Achim Wirth

Louis Gostiaux

Pascale Bouruet-Aubertot

François Lott

Riwal Plougonven

et l'Atmosphère"

23-24 mai 2013 Lyon

The objective of the OGOA project is to bring together the French research community working in the field of gravity waves in the atmosphere and the ocean, using observations, laboratory experiments, numerical simulations and analytical calculations. The subjects studied include the generation of gravity waves (tidal, spontaneous, topographic, by instability, by air-sea interaction, by convection and other sub-meso-scale processes), their turbulent dynamics (cascades: direct, inverse, local and non-local), their interaction with the vortical circulation, their separation from the vortical circulation, and their parameterization. The aim of the project is to identify possible future collaborations and project submissions (LEFE, ANR, H202) in the field of gravity waves.

The fundamental aspect of stratified turbulence is studied in DNS by A. Delache et al., and statistical models applied to large scale geophysical flows using St Venant's (shallow water)equations were presented by F. Bouchet. History of science, on the conflation between two distinct definitions of the Doppler shift occurring in the oceanographic literature, was presented by T. Gerkema.

Conclusions

The two days of the conference led to active discussion between the 42 participants. The interaction between the different communities is now reinforced and all participants agreed to pursue this effort further.

The contributions at the OGOA meeting held in Lyon on May 23 and 24, 2013 were grouped in three different fields: atmosphere, ocean and physics. The first two considered the dynamics of gravity waves in the environment using observations, numerical calculations and laboratory experiments dedicated to a specific area, while the third focused on the physics of gravity waves in general, studied by means of laboratory experiments, numerical simulations and theory.

Ocean

One of the major questions in ocean dynamics is to explain and model the temperature and salinity distributions in time-and-space within the ocean. It is a result of the combined action of air-sea fluxes, currents, waves and nonlinear interactions between them and turbulent mixing. Temperature and salinity determine the density structure which constrain the basin-scale currents and overturning circulation. The transport due to internal gravity waves is usually considered as negligible and the focus is on the mixing of water-masses due to the breaking of gravity waves. To determine the spatio-temporal pattern of mixing of water masses in the ocean we have to determine:

1. where and how gravity waves are generated, 2. whereto and how they propagate, [START_REF] Lott | A Climatology of the Gravest Waves in the Equatorial Lower and Middle Stratosphere: Method and comparison between the ERA-40 re-analysis and the LMDz-GCM[END_REF]. where and how they break.

When the above questions are answered the representation of gravity waves in today's ocean models can be considered. In the talks during the OGOA meeting these questions were addressed from different angles.

The generation of gravity waves by the roughness of topography (C. Muller et al.) and small topography as well as spontaneous generation by vortical flow (A. Wirth) was discussed. In the former it is shown that abyssal hills, unresolved in state of the art topographic products, can have a strong impact on internal tides generation, especially over mid-ocean ridges and can locally double the energy flux. While the latter demonstrates that the sub-synoptic scales in the vortical dynamics contribute little to the spontaneous generation of gravity waves.

The generation of solitons by tidal motion is investigated by numerical models and laboratory experiments. In idealized numerical experiments (F. Auclair et al.) investigated the tidal generation of gravity waves and the role of hydraulic control. Simulations on the internal tides dynamics using model calculations with varying resolution and domain size and a realistic topography off the coast of southern California were presented (A. Ponte). High-frequency observations in the Bay of Biscay, one of the most energetic regions for internal tides, evidenced the mechanisms of generation of a train of solitary waves and a parameterization of turbulent mixing induced by internal tides based on microstructure measurements was proposed (Y. Cuypers).

Observations collected in the Mediterranean Sea revealed the presence of strong baroclinic nearinertial waves within anticyclonic eddies, increased dissipation at the top and base of the eddies associated with these waves (P. Bouruet-Aubertot) and increased vertical turbulent diffusivity in these regions and in the weakly stratified eddy core.

Laboratory and numerical experiments on the non-linear dynamics of gravity waves in the Luzon strait were presented (M. Mercier).

Analytical and numerical results on the instability of gravity waves were given (F. Lefeuvre). It is shown that for internal waves generated by geostrophic motions over small scale topography the vertical distribution of turbulent kinetic energy dissipation is set by the vertical structure of inertial oscillations generated during internal lee wave breaking (P. Labreuche et al.).

In the Ionian sea, where stratification is weak, the vertical component of the earth's rotation vector is found to lead to vertical oscillations. This component is usually neglected in the traditional approximation (L. Gostiaux et al.).

