arXiv subjects

Michel Benoit

Publications and source records attributed to Michel Benoit.

11 recordsLinked to original sources

arXiv2026

Recovery of directional wave spectrum from sparse data with compressed sensing

Compressed sensing provides an efficient framework for reconstructing wave signals from reduced measurements. For multi-channel buoy data, the three displacement components exhibit intrinsic correlations, as wave motion contributes simultaneously to all directions according to linear wave theory. Meanwhile, conventional compressed sensing methods based on $\ell_1$-shrinkage tend to underestimate signal energy when sparsity is not strictly satisfied, leading to biased spectral estimation. This paper introduces a group sparsity constraint to promote physically consistent sparse representations across channels. An energy constraint is proposed in the form of a soft lower bound, enabling an isotropic rescaling of the recovered spectrum while preserving its sparse structure. Considering a large volume of buoy data, we demonstrate through a series of experiments that the proposed approach enables compression by retaining a subset of original measurements.

physics.geo-ph↗

arXiv2026

Effect of directionality on extreme wave formation during nonlinear shoaling

Recent studies have shown that, in coastal waters where water depth decreases significantly due to rapid bathymetric changes, the non-equilibrium dynamics (NED) substantially increases the occurrence probability of extreme (rogue) waves. Nevertheless, research on depth-induced NED has been predominantly confined to unidirectional irregular waves, while the role of directionality remains largely unexplored. The scarce studies on multidirectional waves mainly rely on numerical simulations and have yielded conflicting results. In this work, we report on an experimental investigation of wave directionality on the depth-induced non-equilibrium wave statistics. High-order statistical moments, skewness and kurtosis, are used as proxies for the non-equilibrium wave response. Our results indicate that the directional spreading has a minor effect on decreasing the maximum values of these statistical moments. In contrast, the incidence direction plays a significant role in the non-equilibrium wave response, which is attributed to the effective bottom slope.

physics.flu-dyn↗

arXiv2026

Bayesian Optimization for reanalysis and calibration of highly energetic sea state events simulated with a spectral third-generation wave model

Accurate hindcasting of sea state events is a cornerstone of coastal engineering, risk assessment, and climate-related studies, yet it remains limited by uncertainties in physical parameterizations and model structure. This study introduces an automated calibration framework based on Bayesian Optimization (BO) using the Tree-structured Parzen Estimator (TPE) to constrain key dissipative processes in the ANEMOC-3 hindcast wave model, including bottom-friction losses, depth-induced wave breaking, and dissipation driven by wave strong opposing currents. The methodology enables the joint optimization of continuous physical parameters and discrete model structure choices within a unified probabilistic search space, significantly reducing model-observation misfit. Calibration is conducted over the high energy storm conditions of February 2014, while transferability is assessed both temporally and spatially, through independent validation on January 2014 and January 2018 events and across a network of offshore and coastal buoy observations. The optimized configurations retain skill beyond the calibration period and across observation sites, yielding systematically improved agreement with buoy measurements in terms of bias, root mean square error, and scatter index relative to the reference configuration. These results highlight the potential of Bayesian Optimization as a scalable and robust framework for automating the calibration of complex wave hindcast systems. Future developments will address multi-objective optimization, uncertainty quantification, and the integration of complementary observational datasets.

physics.ao-ph↗

arXiv2025

Evolution of extreme nonlinear wave fields over strongly reflective plane beaches

The description of complex wave processes, in addition to the shoaling problem, is often cumbersome even for the evolution of regular waves. For reflection under the regime of wave breaking, the surf similarity is generally accepted as the leading parameter controlling the reflection rates and types of breakers. Although little is known about the effect of reflection rates on the formation of extreme nonlinear waves, some debate has arisen regarding whether high reflection rates enhance the nonlinearity at the tail of the wave height distribution. In this work, we provide theoretical evidence that at very steep beaches of smooth composition, the reflection rate near unity will tend to stabilize the excess kurtosis otherwise generated by shoaling and controlled in magnitude by the bottom slope magnitude. We further verified this result through fully nonlinear numerical simulations, reaching a good agreement.

