Predictions are then issued through the propagation in time and space of the parameterized wave model. The applicability of the methodology is validated using observations of both unidirectional and directional wave fields, obtained at differentinstants to compensate for their strong spatial non-uniformity. The relative performance comparison between ICWM and lower-order wave models highlights the improvements due to the modeling of wave nonlinearities, especially those pertaining to the correction of the dispersion relation. A demonstration of the usefulness of ICWM is then provided by meansof a procedure that is fully validated experimentally in a wave tank.Les recherches présentées dans le cadre de cette thèse portent sur le traitement de mesures par télédétection optique de la surface océanique en vue de la prédiction de champs de vagues au voisinage d’une structure marine, information cruciale pour l’analyse et le contrôle d’une large gamme d’opérations en mer. Elles visent notamment à inclure, à moindre coût calcul, la modélisation de phénomènes nonlinéaires, conservant une représentation réaliste de la surface en cas d’état de mer sévère. Une approche Lagrangienne faiblement nonlinéaire (ICWM), dont les propriétéshydrodynamiques sont étudiées par intercomparaison avec des modèles de référence, est sélectionnée pour la description de la surface libre. Le problème de prédiction est formulé comme un problème inverse dont le but est de faire correspondre la solution décrite par le modèle de vagues à des observations, composées ici d’élévations de surface mesurées par un capteur lidar synthétique balayant la surface en incidence rasante. Les prédictions résultent de la propagation en temps/espace du modèle ainsi paramétré. L’applicabilité de la méthodologie est validée à l’aide d’observations de champs de vagues unidirectionnels et directionnels, acquises à des instants différents pour pallier à leur forte nonuniformité spatiale. La comparaison relative des performances de ICWM et de modèles d’ordre inférieur met en évidence les améliorations dues à la modélisation des non-linéarités, notamment celles issues de la correction de la relation dedispersion. Une démonstration de la pertinence de l’utilisation de ICWM est ensuite proposée au moyen d’une procédure entièrement validée expérimentalement en bassin de houle

Nonlinear deterministic reconstruction and prediction of remotely measured ocean surface waves

Algorithms for reconstructing and predicting nonlinear ocean wave fields from remote measurements are presented. Three types of synthetic observations are used to quantify the influence of remote measurement modulation mechanisms on the algorithms’ performance. First, the observations correspond to randomly distributed surface elevations. Then, they are related to a marine radar model – the second type takes the wave shadowing modulation into account whereas the third one also includes the tilt modulation. The observations are numerically generated based on unidirectional waves of various steepness values. Linear and weakly nonlinear prediction algorithms based on analytical models are considered, as well as a highly nonlinear algorithm relying on the high-order spectral (HOS) method. Reconstructing surfaces from shadowed observations is found to have an impact limited to the non-visible regions, while tilt modulation affects the reconstruction more generally due to the indirect, more complex extraction of wave information. It is shown that the accuracy of the surface reconstruction mainly depends on the correct modelling of the wave shape nonlinearities. Modelling the nonlinear correction of the dispersion relation, in particular the frequency-dependent wave phase effects in the case of irregular waves, substantially improves the prediction. The suitability of the algorithms for severe wave conditions in finite depth and using non-perfect observations is assessed through wave tank experiments. It shows that only the third-order HOS solution predicts the right amplitude and phase of an emerging extreme wave, emphasizing the relevance of the corresponding physical modelling

The Influence of Characteristic Sea State Parameters on the Accuracy of Irregular Wave Field Simulations of Different Complexity