Atmosphere

Today, climate and weather prediction models attempt to well represent the dynamics of the middle atmosphere. For this purpose they need to have about the right amount of gravity waves, which drive a substantial part of the global Brewer-Dobson circulation that builds up the large-scale winds in mid-latitudes. The gravity waves also participate to the forcing of the quasi-biennal oscillations in the tropics. These waves, occurring on rather short scales, are not well resolved in global models and hence need to be parametrized. The present-day parameterizations try to relate the waves to their sources in the troposphere, like convection (P. Maury et al.), and these relations with the sources are clearly beneficial. We need now to relate the GWs to their potential sources in the midlatitudes, and for this theoretical works are now completed to do this in closed mathematical form (Lott et al.). One problem when we adjust models and parameterizations, is that the parameterized waves can replace large-scale waves, e.g. that we correct a systematic error on the waves, that models should explicitly represent. In these two respects, the relation with the sources and the realism of the parameterized GWs field, observations are crucial. Nevertheless, operational radiosondes observations do not reach the altitudes of interest and satellites do not have access to the entire spectra of the small-scale gravity waves. For this reason, the long-duration superpressure balloons flying in the lower stratosphere and presented by A. Hertzog et al. provide information of great significance. On top of characteristic zonal mean values of the GWs drag, they also provide informations on gravity wave sources, and also on their intermittency. In this sense they support the stochastic approach used in the present day parameterizations (P. Maury et al.). In this process of using observations to guide and assess parameterizations in models, an important step is also done in term of regional modeling with high resolution models (Plougonven et al.). Simulations carried out for the period and domain where the super-pressure balloons flew provide a complementary description of the wave field, but also of the tropospheric flow generating the waves, allowing the investigation of non-orographic sources.

Results on the dynamics of gravity waves in deep alpine valleys were presented by (Staquet et al.) They found that the oscillatory motions associated with the IGWs generated by katabatic winds are distinct from those of the katabatic winds. The IGW frequency was found to be independent of the slope angle and about 0.8N. Paci et al. presented results of laboratory experiments performed in Toulouse on the interaction of flow with topography, the rotor dynamics and the wave capture above the topography.

Physics

Internal waves in the atmosphere and in the ocean raise fundamental questions to the physicists. There is now a strong activity in that field, in laboratories directly affiliated to INSU but also to INP and INSIS. Internal gravity waves are hence a subject potentially driving interdisciplinarity in the French research framework.

A first set of presentations used a newly designed wavemaker to study the fate of internal waves in a stratified medium. Venaille et al. measured the mean flow induced by the viscous dissipation of the waves, which is in principle the analogy of the deposit of momentum by breaking waves in the upper atmosphere. H. Scolan et al. studied the fate of internal waves in a closed domain, and the instability occurring in the presence of an attractor. B. Bourget et al. observed for the first time in the laboratory the detailed process of the parametric subharmonic instability (PSI), which is one of the mechanism of dissipation and energy transfer to smaller scales for internal waves.

The wake of moving objects in a stratified medium is also studied as a model for topographically induced internal waves (mountain lee waves in the atmosphere or in the oceans, as recently shown in the Antarctic Circumpolar Current Les premiers résultats de cette expérience montrent une forte influence de la rotation sur le phénomène de convection : l'organisation habituelle en grands rouleaux est remplacée, lors du cas avec rotation, par des colonnes montantes et descendantes à plus petite échelle. Une étude plus précise de l'évolution des températures, que nous avons mesurées dans la cuve sur une ligne verticale, et du front convectif, permettra d'obtenir des informations plus quantitative sur le rôle de la rotation dans ce phénomène.

B. Bourget, T. Dauxois, S. Joubaud, and P. Odier. Experimental study of parametric subharmonic instability for internal plane waves. J. Fluid Mech., 723:1-20, 2013. Réunion OGOA, 23-24 mai 2013, session : Physique 1

Antoine Venaille (ENS de Lyon)

Écoulement moyen induit par l'atténuation d'une onde de gravité.

Antoine Venaille,,Guilhem Bordes, Sylvain Joubaud, Philippe Odier, Thierry Dauxois Laboratoire de Physique de L'ENS de Lyon Nous présenterons un dispositif expérimental qui permet d'observer la formation d'un vortex dans un fluide stratifié forcé par un générateur d'ondes internes de gravité.

Nous proposerons une explication pour la formation de ce vortex à l'aide d'un développement asymptotique en échelles multiples. Les deux ingrédients essentiels pour la formation de l'écoulement moyen sont :

1. une source localisée en espace 2. un mécanisme d'atténuation de l'amplitude de l'onde.

Cela nous amènera à discuter du rôle de la viscosité et de la diffraction.

