arXiv subjects

Frédéric Dias

Publications and source records attributed to Frédéric Dias.

At least 19 recordsLinked to original sources

arXiv2023

Localization landscape for interacting Bose gases in one-dimensional speckle potentials

While the properties and the shape of the ground state of a gas of ultracold bosons are well understood in harmonic potentials, they remain for a large part unknown in the case of random potentials. Here, we use the localization-landscape (LL) theory to study the properties of the solutions to the Gross-Pitaevskii equation (GPE) in one-dimensional (1D) speckle potentials. In the cases of attractive interactions, we find that the LL allows one to predict the position of the localization center of the ground state (GS) of the GPE. For weakly repulsive interactions, we point out that the GS of the quasi-1D GPE can be understood as a superposition of a finite number of single-particle states, which can be computed by exploiting the LL. For intermediate repulsive interactions, we introduce a Thomas-Fermi-like approach for the GS which holds in the smoothing regime, well beyond the usual approximation involving the original potential. Moreover, we show that, in the Lifshitz glass regime, the particle density and the chemical potential can be well estimated by the LL. Our approach can be applied to any positive-valued random potential endowed with finite-range correlations and can be generalized to higher-dimensional systems.

cond-mat.quant-gas↗

arXiv2020

Extreme wave runup on a vertical cliff

Wave impact and run-up onto vertical obstacles are among the most important phenomena which must be taken into account in the design of coastal structures. From linear wave theory, we know that the wave amplitude on a vertical wall is twice the incident wave amplitude with weakly nonlinear theories bringing small corrections to this result. In this present study, however, we show that certain simple wave groups may produce much higher run-ups than previously predicted, with particular incident wave frequencies resulting in run up heights exceeding the initial wave amplitude by a factor of 5, suggesting that the notion of the design wave used in coastal structure design may need to be revisited. The results presented in this study can be considered as a note of caution for practitioners, on one side, and as a challenging novel material for theoreticians who work in the field of extreme wave - coastal structure interaction.

physics.class-ph↗

arXiv2020

Modelling with Volna-OP2: Towards tsunami threat reduction

Accurate and efficient tsunami modelling is essential for providing tsunami forecasts and hazard assessments. Volna-OP2 is a finite volume solver of the nonlinear shallow water equations and its capabilities of producing both faster than real time ensembles and high resolution inundation studies are presented here. The code is massively parallelised and can utilise various high performance computing architectures. When an earthquake is detected there is always some uncertainty on the source parameters. Generating a faster than real time ensemble for maximum wave heights which captures this uncertainty would be of great benefit to tsunami warning centres. The 2003 Boumerdes earthquake (Algeria) acts as a test case for showing Volna-OP2's ability at rapidly forecasting regional maximum wave heights. Drawing on various earthquake sources proposed in the literature and scaling the magnitudes to mimic uncertainty on the source, 20 separate earthquake realisations are simulated for 4 hours real time in 97s on two Nvidia V100 GPUs. Further a reduced ensemble of the Lisbon 1755 tsunami with an emphasis on the effects to the Irish coastline is presented. Where again various earthquake sources have been drawn from the literature and simulated on a regional scale. Finally, a pilot study which builds upon the reduced ensemble results investigates the inundation of a Lisbon tsunami on key sections of the Irish coastline. The results of this pilot study highlight that the inundation is constrained to low-lying areas with maximum run-up heights of $\approx 3.4m$ being found.

physics.ao-ph↗

arXiv2020

Numerical simulation of wave impact on a rigid wall using a two-phase compressible SPH method

In this paper, an SPH method based on the SPH-ALE formulation is used for modelling two-phase flows with large density ratios and realistic sound speeds. The SPH scheme is further improved to circumvent the tensile instability that may occur in the SPH simulations. The two-phase SPH solver is then used to model a benchmark problem of liquid impact on a rigid wall. The results are compared with an incompressible Level Set solver. Furthermore, a wave impact on a rigid wall with a large entrained air pocket is modelled. The SPH simulation is initialised by the output of a fully non-linear potential flow solver. The pressure distribution, velocity field and impact pressure are then analysed.

