Evidence for supersonic turbulence in the upper atmosphere of Jupiter
Science, 1996
Spectra of the hydrogen Lyman alpha (Ly-alpha) emission line profiles of the jovian dayglow, obta... more Spectra of the hydrogen Lyman alpha (Ly-alpha) emission line profiles of the jovian dayglow, obtained by the Goddard High Resolution Spectrograph on the Hubble Space Telescope, appear complex and variable on time scales of a few minutes. Dramatic changes occur in the Ly-alpha bulge region at low latitudes, where the line profiles exhibit structures that correspond to supersonic velocities of the order of several to tens of kilometers per second. This behavior, unexpected in a planetary atmosphere, is evidence for the particularly stormy jovian upper atmosphere, not unlike a star's atmosphere.
Topographic Rossby waves in a channel with linearly slopping bottom on the f-plane are investigat... more Topographic Rossby waves in a channel with linearly slopping bottom on the f-plane are investigated experimentally and theoretically by employing a barotropic linearized shallow water equation model that is solved numerically and analytically. The calculated dispersion relations are shown to be significantly smaller (by a factor of 2-5) than those of the (classical) harmonic theory and the gap increases with the channel width and with the bottom slope. The numerical calculations were compared to experimental results obtained in the 13m diameter rotating table of LEGI-Coriolis (France). The linear slope in the experiments is 10% and the wave's period and wavenumber were measured using a Particle Imaging Velocimetry (PIV) system. The experimental results regarding the dispersion relation and the radial structure of the radial velocity were in excellent agreement with the (numerically derived) theoretical predictions. These results clearly showed that in wide channels the radial ve...
This paper investigates the interaction of solid particles with giant vortices, suspected to surv... more This paper investigates the interaction of solid particles with giant vortices, suspected to survive during many rotation periods in the protoplanetary disk. It is found that these vortices can capture and concentrate large amounts of the solid particles. The strong efficiency of this mechanism make them the most favourable places where to form the planetesimals.
Application of laboratory experiments to assess the error introduced by the imposition of “wall” boundary conditions in shelf models
Ocean Modelling, 2012
For mathematical and numerical reasons the physical boundary condition of regularity of solutions... more For mathematical and numerical reasons the physical boundary condition of regularity of solutions (i.e. finite amplitude) at the singular point of vanishing water depth (the shoreline) imposed on wavelike solutions on the continental shelf is replaced by “no normal flow” condition in analytical and numerical studies of continental shelf waves. This “no normal flow” condition that circumvents the mathematical subtlety
Low-frequency waves that develop in a shallow layer of fluid, contained in a channel with linearl... more Low-frequency waves that develop in a shallow layer of fluid, contained in a channel with linearly slopping bottom and rotating with uniform angular speed are investigated theoretically and experimentally. Exact numerical solutions of the eigenvalue problem, obtained from the linearized shallow water equations on the f-plane, show that the waves are trapped near the channel's shallow wall and propagate along it with the shallow side on their right in the Northern hemisphere. The phase speed of the waves is slower compared with that of the harmonic theory in which bottom slope is treated inconsistently. A first-order approximation of the cross-channel dependence of the coefficient in the eigenvalue equation yields an approximation of the cross-channel velocity eigenfunction as an Airy function, which, for sufficiently wide channels, yields an explicit expression for the wave's dispersion relation. The analytic solutions of the eigenvalue problem agree with the numerical solut...
We test a new statistical theory of organized structures in two-dimensional turbulence by direct ... more We test a new statistical theory of organized structures in two-dimensional turbulence by direct numerical stimulations of the Navier-Stokes equations, using a pseudo-spectral method. We apply the theory to the final equilibrium state of a shear layer evolving from a band of uniform vorticity : a relationship between vorticity and stream function is predicted by maximizing an entropy with the constraints due the constants of the motion. A partial differential equation for the stream function is then obtained. In the particular case of a very thin initial vorticity band, the Stuart's vortices appear to be a family of solutions for this equation. In more general cases we do not solve the equation, but we test the theory by inspecting the relationship between stream function and vorticity in the final equilibrium state of the numerical computation. An excellent agreement is obtained in regions with strong vorticity mixing. However, local equilibrium is obtained before a complete mixing can occur in the whole fluid domain.
The Comptes rendus de l'Académie des sciences throughout history / Les Comptes rendus de l'Académ... more The Comptes rendus de l'Académie des sciences throughout history / Les Comptes rendus de l'Académie des sciences à travers l'histoire Foucault and the rotation of the Earth
Experimental results for the evolution of the probability distribution function (PDF) of a scalar... more Experimental results for the evolution of the probability distribution function (PDF) of a scalar mixed by a turbulence flow in a channel are presented. The sequence of PDF from an initial skewed distribution to a sharp Gaussian is found to be non universal. The route toward homogeneization depends on the ratio between the cross sections of the dye injector and the channel. In link with this observation, advantages, shortcomings and applicability of models for the PDF evolution based on a self-convolution mechanisms are discussed.