Bordes, Guilhem; Venaille, Antoine; Joubaud, Sylvain; Odier, Philippe; Dauxois, Experimental observation of a strong mean flow induced by internal gravity waves, Physics of Fluids, Volume 24, Issue 8, (2012) Réunion OGOA, 23-24 mai 2013, session : Physique 1

Jan-Bert Flor (LEGI)

Ondes et instabilités de fronts en milieu tournant et stratifié. In a valley sheltered from strong synoptic effects, the dynamics of the valley atmosphere at night are dominated by katabatic winds. In a stably stratified atmosphere, these winds undergo temporal oscillations, whose frequency is given by Nsinθ for an infinitely long slope of constant slope angle θ, N being the buoyancy frequency. Such an unsteady flow in a stably stratified atmosphere may also generate internal gravity waves (IGWs) (Figure 1). Réunion OGOA, 23-24 mai 2013, session : Atmosphère

Alexandre Paci (Meteo France)

Veine hydraulique stratifiée de Toulouse: quelques expériences de laboratoire sur les ondes internes topographiques dans l'atmosphère First, the realism of the simulated waves is assessed by comparison to the observations. A satisfactory overall agreement is found, but different behaviour is noted for orographic waves (overestimation in the simulations relative to the observations) and non-orographic waves (underestimation).

Second, the gravity-wave field is analyzed in more detail. It is necessary to quantify orographic and non-orographic waves separately. Orographic waves are larger and more intermittent, yet affect only a limited geographical region. Hence their overall contribution to momentum fluxes entering the stratosphere is comparable to that of non-orographic sources. A diagnostic for intermittency, the Gini coefficient, is proposed.

Third, in order to better identify non-orographic sources, case studies are carried out for episodes of intense momentum fluxes over the Southern Ocean, far from islands. The emitted gravity waves occur over intense and rapid cyclogenesis events (polar lows). It appears that, despite the high latitude, moist effects play a crucial rôle in the emission of the gravity waves. Réunion OGOA, 23-24 mai 2013, session : Atmosphère

P. Maury (LMD)

A stochastic parameterization of the gravity waves due to convection and impact on the equatorial stratosphere P. Maury, L. Guez, and F. Lott (LMD, Paris)

A formalism is proposed to represent the gravity waves due to convection in a General Circulation Model that includes a well resolved stratosphere. It is based on a stochastic approach, where an ensemble of monochromatic waves is built up, by launching few waves at each time step, and by cumulating the effect of these waves via an AR1 relation between the GWs tendency at a given time step and that at the next time step. Some properties of each waves are chosen randomly, like their wavenumbers and frequencies and with fixed probability distribution. Their amplitude nevertheless, is directly related to the precipitation, translating it in an heating rate and using linear theory to predict the amplitude of the waves such a heating can produce.

First, off-line tests are done using re-analysis and global precipitation data. They illustrate that the scheme launches GWs momentum fuxes that are much more heratic then when uniform sources are considered. This makes that the scheme has a tendency to act at lower level then when uniform sources are considered. We then verify that the parameterization, when applied to a General Simulation Model (GCM) with high vertical resolution in the stratosphere (dz~500m) is able to produce a Quasi-Biennial Oscillation (QBO), and to improve the Semi-Annual Oscillation (SAO).

1. Lott, F., L. Guez, and P. Maury 2012: A stochastic parameterization of non-orographic gravity waves: Formalism and impact on the equatorial stratosphere, Geophys. Res. Lett., 39, L06807, doi:10.1029/2012GL051001.

2. Lott, F and L. Guez 2013: A stochastic parameterization of the gravity waves due to convection and impact on the equatorial stratosphere, J. Geophys. Res., Submitted.

A. Hertzog (LMD)

Gravity-wave characteristics derived from quasi-Lagrangian balloon flights in the stratosphere A. Hertzog, R. Plougonven, V. Jewtoukoff (LMD) R. A. Vincent (U. of Adelaide)

Most of our observational knowledge of gravity waves in the atmosphere comes from vertical profiles performed by ground-based instruments (radar, lidar), radiosoundings or space-borne instruments. Superpressure balloon flights on the other hand provide the opportunity to sample the atmosphere along quasi-Lagrangian trajectories, like drifters in the oceans.

The presentation will be devoted to presenting elements describing how gravity-wave characteristics are deduced from observations collected during those specific long-duration balloon flights. This technique will be applied to recent measurements over Antarctica and the surrounding oceans during the framework of the international Concordiasi project. The Concordiasi observations have in particular enabled us to estimate gravity-wave momentum fluxes, which are a useful constraint to gravity-wave drag parameterization used in atmosphere general circulation models. Momentum flux maps produced with this dataset are also used to identify major wave sources and to emphasize the large spatial heterogeneity of wave activity in the southern polar regions.

Last, by constructing probability distribution functions of momentum fluxes, we will show observational evidence that gravity-wave activity in the stratosphere is highly intermittent. Yet, the wave intermittency varies significantly according to the wave sources, and is higher over mountain ranges than everywhere else. Future similar balloon flights will be performed in the tropics, and will particularly address the problem of wave generation by tropospheric convection. Laboratory experiments would likely be very helpful to study the efficiency of such wave source, and to provide the characteristics of the generated waves. Réunion OGOA, 23-24 mai 2013, session : Atmosphère

Francois Lott (LMD)

Gravity Waves Produced by Potential Vorticity Anomalies

Francois Lott, R. Plougonven (LMD, Paris) J. Vanneste (University of Edimburg)

The gravity waves (GWs) produced by potential vorticity (PV) anomalies in a vertical wind shear are evaluated for an unbounded rotating stratified flow. In this set-up, the disturbances have two inertial layers, one on each side of the PV anomaly that produces them. Between these layers the disturbance is well predicted by the quasi-geostrophic theory, beyond these layers it corresponds to propagating GWs.