nlin.PS↗

arXiv2023

Effect of shoaling length on rogue wave occurrence

The impact of shoaling on linear water waves is well-known, but it has only been recently found to significantly amplify both the intensity and frequency of rogue waves in nonlinear irregular wave trains atop coastal shoals. At least qualitatively, this effect has been partially attributed to the "rapid'" nature of the shoaling process, i.e., shoaling occurs over a distance far shorter than that required for waves to modulate themselves and adapt to the reduced water depth. Through the development of a theoretical model and highly accurate nonlinear simulations, we disentangle the respective effects of the slope length and the slope gradient of a shoal and focus on the slope length to investigate the rapidness of the shoaling process on the evolution of key statistical and spectral sea-state parameters. Provided the shoal slope is 1/10 or steeper, our results indicate that the non-equilibrium dynamics is involved even for rather short shoaling lengths and becomes dominant in the regime of large lengths. When the non-equilibrium dynamics governs the wave evolution, further extending the slope length no longer influences the statistical and spectral measures. Thus, the shoaling effect on rogue waves is mainly driven by the slope magnitude rather than the slope length. Moreover, the simulations show that a higher cut-off frequency of the wave spectrum has a smaller impact on wave statistics than expected for a flat bottom in deep water and that insufficient attenuation of low-frequency waves at the downstream domain boundary has notable influence on wave statistics atop the shoal.

physics.flu-dyn↗

arXiv2021

Assessment of one-way coupling methods from a potential to a viscous flow solver based on domain- and functional-decomposition for fixed submerged bodies in nonlinear waves

To simulate the interaction of ocean waves with marine structures, coupling approaches between a potential flow model and a viscous model are investigated. The first model is a fully nonlinear potential flow (FNPF) model based on the Harmonic Polynomial Cell (HPC) method, which is highly accurate and best suited for representing long distance wave propagation. The second model is a CFD code, solving the Reynolds-Averaged Navier-Stokes (RANS) equations within the \openfoam toolkit, more suited to represent viscous and turbulent effects at local scale in the body vicinity. Two one-way coupling strategies are developed and compared in two dimensions, considering fully submerged and fixed structures. A domain decomposition (DD) strategy is first considered, introducing a refined mesh in the body vicinity on which the RANS equations are solved. Boundary conditions and interpolation operators from the FNPF results are developed in order to enforce values at its outer boundary. The second coupling strategy considers a decomposition of variables (functional decomposition, FD) on the local grid. As the FNPF simulation provides fields of variables satisfying the irrotational Euler equations, complementary velocity and pressure components are introduced as the difference between the total flow variables and the potential ones. Those complementary variables are solutions of modified RANS equations. Comparisons are presented for nonlinear waves interacting with a horizontal cylinder of rectangular cross-section. The loads exerted on the body computed from the four simulation methods (standalone FNPF, standalone CFD, DD and FD coupling schemes) are compared with experimental data. It is shown that both coupling approaches produce an accurate representation of the loads and associated hydrodynamic coefficients over a large range of incident wave steepness and Keulegan-Carpenter number.

physics.flu-dyn↗

arXiv2020

Development and validation of a numerical wave tank based on the Harmonic Polynomial Cell and Immersed Boundary methods to model nonlinear wave-structure interaction

A fully nonlinear potential Numerical Wave Tank (NWT) is developed in two dimensions, using a combination of the Harmonic Polynomial Cell (HPC) method for solving the Laplace problem on the wave potential and the Immersed Boundary Method (IBM) for capturing the free surface motion. This NWT can consider fixed, submerged or wall-sided surface piercing, bodies. To compute the flow around the body and associated pressure field, a novel multi overlapping grid method is implemented. Each grid having its own free surface, a two-way communication is ensured between the problem in the body vicinity and the larger scale wave propagation problem. Pressure field and nonlinear loads on the structure are computed by solving a boundary value problem on the time derivative of the potential. The stability and convergence properties of the solver are studied basing on extensive tests with standing waves of large to extreme wave steepness, up to $H/\lambda=0.2$ ($H$ is the crest-to-trough wave height and $\lambda$ the wavelength). Ranges of optimal time and spatial discretizations are determined and high-order convergence properties are verified, first without using any filter. For cases with either high level of nonlinearity or long simulation duration, the use of mild Savitzky-Golay filters is shown to extend the range of applicability of the model. Then, the NWT is tested against two wave flume experiments, analyzing forces on bodies in various wave conditions. First, nonlinear components of the vertical force acting on a small horizontal circular cylinder with low submergence below the mean water level are shown to be accurately simulated up to the third order in wave steepness. The second case is a dedicated experiment with a floating barge of rectangular cross-section. This very challenging case (body with sharp corners in large waves) allows to examine the behavior (...to continue...)

physics.flu-dyn↗

arXiv2019

Comparing methods of modeling depth-induced breaking of irregular waves with a fully nonlinear potential flow approach

