Shear induced breaking of large internal solitary waves

The stability properties of 24 experimentally generated internal solitary waves (ISWs) of extremely large amplitude, all with minimum Richardson number less than 1/4, are investigated. The study is supplemented by fully nonlinear calculations in a three-layer fluid. The waves move along a linearly stratified pycnocline (depth h2) sandwiched between a thin upper layer (depth h1) and a deep lower layer (depth h3), both homogeneous. In particular, the wave-induced velocity profile through the pycnocline is measured by particle image velocimetry (PIV) and obtained in computation. Breaking ISWs were found to have amplitudes (a1) in the range a1>2.24 √h1h2(1+h2/h1), while stable waves were on or below this limit. Breaking ISWs were investigated for 0.27 0.86 and stable waves for Lx/λ < 0.86. The results show a sort of threshold-like behaviour in terms of Lx/λ. The results demonstrate that the breaking threshold of Lx/λ = 0.86 was sharper than one based on a minimum Richardson number and reveal that the Richardson number was found to become almost antisymmetric across relatively thick pycnoclines, with the minimum occurring towards the top part of the pycnoclinePostprintPeer reviewe

On the contribution of the horizontal sea-bed displacements into the tsunami generation process

The main reason for the generation of tsunamis is the deformation of the bottom of the ocean caused by an underwater earthquake. Usually, only the vertical bottom motion is taken into account while the horizontal co-seismic displacements are neglected in the absence of landslides. In the present study we propose a methodology based on the well-known Okada solution to reconstruct in more details all components of the bottom coseismic displacements. Then, the sea-bed motion is coupled with a three-dimensional weakly nonlinear water wave solver which allows us to simulate a tsunami wave generation. We pay special attention to the evolution of kinetic and potential energies of the resulting wave while the contribution of the horizontal displacements into wave energy balance is also quantified. Such contribution of horizontal displacements to the tsunami generation has not been discussed before, and it is different from the existing approaches. The methods proposed in this study are illustrated on the July 17, 2006 Java tsunami and some more recent events.Comment: 30 pages; 14 figures. Accepted to Ocean Modelling. Other authors papers can be downloaded at http://www.lama.univ-savoie.fr/~dutykh

Practical use of variational principles for modeling water waves

This paper describes a method for deriving approximate equations for irrotational water waves. The method is based on a 'relaxed' variational principle, i.e., on a Lagrangian involving as many variables as possible. This formulation is particularly suitable for the construction of approximate water wave models, since it allows more freedom while preserving the variational structure. The advantages of this relaxed formulation are illustrated with various examples in shallow and deep waters, as well as arbitrary depths. Using subordinate constraints (e.g., irrotationality or free surface impermeability) in various combinations, several model equations are derived, some being well-known, other being new. The models obtained are studied analytically and exact travelling wave solutions are constructed when possible.Comment: 30 pages, 1 figure, 62 references. Other author's papers can be downloaded at http://www.denys-dutykh.com

Deterministic numerical modelling of three-dimensional rogue waves on large scale with presence of wind

Oceanic rogue waves are a subject of great interest and can cause devastating consequences. Rogue waves are abnormal in that they stand out from the waves that surround them. Rogue waves are often observed accompanied by high wind in reality, and some earlier studies have demonstrated that the energy input due to the wind can enhance the dynamics of the rogue waves, which further causes huge concern about the safety of the human’s oceanic activities. Thus it is important, to better understand the mechanisms between the wind-wave interactions and to study the rogue waves with the presence of wind, especially on a three-dimensional large scale. In this study, numerical simulations are performed by using the Enhanced Spectral Boundary Integral (ESBI) method based on the fully nonlinear potential theory, in order to investigate the effects of wind on the rogue waves. The wind effects are introduced by imposing a wind-driven pressure on the free surface, which is empirically formulated based on intensive numerical investigation using multiple-phase Navier-Stokes solver. The results of the simulation confirm that the presented ESBI can produce satisfactory results on the formation of rogue waves under the action of wind. It provides a foresight of modelling rogue waves with presence of wind on a large scale in a phase-resolved fashion, which may motivate relevant studies in the futur

Formations à la recherche documentaire pour les écoles doctorales : spécificités du droit

Cet article est le résultat de mon expérience de la formation à la recherche documentaire à l’intention de doctorants en sciences juridiques et celui d’une réflexion menée dans le cadre d’un travail universitaire. D’une part, je suis amenée à proposer et assurer des formations dans le cadre d’écoles doctorales de droit de Paris I, Paris II et Paris X. Ces formations se sont construites progressivement en réponse à des demandes explicites et, pour certaines d’entre elles en collaboration avec ..

Solitary wave interaction in a compact equation for deep-water gravity waves

In this study we compute numerical traveling wave solutions to a compact version of the Zakharov equation for unidirectional deep-water waves recently derived by Dyachenko & Zakharov (2011) Furthermore, by means of an accurate Fourier-type spectral scheme we find that solitary waves appear to collide elastically, suggesting the integrability of the Zakharov equation.Comment: 8 pages, 5 figures, 23 references. Other author's papers can be downloaded at http://www.lama.univ-savoie.fr/~dutykh/ . arXiv admin note: text overlap with arXiv:1204.288

Désordres dans la photographie amateur et anonyme

« Car, concluait Lester Nowak, il ne fallait pas s’y tromper : cette œuvre était une image de la mort de l’art, une réflexion spéculaire sur ce monde condamné à la répétition infinie de ses propres modèles. Et ces variations minuscules de copie à copie, qui avaient tant exacerbé les visiteurs, étaient peut-être l’expression ultime de la mélancolie de l’artiste : comme si, peignant la propre histoire de ses œuvres à travers l’histoire des œuvres des autres, il avait pu, un instant, faire semb..

A hybrid model for simulating rogue waves in random seas on a large temporal and spatial scale

A hybrid model for simulating rogue waves in random seas on a large temporal and spatial scale is proposed in this paper. It is formed by combining the derived fifth order Enhanced Nonlinear Schrödinger Equation based on Fourier transform, the Enhanced Spectral Boundary Integral (ESBI) method and its simplified version. The numerical techniques and algorithm for coupling three models on time scale are suggested. Using the algorithm, the switch between the three models during the computation is triggered automatically according to wave nonlinearities. Numerical tests are carried out and the results indicate that this hybrid model could simulate rogue waves both accurately and efficiently. In some cases discussed, the hybrid model is more than 10 times faster than just using the ESBI method, and it is also much faster than other methods reported in the literature