This GW signal is predicted analytically using a Green's function method. The Green's functions used belong to the continuum of solutions of the non-geostrophic Eady problem of baroclinic instability. We find that the non-dimensional EP-flux of the GWs in the far field is approximately exp(-pi N/Uz)/8, where N is the Brunt-Vaisala frequency and Uz the wind shear. Between the two inertial layers the EP-flux is twice that outside of them,which means that substantial wave-flow interactions occur in the inertial layers. This formula is found to be useful for a large range of PV distribution, is easy to translate in dimensional form and from the large scale flow characteristics.

The case of a PV disturbance with amplitude 1PVU and depth 1km is then analysed. When this disturbance enters in the troposphere, the EP-fluxes are between 0.1mPa and 100mPa when the Richardson number J=N/Uz is between 1 and 10. These values compare with those observed in the low stratosphere, which suggests that we have identified a substantial GW source, and that this source can be parameterized in GCMs.

Océan 1

Réunion OGOA, 23-24 mai 2013, session : Océan 1

Caroline Muller (LadhyX)

Abyssal Hill Roughness Impact on Internal Tide Generation: Linear Theory Réunion OGOA, 23-24 mai 2013, session : Océan 1

Aurélien Ponte (LPO)

Modélisation de la marée interne en Californie du Sud.

Aurélien Ponte (LPO)

Les ondes de marée interne sont produites lorsque les courants de marée rencontrent des variations bathymétriques et perturbent la stratification océanique. Une fois générées, ces ondes peuvent ensuite se propager sur des distances considérables O(1000km). Les raisons motivant l'étude de la marée interne sont multiples. Elle affecte, entre autre, notre habilité à interpréter les données altimétriques et le fonctionnement des sonars. Elle contribue également au mélange océanique. Je montrerais les résultats d'une série de simulations numériques qui met en lumière le problème posé par la propagation à longue distance de la marée interne pour la simulation régionale de marée. Cette propagation se traduit concrètement par une sensibilité des simulations de marée à la taille du domaine numérique utilisé. Plus fondamentalement, ceci motive le besoin de comprendre les modalités de propagation et de dissipation de la marée interne. Durant la campagne MOUTON des mesures hydrologiques et du courant à fine échelle ont été réalisées conjointement à des mesures de microstructure au centre du golfe de Gascogne afin de caractériser la dynamique des ondes internes de marée et le mélange associé. Ces mesures ont été réalisées à un soixantaine de km du point de résurgence du rayon de marée interne ou études théoriques et numériques prédisent une conversion du rayon de marée en ondes interfaciales de mode relativement élevé (mode 3) ainsi qu'une évolution non linéaire et non hydrostatique de ce mode en ondes solitaires. Des ondes de marée interne de grande amplitude qui se projettent principalement sur les modes 3 et 4 sont mises en évidence par nos observations, celles-ci génèrent des ondes solitaires de mode 1 piégées dans la thermocline. Ces ondes sont à l'origine d'une fine bande de cisaillement dans la thermocline qui est associé à un taux de dissipation important. Ce taux de dissipation est encore amplifié par le passage des ondes solitaires. En dehors des périodes d'observation d'ondes solitaires le taux de dissipation mesuré est en bonne accord avec la paramétrisation fine échelle de MacKinnon et Gregg (MG 2003). Celle-ci s'applique à un champ d'ondes internes dominés par des ondes basse fréquence, ce qui est cohérent avec un signal de marée interne dominant. En revanche les observations du taux de dissipation sont en désaccord avec la paramétristaion de Gregg-Henyey (GH 1989) qui s'appuie sur l'hypothèse d'un champ d'ondes internes modélisé par le continuum d'ondes de Garrett et Munk. La paramétrisation MG est connue pour être valable en milieu côtier, nos observations montrent que celle-ci peut également s'appliquer à l'océan profond lorsque le champ d'ondes internes est dominé par quelques modes basse fréquence associé à la marée interne. Afin de compléter les études précédentes , nous avons réalisé une expérience à grande échelle à la plateforme Coriolis, table tournante de 13m de diamètre, la plus grande au monde. Nous avons reproduit le forçage de la marée, générant un écoulement oscillant sur une maquette réaliste du détroit, avec une stratification similaire aux observations océaniques. La mise à l'échelle du laboratoire a été réalisée tout en préservant le régime dynamique associé au problème océanique (nombre de Froude, criticalité, excursion de la marée, etc.). Je présenterai les principaux résultats obtenus en lien avec les observations existantes.

