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Energy cascade in internal wave attractors [article]

Christophe Brouzet, Sylvain Joubaud, Thierry Dauxois
2016 arXiv   pre-print
One of the pivotal questions in the dynamics of the oceans is related to the cascade of mechanical energy in the abyss and its contribution to mixing. Here, we propose internal wave attractors in the large amplitude regime as a unique self-consistent experimental and numerical setup that models a cascade of triadic interactions transferring energy from large-scale monochro-matic input to multi-scale internal wave motion. We also provide signatures of a discrete wave turbulence framework for
more » ... rnal waves. Finally, we show how beyond this regime, we have a clear transition to a regime of small-scale high-vorticity events which induce mixing. Introduction.
arXiv:1602.06852v1 fatcat:jwxx6myexfeg3ouja4qri7jd74

New (Internal) Wave Generation - Laboratory Experiments [article]

Manikandan Mathur, Matthieu Mercier, Thierry Dauxois, Thomas Peacock
2009 arXiv   pre-print
In this fluid dynamics video, we demonstrate the experimental generation of various internal wave fields using a novel wave generator. Specifically, uni-directional internal wave beams and vertical modes 1 and 2 are generated and visualized using Particle Image Velocimetry. Further details and analysis of these experiments can be found in [1].
arXiv:0910.3438v1 fatcat:tejj5fzswjecrpvisezgb5jota

Serge Aubry

Thierry Dauxois, Robert MacKay, George Tsironis
2006 Physica D : Non-linear phenomena  
This special issue of Physica D is dedicated to Serge Aubry's influence and achievements, for his 60th birthday. It is an outgrowth from a conference on "Nonlinear Physics: Condensed Matter, Dynamical Systems and Biophysics" which was held in his honour at the Institut Henri Poincaré, Paris, 30-31 May 2005. Serge Aubry is a remarkably creative and inspiring physicist. He has made great contributions to nonlinear phenomena in solid-state physics, dynamical systems theory and biological physics.
more » ... is approach combines attention to experimental results, deep physical insight, formulation of key problems, incisive numerical simulation, innovative use of mathematics, unconventional interpretations and imaginative predictions. Let us survey his main achievements.
doi:10.1016/j.physd.2006.02.001 fatcat:y3amxu4gkfac5kaysnh5yrbtla

Breaking of internal waves parametrically excited by ageostrophic anticyclonic instability [article]

Yohei Onuki, Sylvain Joubaud, Thierry Dauxois
2022 arXiv   pre-print
A gradient-wind balanced flow with an elliptic streamline parametrically excites internal inertia-gravity waves through ageostrophic anticyclonic instability (AAI). This study numerically investigates the breaking of internal waves and the following turbulence generation resulting from the AAI. In our simulation, we periodically distort the calculation domain following the streamlines of an elliptic vortex and integrate the equations of motion using a Fourier spectral method. This technique
more » ... les us to exclude the overall structure of the large-scale vortex from the computation and concentrate on resolving the small-scale waves and turbulence. From a series of experiments, we identify two different scenarios of wave breaking conditioned on the magnitude of the instability growth rate scaled by the buoyancy frequency, λ/N. First, when λ/N≳0.008, the primary wave amplitude excited by AAI quickly goes far beyond the overturning threshold and directly breaks. The resulting state is thus strongly nonlinear turbulence. Second, if λ/N≲0.008, weak wave-wave interactions begin to redistribute energy across frequency space before the primary wave reaches a breaking limit. Then, after a sufficiently long time, the system approaches a Garrett-Munk-like stationary spectrum, in which wave breaking occurs at finer vertical scales. Throughout the experimental conditions, the growth and decay time scales of the primary wave energy are well correlated. However, since the primary wave amplitude reaches a prescribed limit in one scenario but not in the other, the energy dissipation rates exhibit two types of scaling properties. This scaling classification has similarities and differences with D'Asaro and Lien's (2000) wave-turbulence transition model.
arXiv:2207.05581v1 fatcat:nwfywdzh5ngari3vz7677bi3vy

Linear and nonlinear regimes of an inertial wave attractor [article]