physics.flu-dyn↗

arXiv2020

Performance analysis of Volna-OP2 -- massively parallel code for tsunami modelling

The software package Volna-OP2 is a robust and efficient code capable of simulating the complete life cycle of a tsunami whilst harnessing the latest High Performance Computing (HPC) architectures. In this paper, a comprehensive error analysis and scalability study of the GPU version of the code is presented. A novel decomposition of the numerical errors into the dispersion and dissipation components is explored. Most tsunami codes exhibit amplitude smearing and/or phase lagging/leading, so the decomposition shown here is a new approach and novel tool for explaining these occurrences. It is the first time that the errors of a tsunami code have been assessed in this manner. To date, Volna-OP2 has been widely used by the tsunami modelling community. In particular its computational efficiency has allowed various sensitivity analyses and uncertainty quantification studies. Due to the number of simulations required, there is always a trade-off between accuracy and runtime when carrying out these statistical studies. The analysis presented in this paper will guide the user towards an acceptable level of accuracy within a given runtime.

physics.comp-ph↗

arXiv2020

Energy of tsunami waves generated by bottom motion

In the vast literature on tsunami research, few articles have been devoted to energy issues. A theoretical investigation on the energy of waves generated by bottom motion is performed here. We start with the full incompressible Euler equations in the presence of a free surface and derive both dispersive and non-dispersive shallow-water equations with an energy equation. It is shown that dispersive effects only appear at higher order in the energy budget. Then we solve the Cauchy-Poisson problem of tsunami generation for the linearized water wave equations. Exchanges between potential and kinetic energies are clearly revealed.

physics.ao-ph↗

arXiv2014

Instabilities, breathers and rogue waves in optics

Optical rogue waves are rare yet extreme fluctuations in the value of an optical field. The terminology was first used in the context of an analogy between pulse propagation in optical fibre and wave group propagation on deep water, but has since been generalized to describe many other processes in optics. This paper provides an overview of this field, concentrating primarily on propagation in optical fibre systems that exhibit nonlinear breather and soliton dynamics, but also discussing other optical systems where extreme events have been reported. Although statistical features such as long-tailed probability distributions are often considered the defining feature of rogue waves, we emphasise the underlying physical processes that drive the appearance of extreme optical structures.

physics.optics↗

arXiv2013

Can Small Islands Protect Nearby Coasts From Tsunamis? An Active Experimental Design Approach

Small islands in the vicinity of the mainland are believed to offer protection from wind and waves and thus coastal communities have been developed in these areas. However, what happens when it comes to tsunamis is not clear. Will these islands act as natural barriers ? Recent post-tsunami survey data, supported by numerical simulations, reveal that the run-up on coastal areas behind small islands was significantly higher than on neighboring locations not affected by the presence of the island. To study the conditions of this run- up amplification, we solve numerically the nonlinear shallow water equations (NSWE). We use the simplified geometry of a conical island sitting on a flat bed in front of a uniform sloping beach. By doing so, the experimental setup is defined by five physical parameters, namely the island slope, the beach slope, the water depth, the distance between the island and the plane beach and the incoming wavelength, while the wave height was kept fixed. The objective is twofold: Find the maximum run-up amplification with the least number of simulations. To achieve this goal, we build an emulator based on Gaussian Processes to guide the selection of the query points in the parameter space.

physics.flu-dyn↗

arXiv2013

Run-up amplification of transient long waves

The extreme characteristics of long wave run-up are studied in this paper. First we give a brief overview of the existing theory which is mainly based on the hodograph transformation (Carrier & Greenspan, 1958). Then, using numerical simulations, we build on the work of Stefanakis et al. (2011) for an infinite sloping beach and we find that resonant run-up amplification of monochromatic waves is robust to spectral perturbations of the incoming wave and resonant regimes do exist for certain values of the frequency. In the setting of a finite beach attached to a constant depth region, resonance can only be observed when the incoming wavelength is larger than the distance from the undisturbed shoreline to the seaward boundary. Wavefront steepness is also found to play a role in wave run-up, with steeper waves reaching higher run-up values.