François Lefeuvre (LadHyX)

Le role des ondes internes dans le mélange océanique

François Lefeuvre (LadHyX) Afin d'améliorer les modèles climatiques actuels, il est nécessaire de mieux comprendre les mécanismes d'instabilité de la marée interne. En effet, le mélange induit par l'instabilité, donc le déferlement, des ondes internes n'est pas bien compris et quantifié. Ce déferlement peut avoir plusieurs causes:

• l'instabilité de KelvinHelmoltz,

• l'instabilité convective,

• l'instabilité due aux intéractions ondesondes.

Le but de ce projet est donc de pouvoir prédire précisément la déperdition énergétique associée à ces ondes internes en fonction de la topographie sousmarine de la zone considérée.

Achim Wirth (LEGI)

Inertia-Gravity Waves generated by near Balanced Flow in 2 Layer Shallow Water Turbulence on the beta Plane Réunion OGOA, 23-24 mai 2013, session : Océan 2

Pierre Labreuche (LEGI)

Dissipation of internal waves generated by geostrophic motions over small scale topography

Pierre Labreuche (LEGI)

Deep reaching geostrophic flows in the Southern Ocean are suspected to energize internal lee waves close to bottom topography. Recent studies suggest that these internal lee waves generated in the Southern Ocean could largely be dissipated close to bottom topography. Nikurashin and Ferrari (2010b) proposed from two-dimensionnal numerical simulations that such bottom intensification may result from coupling between these waves and inertial oscillations. We have studied the spatial distribution of turbulent kinetic energy dissipation resulting from this coupling. For this purpose, we performed a series of two-dimensionnal non-hydrostatic numerical simulations of a geostrophic flow over an idealized topography for a range of physical and numerical parameters. We have shown that, in this particular flow configuration, the vertical distribution of turbulent kinetic energy dissipation is set by the vertical structure of inertial oscillations generated during internal lee wave breaking. We also extended the theory of Nikurashin and Ferrari (2010b) in order to predict the vertical structure of these inertial oscillations from large scale parameters (Labreuche et al. 2013, submitted). The presentation will focus on the critical height below which most of the dissipation occurs, as well as the amount of dissipation taking place.

Pascale Bouruet-Aubertot (LOCEAN)

Characterization of turbulence from a fine-scale parameterization and microstructure measurements in the Mediterranean Sea during the BOUM experiment

One of the main purposes of the BOUM experiment was to find evidence of the possible impact of submesoscale dynamics on biogeochemical cycles. To this aim physical as well as biogeochemical data were collected along a zonal transect through the western and eastern basins of the Mediterranean sea. Along this transect 3 day fixed point stations were performed within anticyclonic eddies during which microstructure measurements of the temperature gradient were collected over the top 100m of the water column. We focus here on the characterization of turbulent mixing.

The analysis of microstructure measurements revealed a high level of turbulent kinetic energy (TKE) dissipation rate in the seasonal pycnocline and a moderate level below with mean values of the order of 10-6W.kg-1 and 10-8 W.kg-1 respectively. The Gregg Henyey (Gregg 1989) fine-scale parameterization of TKE dissipation rate produced by internal wave breaking, and adapted here following Polzin (1995) to take into account the strain to shear ratio was first compared to these direct measurements with favorable results. The parameterization was then applied to the whole data set. Within the eddies, a significant increase of dissipation at the top and base of eddies associated with strong near inertial waves is observed. Vertical turbulent diffusivity is increased both in these regions and in the weakly stratified eddy core. The stations collected along the East West transect provide an overview of parameterized TKE dissipation rates and vertical turbulent diffusivity over a latitudinal section of the Mediterranean sea. Strong TKE dissipation rate are found within the first 500m and up to 1500 m above the bottom. Close to the bottom where the stratification is weak the inferred vertical turbulent diffusivity can reach Kz~10-3m2.s-1 and may therefore have a strong impact on the upward diffusive transport of deep waters masses.

