arXiv subjects

Joël Sommeria

Publications and source records attributed to Joël Sommeria.

12 recordsLinked to original sources

arXiv2024

Space-time statistics of 2D soliton gas in shallow water studied by stereoscopic surface mapping

We describe laboratory experiments in a 2D wave tank that aim at building up and monitor 2D shallow water soliton gas. The water surface elevation is obtained over a large ($\sim 100\,\text{m}^2$) domain, with centimetre-resolution, by stereoscopic vision using two cameras. Floating particles are seeded to get surface texture and determine the wave field by image correlation. With this set-up, soliton propagation and multiple interactions can be measured with a previously unreachable level of detail. The propagation of an oblique soliton is analysed, the amplitude decay and local incidence are compared to analytical predictions. We further present two cases of 2D soliton gas, emerging from multiple line solitons with random incidence ($|θ|<30^\circ$) and from irregular random waves forced with a {\sc jonswap} spectrum ($|θ|<45^\circ$). To our knowledge, those are the first observations of random 2D soliton gas for gravity waves. In both cases Mach reflections and Mach expansions result in solitons that mainly propagate in directions perpendicular to the wave-makers.

physics.flu-dyn↗

arXiv2023

From internal waves to turbulence in a stably stratified fluid

We report on the statistical analysis of stratified turbulence forced by large-scale waves. The setup mimics some features of the tidal forcing of turbulence in the ocean interior at submesoscales. Our experiments are performed in the large-scale Coriolis facility in Grenoble which is 13 m in diameter and 1 m deep. Four wavemakers excite large scale waves of moderate amplitude. In addition to weak internal wave turbulence at large scales, we observe strongly nonlinear waves, the breaking of which triggers intermittently strong turbulence at small scales. A transition to strongly nonlinear turbulence is observed at smaller scales. Our measurements are reminiscent of oceanic observations. Despite similarities with the empirical Garrett & Munk spectrum that assumes weak wave turbulence, our observed energy spectra are rather be attributed to strongly nonlinear internal waves.

physics.flu-dyn↗

arXiv2022

Experimental observations of internal wave turbulence transition in a stratified fluid

Recent developments of the weak turbulence theory applied to internal waves exhibit a power-law solution of the kinetic energy equation close to the oceanic Garrett \& Munk spectrum, confirming weakly nonlinear wave interactions as a likely explanation of the observed oceanic spectra. However, finite-size effects can hinder wave interactions in bounded domains, and observations often differ from theoretical predictions. This article studies the dynamical regimes experimentally developing in a stratified fluid forced by internal gravity waves in a pentagonal domain. We find that by changing the shape and increasing the dimensions of the domain, finite-size effects diminish and wave turbulence is observed. In this regime, the temporal spectra decay with a slope compatible with the Garrett-Munk spectra. Different regimes appear by changing the forcing conditions, namely discrete wave turbulence, weak wave turbulence, and strongly stratified turbulence. The buoyancy Reynolds number $Re_b$ marks well the transitions between the regimes, with weak wave turbulence occurring for $1\lesssim Re_b\lesssim 3.5$ and strongly non-linear stratified turbulence for higher $Re_b$.

physics.flu-dyn↗

arXiv2020

An effective two-dimensional model for MHD flows with transverse magnetic field

This paper presents a model for quasi two-dimensional MHD flows between two planes with small magnetic Reynolds number and constant transverse magnetic field orthogonal to the planes. A method is presented that allows to take 3D effects into account in a 2D equation of motion thanks to a model for the transverse velocity profile. The latter is obtained by using a double perturbation asymptotic development both in the core flow and in the Hartmann layers arising along the planes. A new model is thus built that describes inertial effects in these two regions. Two separate classes of phenomena are thus pointed out : the one related to inertial effects in the Hartmann layer gives a model for recirculating flows and the other introduces the possibility of having a transverse dependence of the velocity profile in the core flow. The ''recirculating'' velocity profile is then introduced in the transversally averaged equation of motion in order to provide an effective 2D equation of motion. Analytical solutions of this model are obtained for two experimental configurations : isolated vortices aroused by a point electrode and axisymmetric parallel layers occurring in the MATUR (MAgneticTURbulence) experiment. The theory is found to give a satisfactory agreement with the experiment so that it can be concluded that recirculating flows are actually responsible for both vortices core spreading and excessive dissipative behavior of the axisymmetric side wall layers.