physics.class-ph↗

arXiv2012

The Force of a Tsunami on a Wave Energy Converter

With an increasing emphasis on renewable energy resources, wave power technology is fast becoming a realistic solution. However, the recent tsunami in Japan was a harsh reminder of the ferocity of the ocean. It is known that tsunamis are nearly undetectable in the open ocean but as the wave approaches the shore its energy is compressed creating large destructive waves. The question posed here is whether a nearshore wave energy converter (WEC) could withstand the force of an incoming tsunami. The analytical 3D model of Renzi & Dias (2012) developed within the framework of a linear theory and applied to an array of fixed plates is used. The time derivative of the velocity potential allows the hydrodynamic force to be calculated.

physics.ao-ph↗

arXiv2012

On the modelling of tsunami generation and tsunami inundation

While the propagation of tsunamis is well understood and well simulated by numerical models, there are still a number of unanswered questions related to the generation of tsunamis or the subsequent inundation. We review some of the basic generation mechanisms as well as their simulation. In particular, we present a simple and computationally inexpensive model that describes the seabed displacement during an underwater earthquake. This model is based on the finite fault solution for the slip distribution under some assumptions on the kinematics of the rupturing process. We also consider an unusual source for tsunami generation: the sinking of a cruise ship. Then we review some aspects of tsunami run-up. In particular, we explain why the first wave of a tsunami is sometimes less devastating than the subsequent waves. A resonance effect can boost the waves that come later. We also look at a particular feature of the 11 March 2011 tsunami in Japan - the formation of macro-scale vortices - and show that these macro-scale vortices can be captured by the nonlinear shallow water equations.

physics.ao-ph↗

arXiv2011

On the use of finite fault solution for tsunami generation problems

The present study is devoted to the problem of tsunami wave generation. The main goal of this work is two-fold. First of all, we propose a simple and computationally inexpensive model for the description of the sea bed displacement during an underwater earthquake, based on the finite fault solution for the slip distribution under some assumptions on the dynamics of the rupturing process. Once the bottom motion is reconstructed, we study waves induced on the free surface of the ocean. For this purpose we consider three different models approximating the Euler equations of the water wave theory. Namely, we use the linearized Euler equations (we are in fact solving the Cauchy-Poisson problem), a Boussinesq system and a novel weakly nonlinear model. An intercomparison of these approaches is performed. The developments of the present study are illustrated on the 17 July 2006 Java event, where an underwater earthquake of magnitude 7.7 generated a tsunami that inundated the southern coast of Java.

physics.ao-ph↗

arXiv2011

Local Runup Amplification By Resonant Wave Interactions

Until now the analysis of long wave runup on a plane beach has been focused on finding its maximum value, failing to capture the existence of resonant regimes. One-dimensional numerical simulations in the framework of the Nonlinear Shallow Water Equations (NSWE) are used to investigate the Boundary Value Problem (BVP) for plane and non-trivial beaches. Monochromatic waves, as well as virtual wave-gage recordings from real tsunami simulations, are used as forcing conditions to the BVP. Resonant phenomena between the incident wavelength and the beach slope are found to occur, which result in enhanced runup of non-leading waves. The evolution of energy reveals the existence of a quasi-periodic state for the case of sinusoidal waves, the energy level of which, as well as the time required to reach that state, depend on the incident wavelength for a given beach slope. Dispersion is found to slightly reduce the value of maximum runup, but not to change the overall picture. Runup amplification occurs for both leading elevation and depression waves.

physics.class-ph↗

arXiv2011

The VOLNA code for the numerical modelling of tsunami waves: generation, propagation and inundation