1. Cuypers, Y., Bouruet-Aubertot, P., Marec, C., Fuda, J.L. Characterization of turbulence and validation of a fine-scale parametrization in the Mediterranean Sea during the BOUM experiment Biogeosciences Discuss., 8, 8961-8998 Geophysical flows are highly turbulent, yet embody large-scale coherent structures, such as ocean rings, jets, and large-scale circulations. Understanding how these structures appear and predicting their shape are major theoretical challenges. The statistical mechanics approach to geophysical flows is a powerful complement to more conventional theoretical and numerical methods. In the inertial limit, it allows to describe, with only a few thermodynamical parameters, the longtime behavior of the largest scales of the flow. Recent studies in quasi-geostrophic models provide encouraging results: a model of the Great Red Spot of Jupiter, an explanation of the drift properties of ocean rings, the inertial structure of midbasin eastward jets, bistability phenomena in complex turbulent flows, and so on. Generalization to more comprehensive hydrodynamical models, which include gravity wave dynamics and allow for the possibility of energy transfer through wave motion, would be extremely interesting. Namely, both are essential in understanding the geophysical flow energy balance. However, due to difficulties in essential theoretical parts of the statistical mechanics approach, previous methods describing statistical equilibria were up to now limited to the use of quasi-geostrophic models. The current study fills this gap. The new theory we propose describes geophysical phenomena using statistical mechanics applied to the shallow water model, and is easily generalizable to the primitive equations. Invariant measures of the shallow water model are built based on the Hamiltonian structure and the Liouville theorem. The theory predicts a balanced large scale flow that contains only a fraction of the initial energy. The excess of energy is stored among all accessible gravity wave degrees of freedom. The theory thus predicts the fraction of energy dissipated through interaction between the vortical part of the dynamics and wave motions. The small insert is a snapshot of the potential vorticity field showing the tendency of a freely quasi-geostrophic flow to self-organize into a large scale anticyclonic vortex above a topographic bump, which is predicted by equilibriums statistical mechanics. This flow is characterized by its microscopic enstrophy Z0 and its energy Eg. We show that this self-organization phenomenon is robust for shallow water equations, but that some of the energy of the large scale flow is lost into inertial-gravity waves (energy Ew). For an initial entrophy Z0 and a an initial total energy E, we predict the ratio Eg/Ew. The two key parameters are the enstrophy Zb of the flow at rest and the total energy E. The inverse temperature associated with the quasi-gesotrophic flow is related to the wwaves through βg=1/Ew. At high temperature, the quasi-geotrophic potential vorticity if fully homogenized. At low temperature, we recover Fofonoff flow that follows topography contours.

Figure 1 :

 1 Figure 1: Observation de la zone convective (en bas) et de la zone diffusive (en haut) par la technique de Schlieren synthétique. Gauche: sans rotation -Droite : avec rotation à 15 rpm.

Figure 1 :

 1 Figure 1: a) Dispositif expérimental. b) Observation du dipole dans une coupe horizontale

  2. L.R.M. Maas, D. Benielli, J. Sommeria, and F.-P.A. Lam, Nature 388, 557 (1997).

  3. N. Grisouard, C. Staquet, and I. Pairaud, J. Fluid Mech. 614, 1 (2008). 4. J. Hazewinkel, P. van Breevort, S.B. Dalziel, and L.R.M. Maas, J. Fluid Mech. 598, 373 (2008). 5. J. Hazewinkel, C. Tsimitri, L.R.M. Maas, S.B. Dalziel, Phys. Fluids 22, 107 (2010). 6. L. Gostiaux, H. Didelle, S. Mercier, and T. Dauxois, Exps. Fluids 42, 123 (2007).

Figure 1 Réunion

 1 Figure 1

Figure 1 :Figure 1 :

 11 Figure 1: Déplacement (en haut) et pente (en bas) des lignes isopycnales dans le plan vertical de symétrie d'un tore oscillant horizontalement, mesuré expérimentalement (à gauche) et prédit théoriquement (à droite).

J

  .-B. Flor (Laboratoire des Ecoulements Géophysiques et Industriels, Grenoble, France) H. Scolan (Laboratoire de Physique de l'ENS de Lyon, Lyon, France) R. Verzicco (R. Verzicco, Departemente IM, Universita di Roma "Tor Vergata", Roma, Italy)Fronts occur in the Earth oceans and atmosphere and separate masses of air of fluid of different temperature and different velocities. Their instabilities are relevant to the transport of heat and energy in the oceans and atmosphere, and are therefore very relevant for climate modeling. In this study, a front is generated in the laboratory in a density stratified and differentially rotating fluid, and the corresponding flow is investigated numerically using DNS. In former studies of fronts, mainly the frontal instability has been discusses and baroclinic instability and newly found Rossby Kelvin instability were reported (Flor et al 2011, Scolan 2011, and Scolan et al 2013). The exact state of the interface is very relevant for the type of instability and waves we may expect. We therefore focus on the interfacial dynamics, and consider the diffusion of vorticity and density at an interface as a function of Rossby and Schmidt number. We note the existence of interfacial Ekman layers, observe Kelvin Helmholtz instability and discuss Hölmböe instability as well as other wave types near the interface. 1. Scolan H., (2011). Dynamique et stabilité de fronts : phenomenes ag eostrophiques. PhD Thesis, Université de Grenoble, Grenoble. 2. J.-B. Flor, H. Scolan and J. Gula (2011) Frontal instabilities and waves in a differentially rotating fluid. J. Fluid Mech. 685, p532-542 3. H, Scolan, J.-B. Flór, and R. Verzicco (2013) Frontal instabilities at a density-shear interface in a rotating two-layer stratified fluid. 4. Modeling Atmospheric and Oceanic Fluid Flows: Insights From Laboratory Experiments, AGU Books. In press.