The modeling of wave breaking dissipation in coastal areas is investigated with a fully nonlinear and dispersive wave model. The wave propagation model is based on potential flow theory, which initially assumes non-overturning waves. Including the impacts of wave breaking dissipation is however possible by implementing a wave breaking initiation criterion and dissipation mechanism. Three criteria from the literature, including a geometric, kinematic, and dynamic-type criterion, are tested to determine the optimal criterion predicting the onset of wave breaking. Three wave breaking energy dissipation methods are also tested: the first two are based on the analogy of a breaking wave with a hydraulic jump, and the third one applies an eddy viscosity dissipative term. Numerical simulations are performed using combinations of the three breaking onset criteria and three dissipation methods. The simulation results are compared to observations from four laboratory experiments of regular and irregular waves breaking over a submerged bar, irregular waves breaking on a beach, and irregular waves breaking over a submerged slope. The different breaking approaches provide similar results after proper calibration. The wave transformation observed in the experiments is reproduced well, with better results for the case of regular waves than irregular waves. Moreover, the wave statistics and wave spectra are predicted well in general, and in particular for regular waves. Some differences are observed for irregular wave cases, in particular in the low-frequency range. This is attributed to incomplete absorption of the long waves in the numerical model. Otherwise, the wave spectra in the range $[0.5f_p,\: 5f_p]$ are reproduced well, before, inside, and after the breaking zone for the three irregular wave experiments.

physics.ao-ph↗

arXiv2019

Modeling of depth-induced wave breaking in a fully nonlinear free-surface potential flow model

Two methods to treat wave breaking in the framework of the Hamiltonian formulation of free-surface potential flow are presented, tested, and validated. The first is an extension of Kennedy et al (2000)'s eddy-viscosity approach originally developed for Boussinesq-type wave models. In this approach, an extra term, constructed to conserve the horizontal momentum for waves propagating over a flat bottom, is added in the dynamic free-surface condition. In the second method, a pressure distribution is introduced at the free surface that dissipates wave energy by analogy to a hydraulic jump (Guignard and Grilli, 2001). The modified Hamiltonian systems are implemented using the Hamiltonian Coupled-Mode Theory, in which the velocity potential is represented by a rapidly convergent vertical series expansion. Wave energy dissipation and conservation of horizontal momentum are verified numerically. Comparisons with experimental measurements are presented for the propagation of a breaking dispersive shock wave following a dam break, and then incident regular waves breaking on a mildly sloping beach and over a submerged bar.

physics.flu-dyn↗

arXiv2018

Modeling nonlinear wave-body interaction with the Harmonic Polynomial Cell method combined with the Immersed Boundary Method on a fixed grid

To model the propagation of large water waves and associated loads applied to offshore structures, scientists and engineers have a need of fast and accurate models. A wide range of models have been developped in order to predict wave-fields and hydrodynamic loads at small scale, from the linear potential boundary element method to complete CFD codes, based on the Navier-Stokes equations. Although the latters are well adapted to solve the wave-structure interaction at small scale, their use is limited due to the computational cost of such models and numerical diffusion. Alternative approaches, capturing the nonlinear effects, are thus needed. Shao and Faltinsen [5] proposed an innovative technique, called " harmonic polynomial cell " (HPC) method to tackle this problem. This approach is implemented and tested in 2 dimensions (x, z), first on a standing wave problem and then to evaluate the nonlinear forces acting on a fixed submerged cylinder.

physics.comp-ph↗

arXiv2009

A double-layer Boussinesq-type model for highly nonlinear and dispersive waves

We derive and analyze in the framework of the mild-slope approximation a new double-layer Boussinesq-type model which is linearly and nonlinearly accurate up to deep water. Assuming the flow to be irrotational, we formulate the problem in terms of the velocity potential thereby lowering the number of unknowns. The model derivation combines two approaches, namely the method proposed by Agnon et al. (Agnon et al. 1999, J. Fluid Mech., 399 pp. 319-333) and enhanced by Madsen et al. (Madsen et al. 2003, Proc. R. Soc. Lond. A, 459 pp. 1075-1104) which consists in constructing infinite-series Taylor solutions to the Laplace equation, to truncate them at a finite order and to use Padé approximants, and the double-layer approach of Lynett & Liu (Lynett & Liu 2004, Proc. R. Soc. Lond. A, 460 pp. 2637-2669) allowing to lower the order of derivatives. We formulate the model in terms of a static Dirichlet-Neumann operator translated from the free surface to the still-water level, and we derive an approximate inverse of this operator that can be built once and for all. The final model consists of only four equations both in one and two horizontal dimensions, and includes only second-order derivatives, which is a major improvement in comparison with so-called high-order Boussinesq models. A linear analysis of the model is performed and its properties are optimized using a free parameter determining the position of the interface between the two layers. Excellent dispersion and shoaling properties are obtained, allowing the model to be applied up to deep water. Finally, numerical simulations are performed to quantify the nonlinear behaviour of the model, and the results exhibit a nonlinear range of validity reaching deep water areas.

physics.ao-ph↗