Maxime Brunet, Thierry Dauxois, Pierre-Philippe Cortet
2019 arXiv   pre-print
We present an experimental analysis of the linear and non-linear regimes of an attractor of inertial waves in a trapezoidal cavity under rotation. Varying the rotation rate and the forcing amplitude and wavelength, we identify the scaling laws followed by the attractor amplitude and wavelength in both regimes. In particular, we show that the non-linear scaling laws can be well described by replacing the fluid viscosity in the linear model by a turbulent viscosity, a result that could help
more » ... olating attractor theory to geo/astrophysically relevant situations. We further study the triadic resonance instability of the attractor which is at the origin of the turbulent viscosity. We show that the typical frequencies of the subharmonic waves produced by the instability behaves very differently from previously reported numerical results and from the prediction of the theory of triadic resonance. This behavior might be related to the deviation from horizontal invariance of the attractor in our experiment in relation with the presence of vertical walls of the cavity, an effect that should be at play in all practical situations.
arXiv:1902.00411v1 fatcat:luqpmnm67nh33jnc7g75qlembu

Nonlinear stability of counter‐rotating vortices

Thierry Dauxois
1994 Physics of Fluids  
LETTERS The purpose of this Letters section is to provide mpid dissemination of important new results in the fields regularly covered by Physics of Fluids. Results of extended research should not be presented as a series of letters in place of comprehensive articles Letters cannot exceed three printed pages in length, including space allowed for title, jigures, tabIes, references and an abstract limited to about 100 words. There is a three-month time limit, from date of receipt to acceptance,
more » ... r processing Letter manuscripts. Authors must also submit a brief statement justifying rapid publication in the Letters section.
doi:10.1063/1.868225 fatcat:bcpe6dvjurfsja4i42v7y3iwye

Analytical Estimation of the Maximal lyapunov Exponent in Oscillator Chains [article]

Thierry Dauxois, Stefano Ruffo, Alessandro Torcini
1998 arXiv   pre-print
An analytical expression for the maximal Lyapunov exponent λ_1 in generalized Fermi-Pasta-Ulam oscillator chains is obtained. The derivation is based on the calculation of modulational instability growth rates for some unstable periodic orbits. The result is compared with numerical simulations and the agreement is good over a wide range of energy densities ϵ. At very high energy density the power law scaling of λ_1 with ϵ can be also obtained by simple dimensional arguments, assuming that the
more » ... stem is ruled by a single time scale. Finally, we argue that for repulsive and hard core potentials in one dimension λ_1 ∼√(ϵ) at large ϵ.
arXiv:cond-mat/9803001v1 fatcat:75jhs3ulhngmhosyed37vyq22q

Succession of resonances to achieve internal wave turbulence [article]

Géraldine Davis, Timothée Jamin, Julie Deleuze, Sylvain Joubaud, Thierry Dauxois
2020 arXiv   pre-print
Géraldine Davis 1 , Timothée Jamin 1 , Julie Deleuze 1 , Sylvain Joubaud 1,2 , Thierry Dauxois 1 1. Univ Lyon, ENS de Lyon, Univ Claude Bernard, CNRS, Laboratoire de Physique, Lyon, France 2.  ... 
arXiv:2004.12625v1 fatcat:zjke5kyqcvhpjlkr2mwgiruosq

Internal Waves in Laboratory Experiments [chapter]

Bruce Sutherland, Thierry Dauxois, Thomas Peacock
2014 Modeling Atmospheric and Oceanic Flows  
Recent laboratory methods developed to generate and to analyze internal waves have revealed important insights that sometimes guide and sometimes challenge theoretical predictions and the results of numerical simulations. Here we focus upon observations of internal waves generated by oscillatory or uniform flow over a solid boundary in a continuously stratified fluid. In the laboratory such flows are often examined by moving the boundary in an otherwise stationary ambient. This can be done by
more » ... cillating or towing an object, or by sequentially oscillating a series of plates to simulate a translating or standing-wave-like boundary. The generated waves are sometimes visualized and measured using a non-intrusive optical method called synthetic schlieren. This takes advantage of the changes of the refractive index with salinity which differentially bends light passing through salt-stratified fluid, a property that hampers the use of more standard non-intrusive observation methods such as Particle Image Velocimetry (PIV). From schlieren images, filtering methods can be applied to distinguish between leftward and rightward as well as upward and downward propagating two-dimensional waves. Inverse tomographic techniques can be employed to measure the structure and amplitude of axisymmetric and relatively simple three-dimensional disturbances. Increasingly PIV has been used, sometimes in connection with synthetic schlieren, to measure the velocity field associated with vertically propagating internal waves, internal wave modes and internal solitary waves. Implications and applications to oceanographic internal waves are discussed.
doi:10.1002/9781118856024.ch10 fatcat:q6t4tc7f5bc2nekdyep2bfjnk4