Figure 1 :

 1 Figure 1: Typical observations of mall scale waves at the frontal region with (a) Holmboe waves, and (b) Kelvin Helmholtz waves. In (c) necessary conditions for Kelvin Helmholtz and Holmboe waves are not satisfied. The waves are observed in (a) the stable regime (b), the Rossby Kelvin regime, and (c) the baroclinic unstable regime.

Figure 1 :

 1 Figure 1: Visualisation à la fluoresceine du Mode L (Re=195, F=0.65).

1 .

 1 Largeron Y., Staquet C. & Chemel C. 2013 Characterization of oscillating motions in the stable atmosphere of a deep valley. Boundary Layer Meteorology, DOI 10.1007/s10546-013-9825-y.

Figure 1 :

 1 Figure 1: Vertical cross-section of a valley of idealized shape in a stably-stratified atmosphere.Contours of the vertical component of the velocity field are displayed, which attest of the generationof an internal gravity wave field from the katabatic flow (flowing along the slopes but hardly visibleon the figure). The wave amplitude is about ten times smaller than the katabatic flow amplitude.

1 .

 1 Knigge C., D. Etling, A. Paci and O. Eiff (2010) : Laboratory experiments on mountain induced rotors, Quarterly Journal Royal Meteorological Society, 136 : 442-450, doi :10.1002/qj.564 2. Dossmann Y., A. Paci, F. Auclair and J. W. Floor (2011) : Simultaneous velocity and density measurements for an energy-based approach to internal waves generated over a ridge, Experiments in Fluid, 51 (4) : 1013-1028, doi :10.1007/s00348-011-1121-3 3. Dossmann Y., F. Auclair and A. Paci (2013) : Topographically induced internal solitary waves in a pycnocline : primary generation and topographic control, Phys. Fluids 25 (066601), doi :10.1063/1.4808163

Figure 1 :

 1 Figure 1: Vue de la grande hydraulique stratifiée de Toulouse

1 .

 1 Hertzog, A., et al (2008) : Estimation of gravity-wave momentum fluxes and phase speeds from long-duration stratospheric balloon flights. 2. Results from the Vorcore campaign in Antarctica, J. Atmos. Sci., 65, p3065-3070. 2. Plougonven, R., et al (2013) : Gravity waves over Antarctica and the Southern Ocean: consistent momentum fluxes in mesoscale simulations and stratospheric balloon observations, Q.J. Roy. Met. Soc., 139, p101-118.

Figure 1 :

 1 Figure 1: Zonal momentum fluxes at ~19 km from the simulations (left) and the balloon observations (right), averaged over the period 21/10 -18/12/2005. The simulations are sampled at times and locations where balloons were present (see Plougonven et al 2013). Color range is voluntarily limited to [-5 ; 5] hPa, in order to reveal the spatial structure over the ocean.

Figure 1 :

 1 Figure 1: When the GWs amplitude is related to precipitations, the launched fluxes become much more erratic, fewer GWS of larger amplitude are launched than when the sources are uniform and un-specified (b and d).

1 .

 1 Boccara, G., A. Hertzog, R. A. Vincent, et F. Vial, Estimation of gravity wave momentum flux and phase speeds from quasi-Lagrangian stratospheric balloon flights. 1: Theory and simulations, J. Atmos. Sci., 65, 3042-3055, 2008.

Figure 1 :

 1 Figure 1: Left :Trajectories of the 19 long-duration balloons lauched from McMurdo, Antarctica in September-October 2010; right : Gravity-wave absolute momentum flux derived from the balloon observations over the whole campaign (September-January)

1 .

 1 Lott F., R. Plougonven, and J. Vanneste, Gravity waves generated by sheared potentialvorticity anomalies, Journal of the Atmospheric Sciences, 67, 157-170, 2010. doi: 10.1175/2009JAS3134.1 2. Lott, F., R. Plougonven, and R. Vanneste, 2012: Gravity waves generated by sheared three dimensional potential vorticity anomalies,69, 2134-2151. doi: http://dx.doi.org/10.1175/JAS-D-11-0296.1

Figure 1 :

 1 Figure 1: L'anomalie de tourbillon potentiel (en traits noirs) produit un champ de vitesse verticale, qui loins des niveaux critiques inertiels devient un champ d'ondes de gravité.