physics.flu-dyn↗

arXiv2020

Generation of weakly nonlinear turbulence of internal gravity waves in the Coriolis facility

We investigate experimentally stratified turbulence forced by waves. Stratified turbulence is present in oceans and it is expected to be dominated by nonlinear interaction of internal gravity waves as described by the Garrett & Munk spectrum. In order to reach turbulent regimes dominated by stratification we use the Coriolis facility in Grenoble (France) which large size enables us to reach regimes with both low Froude number and large Reynolds number. Stratification is obtained by using vertically linearly varying salt concentration and we force large scale waves in a $6\times6\times 1$ m$^3$ domain. We perform time-resolved PIV to probe the space-time structure of the velocity field. We observe a wide band spectrum which is made of waves. Discrete modes are observed due to the square shape of the flow container as well as a continuum part which appears consistent with an axisymmetric superposition of random weakly nonlinear waves. Our observations support the interpretation of turbulence of a strongly stratified fluid as wave turbulence of internal waves although our spectrum is quite different from the Garrett & Munk spectrum. Weak turbulence proceeds down to a small cutoff length scale (the buoyancy wavelength) at which a transition to more strongly nonlinear turbulence is expected.

physics.flu-dyn↗

arXiv2020

2D models for MHD flows

A new model is proposed for low $Rm$ MHD flows which remain turbulent even in the presence of a magnetic field. These flows minimize the Joule dissipation because of their tendency to become two-dimensional and, therefore to suppress all induction effects. However, some small three-dimensional effects, due to inertia and to the electric coupling between the core flow and the Hartmann layers, are present even within the core flow. This new model, which may be seen as an improvement of the Sommeria-Moreau 2D model, introduces this three-dimensionality as a small perturbation. It yields an equation for the average velocity over the magnetic field lines, whose solution agrees well with available measurements performed on isolated vortices.

physics.flu-dyn↗

arXiv2020

Numerical simulations of an effective two-dimensional model for flows with a transverse magnetic field

This paper presents simulations of the 2d model developed by Pothérat at al (\emph{J. Fluid Mech}, 2000) for MHD flows between two planes with a strong transverse homogeneous and steady magnetic field, accounting for moderate inertial effects in Hartmann layers. We first show analytically how the additional terms in the equations of motion accounting for inertia, soften velocity gradients in the horizontal plane, and then we implement the model on a code to carry out numerical simulations to be compared with available experimental results. This comparison shows that the new model can give very accurate results as long as the Hartmann layer remains laminar. Both experimental velocity profiles and global angular momentum measurements are closely recovered, and local and global Ekman recirculations are shown to alter significantly the aspect of the flow as well as the global dissipation.

physics.flu-dyn↗

arXiv2020

Effective boundary conditions for magnetohydrodynamic flows with thin Hartmann layers

Here we build some effective boundary conditions to be used in numerical calculations in order to avoid the thin meshing usually required in problems involving Hartmann layers near a locally plane wall. Wall model are provided for both tangential and normal electric current density and velocity. In particular, a condition on the normal derivative of the tangential velocity is derived. A wide variety of problems is covered as the only restriction is that the magnetic Reynolds number has to be large at the scale of the Hartmann layer. The cases of perfectly conducting or insulating wall are examined, as well as the case of a thin conducting wall. The newest result is a condition on the normal velocity accounting for inertial effects in the Hartmann layer.

physics.flu-dyn↗

arXiv2019

Identifying four wave resonant interactions in a surface gravity wave turbulence experiment