Gravitation in the Microcanonical Ensemble: Appropriate Scaling Leading to Extensivity and Thermalization [article]

Maxime Champion, Angel Alastuey, Thierry Dauxois, Stefano Ruffo
2012 arXiv   pre-print
We introduce a simple model of hard spheres with gravitational interactions, for which we study a suitable scaling limit. Usual extensive properties are maintained notwithstanding the long range of gravitational interaction. We show that a local thermalization spontaneously emerges within a microcanonical description of the stationary state. In the considered scaling limit, the resulting density profile can be determined in a hydrostatic approach.
arXiv:1210.5592v1 fatcat:hc4ssea6ebcjxcvq6pwipytxu4

Dead Waters: Large amplitude interfacial waves generated by a boat in a stratified fluid [article]

Romain Vasseur, Matthieu Mercier, Thierry Dauxois
2008 arXiv   pre-print
We present fluid dynamics videos of the motion of a boat on a two-layer or three-layer fluid. Under certain specific conditions, this setup generates large amplitude interfacial waves, while no surface waves are visible. The boat is slowed down leading to a peristaltic effect and sometimes even stopped: this is the so-called dead water phenomenon.
arXiv:0810.1702v1 fatcat:wjjyomhionendjmulodbyzmkca

Links between nonlinear dynamics and statistical mechanics in a simple one-dimensional model [article]

Hicham Qasmi, Julien Barre', Thierry Dauxois
2004 arXiv   pre-print
From these calculations, we predict features absent in the Peyrard-Bishop model, although both models are very similar: a Send offprint requests to: Thierry Dauxois a E-mail:Thierry.Dauxois@ens-lyon.fr  ... 
arXiv:cond-mat/0407662v1 fatcat:l4itrkzienf3fmrxzhiuchyyhy

Nonlinear Fate of Internal Wave Attractors

Hélène Scolan, Eugeny Ermanyuk, Thierry Dauxois
2013 Physical Review Letters  
We present a laboratory study on the instability of internal wave attractors in a trapezoidal fluid domain filled with uniformly stratified fluid. Energy is injected into the system via standing-wave-type motion of a vertical wall. Attractors are found to be destroyed by parametric subharmonic instability (PSI) via a triadic resonance which is shown to provide a very efficient energy pathway from long to short length scales. This study provides an explanation why attractors may be difficult or
more » ... mpossible to observe in natural systems subject to large amplitude forcing.
doi:10.1103/physrevlett.110.234501 pmid:25167498 fatcat:fqneqsg6jfgqfj67kmtern4ghi

Modulational instability: first step towards energy localization in nonlinear lattices

Isabelle Daumont, Thierry Dauxois, Michel Peyrard
1997 Nonlinearity  
We study the modulational instability in discrete lattices and we show how the discreteness drastically modifies the stability condition. Analytical and numerical results are in very good agreement. We predict also the evolution of a linear wave in the presence of noise and we show that modulational instability is the first step towards energy localization.
doi:10.1088/0951-7715/10/3/003 fatcat:a4ql2ne5h5dhxfhbhm225y7rom

Dynamics of breather modes in a nonlinear "helicoidal" model of DNA

Thierry Dauxois
1991 Physics Letters A  
We describe the dynamics of breather modes in DNA in terms of a recent lattice model with an additional interaction in order to take into accountthe helicoidal structure ofthe molecule. It is shown that, despite its simplicity, this model exhibits breatherlike modes which can match experimentally observedbubbles propagating along the helix. Numerical simulationsof their propagation show these excitations to be long-lived and suggest that they are physically relevant for DNA.
doi:10.1016/0375-9601(91)90367-h fatcat:gjjbbit5hvhilau5eak5mdne7q
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