The accurate description of the complex genesis and evolution of ocean waves, as well as the associated kinematics and dynamics is indispensable for the design of offshore structures and the assessment of marine operations. In the majority of cases, the water-wave problem is reduced to potential flow theory on a somehow simplified level. However, the nonlinear terms in the surface boundary conditions and the fact that they must be fulfilled on the unknown water surface make the boundary value problem considerably complex. Hereby, the contrary objectives with respect to a very accurate representation of reality and numerical efficiency must be balanced wisely. This paper investigates the influence of characteristic sea state parameters on the accuracy of irregular wave field simulations of different complexity. For this purpose, the high-order spectral method was applied and the underlying Taylor series expansion was truncated at different orders so that numerical simulations of different complexity can be investigated. It is shown that, for specific characteristic sea state parameters, the boundary value problem can be significantly reduced while providing sufficient accuracy

Análisis 3D multiescalado de una ciudad de la Edad del Hierro: el caso de Silla del Papa (Cádiz, España)

International audienc

Phase-Resolved Reconstruction Algorithm and Deterministic Prediction of Nonlinear Ocean Waves From Spatio-Temporal Optical Measurements

We investigate a nonlinear phase-resolved reconstruction algorithm and models for the deterministic prediction of ocean waves based on a large number of spatiooral optical measurements of surface elevations. We consider a single sensor (e.g., LIDAR, stereo-video, etc.) mounted on a fixed offshore structure and remotely measuring fields of free surface elevations. Assuming a uniform distribution of measurement points over the sensor aperture angles, the density of free surface observation points geometrically decreases with the distance from the sensor. Additionally, wave shadowing effects occur, which become more important at small viewing angles (i.e., grazing incidence on the surface). These effects result in observations of surface elevation that are sparsely distributed. Here, based on earlier work by [1], we present and discuss the characteristics of an algorithm, aimed at assimilating such sparse data and able to deterministically reconstruct and propagate ocean surface elevations for their prediction in time and space. This algorithm could assist in the automatic steering and control of a variety of surface vehicles. Specifically, we compare prediction results using linear wave theory and the weakly nonlinear Choppy Wave Model [2, 3], extended here to an improved second order formulation. The latter model is based on an efficient Lagrangian formulation of the free surface and was shown to be able to model wave properties that are important to the proper representation of nonlinear free surfaces, namely wave shape and celerity. Synthetic datasets from highly nonlinear High Order Spectral simulations are used as reference oceanic surfaces. Predicted results are analyzed over an area that evolves in time, using the theoretical amount of information assimilated during the reconstruction of the wave field. For typical horizons of prediction, we discuss the capabilities of our assimilation process for each wave model considered

An improved Lagrangian model for the time evolution of nonlinear surface waves

Accurate real-time simulations and forecasting of phase-revolved ocean surface waves require nonlinear effects, both geometrical and kinematic, to be accurately represented. For this purpose, wave models based on a Lagrangian steepness expansion have proved particularly efficient, as compared to those based on Eulerian expansions, as they feature higher-order nonlinearities at a reduced numerical cost. However, while they can accurately model the instantaneous nonlinear wave shape, Lagrangian models developed to date cannot accurately predict the time evolution of even simple periodic waves. Here, we propose a novel and simple method to perform a Lagrangian expansion of surface waves to second order in wave steepness, based on the dynamical system relating particle locations and the Eulerian velocity field. We show that a simple redefinition of reference particles allows us to correct the time evolution of surface waves, through a modified nonlinear dispersion relationship. The resulting expressions of free surface particle locations can then be made numerically efficient by only retaining the most significant contributions to second-order terms, i.e. Stokes drift and mean vertical level. This results in a hybrid model, referred to as the \u27improved choppy wave model\u27 (ICWM) (with respect to Nouguier et al.\u27s J. Geophys. Res., vol. 114, 2009, p. C09012), whose performance is numerically assessed for long-crested waves, both periodic and irregular. To do so, ICWM results are compared to those of models based on a high-order spectral method and classical second-order Lagrangian expansions. For irregular waves, two generic types of narrow- A nd broad-banded wave spectra are considered, for which ICWM is shown to significantly improve wave forecast accuracy as compared to other Lagrangian models; hence, ICWM is well suited to providing accurate and efficient short-term ocean wave forecast (e.g. over a few peak periods). This aspect will be the object of future work