A novel tool for tsunami wave modelling is presented. This tool has the potential of being used for operational purposes: indeed, the numerical code \VOLNA is able to handle the complete life-cycle of a tsunami (generation, propagation and run-up along the coast). The algorithm works on unstructured triangular meshes and thus can be run in arbitrary complex domains. This paper contains the detailed description of the finite volume scheme implemented in the code. The numerical treatment of the wet/dry transition is explained. This point is crucial for accurate run-up/run-down computations. Most existing tsunami codes use semi-empirical techniques at this stage, which are not always sufficient for tsunami hazard mitigation. Indeed the decision to evacuate inhabitants is based on inundation maps which are produced with this type of numerical tools. We present several realistic test cases that partially validate our algorithm. Comparisons with analytical solutions and experimental data are performed. Finally the main conclusions are outlined and the perspectives for future research presented.

physics.class-ph↗

arXiv2009

A compressible two-fluid model for the finite volume simulation of violent aerated flows. Analytical properties and numerical results

In the study of ocean wave impact on structures, one often uses Froude scaling since the dominant force is gravity. However the presence of trapped or entrained air in the water can significantly modify wave impacts. When air is entrained in water in the form of small bubbles, the acoustic properties in the water change dramatically and for example the speed of sound in the mixture is much smaller than in pure water, and even smaller than in pure air. While some work has been done to study small-amplitude disturbances in such mixtures, little work has been done on large disturbances in air-water mixtures. We propose a basic two-fluid model in which both fluids share the same velocities. It is shown that this model can successfully mimic water wave impacts on coastal structures. Even though this is a model without interface, waves can occur. Their dispersion relation is discussed and the formal limit of pure phases (interfacial waves) is considered. The governing equations are discretized by a second-order finite volume method. Numerical results are presented. It is shown that this basic model can be used to study violent aerated flows, especially by providing fast qualitative estimates.

physics.class-ph↗

arXiv2009

A two-fluid model for violent aerated flows

In the study of ocean wave impact on structures, one often uses Froude scaling since the dominant force is gravity. However the presence of trapped or entrained air in the water can significantly modify wave impacts. When air is entrained in water in the form of small bubbles, the acoustic properties in the water change dramatically. While some work has been done to study small-amplitude disturbances in such mixtures, little work has been done on large disturbances in air-water mixtures. We propose a basic two-fluid model in which both fluids share the same velocities and analyze some of its properties. It is shown that this model can successfully mimic water wave impacts on coastal structures. The governing equations are discretized by a second-order finite volume method. Numerical results are presented for two examples: the dam break problem and the drop test problem. It is shown that this basic model can be used to study violent aerated flows, especially by providing fast qualitative estimates.

physics.class-ph↗

arXiv2009

Influence of sedimentary layering on tsunami generation

The present article is devoted to the influence of sediment layers on the process of tsunami generation. The main scope here is to demonstrate and especially quantify the effect of sedimentation on vertical displacements of the seabed due to an underwater earthquake. The fault is modelled as a Volterra-type dislocation in an elastic half-space. The elastodynamics equations are integrated with a finite element method. A comparison between two cases is performed. The first one corresponds to the classical situation of an elastic homogeneous and isotropic half-space, which is traditionally used for the generation of tsunamis. The second test case takes into account the presence of a sediment layer separating the oceanic column from the hard rock. Some important differences are revealed. We conjecture that deformations in the generation region may be amplified by sedimentary deposits, at least for some parameter values. The mechanism of amplification is studied through careful numerical simulations.

physics.geo-ph↗

arXiv2009

Computational aspects of the Maslov index of solitary waves

When solitary waves are characterized as homoclinic orbits of a finite-dimensional Hamiltonian system, they have an integer-valued topological invariant, the Maslov index. We are interested in developing a robust numerical algorithm to compute the Maslov index, to understand its properties, and to study the implications for the stability of solitary waves. The algorithms reported here are developed in the exterior algebra representation, which leads to a robust and fast algorithm with some novel properties. We use two different representations for the Maslov index, one based on an intersection index and one based on approximating the homoclinic orbit by a sequence of periodic orbits. New results on the Maslov index for solitary wave solutions of reaction-diffusion equations, the fifth-order Korteweg-De Vries equation, and the longwave-shortwave resonance equations are presented. Part 1 considers the case of four-dimensional phase space, and Part 2 considers the case of $2n-$dimensional phase space with $n>2$.

math.AP↗