Selected results are presented from a closely coupled laboratory-numerical model study of the osc... more Selected results are presented from a closely coupled laboratory-numerical model study of the oscillatory flow of a linearly stratified fluid in the vicinity of an isolated submarine canyon. It is shown that the boundary condition applied along the model floor in the numerical experiments is critically important in having the numerical model simulate the laboratory experiments. Furthermore, it is shown that enhanced viscosities, which assure the numerical stability, must be applied with care because they may change the flow fields. A scaling argument is advanced which predicts the strength of the time-mean flow generated by the background current. The sensitivity of the flow field to changes in some of the system parameters is discussed. Finally, some initial results for flows generated in the presence of boundary turbulence are also discussed.
Ice front blocking in a laboratory model of the Antarctic ice shelf
Mass loss from the Antarctic Ice Sheet to the ocean has increased in recent decades, largely beca... more Mass loss from the Antarctic Ice Sheet to the ocean has increased in recent decades, largely because the thinning of its floating ice shelves has allowed the outflow of grounded ice to accelerate. Enhanced basal melting of the ice shelves is thought to be the ultimate driver of change, motivating a recent focus on the processes that control ocean heat transport onto and across the seabed of the Antarctic continental shelf towards the ice. However, the shoreward heat flux typically far exceeds that required to match observed melt rates, suggesting other critical controls. By laboratory experiments on the Coriolis rotating platform, we show that the depth-independent component of the flow towards an ice shelf is blocked by the dramatic step shape of the ice front, and that only the depth-varying component, typically much smaller, can enter the sub-ice cavity. These results are consistent with direct observations of the Getz Ice Shelf system, as shown by Wahlin et al. (Nature 2019, in press). The selected data are velocity fields from a selection of 6 experiments, described in Wahlin et al. (2019), supplementary material, fig 4 and 9. EXP26,30,34 correspond to Fig. 4 a,b,c respectively (barotropic case) EXP44,50,51 correspond to Fig. 9 a,b,c respectively (baroclinic case) The velocity fields are measured by PIV from short image series (bursts) obtained by laser sheet illumination in several quasi-horizontal planes (for Fig 4, N=12 planes vertically separated by 6.2 cm, with 25 images per level, for Fig 9, N=7 planes vertically separated by 5.8 cm, with 19 images per level). The quasi-horizontal planes are parallel to the channel, slanted downward toward the iceshelf with an angle of 1.15 degree. For each experiment, the whole series of velocity fields is provided in /PCO1.png.sback.civ-PCO2.png.sback.civ.mproj (those are obtained by merging velocity fields from the images of two cameras denoted PCO1 and PCO2) velocity fields averaged inside each burst are provided in PCO1.png.sback.civ-PCO2.png.sback.civ.mproj.stat. [...]
The evolution of an internal gravity wave is investigated by direct numerical computations. We co... more The evolution of an internal gravity wave is investigated by direct numerical computations. We consider the case of a standing wave confined in a bounded (square) domain, a case which can be directly compared with laboratory experiments. A pseudo-spectral method with symmetries is used. We are interested in the inertial dynamics occurring in the limit of large Reynolds numbers, so a fairly high spatial resolution is used (1292 or 2572), but the computations are limited to a two-dimensional vertical plane. We observe that breaking eventually occurs, whatever the wave amplitude: the energy begins to decrease after a given time because of irreversible transfers of energy towards the dissipative scales. The life time of the coherent wave, before energy dissipation, is found to be proportional to the inverse of the amplitude squared, and we explain this law by a simple theoretical model. The wave breaking itself is preceded by a slow transfer of energy to secondary waves by a mechanism of resonant interactions, and we compare the results with the classical theory of this phenomenon: good agreement is obtained for moderate amplitudes. The nature of the events leading to wave breaking depends on the wave frequency (i.e. on the direction of the wave vector); most of the analysis is restricted to the case of fairly high frequencies. The maximum growth rate of the inviscid wave instability occurs in the limit of high wavenumbers. We observe that a well-organized secondary plane wave packet is excited. Its frequency is half the frequency of the primary wave, corresponding to an excitation by a parametric instability. The mechanism of selection of this remarkable structure, in the limit of small viscosities, is discussed. Once this secondary wave packet has reached a high amplitude, density overturning occurs, as well as unstable shear layers, leading to a rapid transfer of energy towards dissipative scales. Therefore the condition of strong wave steepness leading to wave breaking is locally attained by the development of a single small-scale parametric instability, rather than a cascade of wave interactions. This fact may be important for modelling the dynamics of an internal wave field.
Monthly Notices of the Royal Astronomical Society, May 1, 1998
We study spherically symmetrical equilibrium states of collisionless stellar systems confined to ... more We study spherically symmetrical equilibrium states of collisionless stellar systems confined to a spherical box. These equilibrium states correspond to the statistics introduced by Lynden-Bell in his theory of 'violent relaxation', and are described by a Fermi-Dirac distribution function. We compute the corresponding equilibrium diagram and show that a global entropy maximum exists for any accessible control parameter. This equilibrium state shows a pronounced separation between a degenerate core and a halo. We therefore check that degeneracy is able to stop the gravitational collapse (of a collisionless system), and we propose a simple model for the 'core-halo' structure. We also discuss the relevance of our study for real galaxies or other astrophysical systems such as massive neutrinos.
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Papers by joel Sommeria