The nonlinear dynamics of waves at the sea surface is believed to be ruled by the Weak Turbulence framework. In order to investigate the nonlinear coupling among gravity surface waves, we developed an experiment in the Coriolis facility which is a 13-m diameter circular tank. An isotropic and statistically stationary wave turbulence of average steepness of 10\% is maintained by two wedge wave makers. The space and time resolved wave elevation is measured using a stereoscopic technique. Wave-wave interactions are analyzed through third and fourth order correlations. We investigate specifically the role of bound waves generated by non resonant 3-wave coupling. Specifically, we implement a space-time filter to separate the dynamics of free waves (i.e. following the dispersion relation) from the bound waves. We observe that the free wave dynamics causes weak resonant 4-wave correlations. A weak level of correlation is actually the basis of the Weak Turbulence Theory. Thus our observations support the use of the Weak Turbulence to model gravity wave turbulence as is currently been done in the operational models of wave forecasting. Although in the theory bound waves are not supposed to contribute to the energy cascade, our observation raises the question of the impact of bound waves on dissipation and thus on energy transfers as well.

physics.flu-dyn↗

arXiv2018

Impact of dissipation on the energy spectrum of experimental turbulence of gravity surface waves

We discuss the impact of dissipation on the development of the energy spectrum in wave turbulence of gravity surface waves with emphasis on the effect of surface contamination. We performed experiments in the Coriolis facility which is a 13-m diameter wave tank. We took care of cleaning surface contamination as well as possible considering that the surface of water exceeds 100~m$^2$. We observe that for the cleanest condition the frequency energy spectrum shows a power law decay extending up to the gravity capillary crossover (14 Hz) with a spectral exponent that is increasing with the forcing strength and decaying with surface contamination. Although slightly higher than reported previously in the literature, the exponent for the cleanest water remains significantly below the prediction from the Weak Turbulence Theory. By discussing length and time scales, we show that weak turbulence cannot be expected at frequencies above 3 Hz. We observe with a stereoscopic reconstruction technique that the increase with the forcing strength of energy spectrum beyond 3~Hz is mostly due to the formation and strenghtening of bound waves.

physics.flu-dyn↗

arXiv2015

Large-scale, realistic laboratory modeling of M2 internal tide generation at the Luzon Strait

The complex double-ridge system in the Luzon Strait in the South China Sea (SCS) is one of the strongest sources of internal tides in the oceans, associated with which are some of the largest amplitude internal solitary waves on record. An issue of debate, however, has been the specific nature of their generation mechanism. To provide insight, we present the results of a large-scale laboratory experiment performed at the Coriolis platform. The experiment was carefully designed so that the relevant dimensionless parameters, which include the excursion parameter, criticality, Rossby, and Froude numbers, closely matched the ocean scenario. The results advocate that a broad and coherent weakly nonlinear, three-dimensional, M2 internal tide that is shaped by the overall geometry of the double-ridge system is radiated into the South China Sea and subsequently steepens, as opposed to being generated by a particular feature or localized region within the ridge system.

physics.ao-ph↗

arXiv2014

The role of fluctuations across a density interface

A statistical mechanics theory for a fluid stratified in density is presented. The predicted statistical equilibrium state is the most probable outcome of turbulent stirring. The slow temporal evolution of the vertical density profile is related to the presence of irreversible mixing, which alters the global distribution of density levels. We propose a model in which the vertical density profile evolves through a sequence of statistical equilibrium states. The theory is then tested with laboratory experiments in a two-layer stably stratified fluid forced from below by an oscillating grid. Quantitative measurements of density fluctuations across the interface are made by planar laser induced fluorescence. These fluctuations are splitted in a "wave" part and a "turbulent" part. The wave part of the density field is well described by a previous theory due to Phillips. We argue that statistical mechanics predictions apply for the turbulent part of the density field sufficiently close to the interface. However inside the mixed layer density fluctuations are instead controlled by a balance between eddy flux downward and dissipation by cascade to small scales. We report exponential tails for the density pdf in this region.

physics.flu-dyn↗