Caroline

  Muller (LadhyX), Angélique Melet (Princeton University/Geophysical Fluid Dynamics Laboratory), Maxim Nikurashin (Institute for Marine and Antarctic Studies, University of Tasmania)Internal tide driven mixing plays a key role in sustaining the deep ocean stratification and meridional overturning circulation. Internal tides can be generated by topographic horizontal scales ranging from hundreds of meters to tens of kilometers. State of the art topographic products hardly resolve scales smaller than ~10 km in the deep ocean, over which abyssal hills are the dominant ocean floor roughness fabric. An evaluation of the impact of abyssal hill roughness on internal-tide generation is presented in this study. The conversion of the M2 barotropic to baroclinic tidal energy is calculated based on the linear wave theory using the Shuttle Radar Topography Mission SRTM30_PLUS bathymetric product at 1/120 degree resolution with and without the addition of synthetic abyssal hill roughness. Internal tide generation by abyssal hills integrates to 0.1 TW globally (i.e. ~10% of the energy flux due to larger topographic scales resolved in standard products) and is dominated by mid-ocean ridges, where abyssal hills roughness is large. Focusing on two regions located over the Mid-Atlantic Ridge and the East Pacific Rise, it is shown that regionally the increase of the energy flux due to abyssal hills can reach up to 100%, or 50% when a crude correction for supercritical slopes contribution is attempted, and that small scales of the bathymetry strongly contribute to the energy conversion. Therefore, abyssal hills, unresolved in state of the art topographic products, can have a strong impact on internal tides generation, especially over mid-ocean ridges. 1. A. Melet, M. Nikurashin, C.J. Muller, S. Falahat, J. Nycander, P. Timko, B. Arbic, J. Goff (2013) "Abyssal Hill Roughness Impact on Internal Tide Generation: Linear Theory", Journal of Geophysical Research -Oceans, Submitted

Figure 1 :

 1 Figure 1: Abyssal Hills contribution to the enrgy flux from the M2 tide into internal tides (in log10, W/m2)

Figure 1 :

 1 Figure 1: Génération d'ondes solitaires au-dessus d'une dorsale océanique: évolution de la pycnocline. (a) Simulation physique dans la veine hydraulique stratifiée de Toulouse, visualisation par stéréo-corrélation, (b) Simulation numérique d'une isopycne à partir du modèle KDV et du modèle SNH, (c) Section verticale de masse volumiquesimulée numériquement (SNH).

1 .

 1 Coastal numerical modelling of tides: sensitivity to domain size and remotely generated internal tide. A. L. S. Ponte, B. Cornuelle. Ocean Modelling, 62:17-26, 2013.

Figure 1 :

 1 Figure 1: Flux d'énergie barocline d'une simulation dans un domaine de 64km x 64km (gauche) et dans un domaine 512km x 512km. La conversion d'énergie barotrope en énergie barocline est indiquée par les contours de couleur.

1 .

 1 Gregg, M. C. (1989). Scaling turbulent dissipation in the thermocline. Journal of Geophysical Research: Oceans (1978-2012), 94(C7), 9686-9698. 2. MacKinnon, J. A., and M. C. Gregg (2003), Mixing on the late-summer New England Shelf-Solibores, shear, and stratification, J. Phys. Oceanogr., 33(7), 1476-1492. 3. Xie, X. H., Cuypers, Y., Bouruet-Aubertot, P., Ferron, B., Pichon, A., Lourenço, A., & Cortes, N. (2013). Large-amplitude internal tides, solitary waves, and turbulence in the central Bay of Biscay. Geophysical Research Letters.

Figure 1 :

 1 Figure 1: Panneau du haut: taux de dissipation (W/kg) les lignes blanches sont des isothermes, panneau du milieu : fréquence Brunt Väisälä , panneau du bas : cisaillement à la puissance 4., les lignes violettes représentent les isothermes 17.3°C and 12.9°C qui délimitent la thermocline

Achim

  Wirth (LEGI) Using a fine resolution numerical model (2×4000² grid-points) of the two layer shallow-water equations of the mid-latitude beta plane dynamics, it is shown that there is no sudden breakdown of balance in the turbulent enstrophy-cascade but a faint and continuous emission of inertia gravity waves. The wave energy accumulates in the equator-ward region of the domain due to the Coriolis parameter depending on latitude and the dispersion relation of inertia gravity waves. 1. Wirth, A., Inertia-Gravity Waves generated by near Balanced Flow in 2 Layer Shallow Water Turbulence on the beta-plane, Nonlin. Processes Geophys., 20, 25-34, 2013.

Figure 1 :

 1 Figure 1: Divergence of the upper layer (in s$^{-1} $) after 250 days. The accumulation of wave-activity is clearly visible in the southern part of the domain. As is the dominance of structures of scale above the (baroclinic) deformation radius.

1 .

 1 Labreuche P., Le Sommer J. and Staquet C., Dissipation of internal waves generated by geostrophic motions over small scale topography. Submitted to Journal of Physical Oceanography. 2. Nikurashin, M. and Ferrari, R. Radiation and dissipation of internal waves generated by geostrophic motions impinging on small-scale topography: Theory. Journal of Physical Oceanography, 40, 1055-1074 (2010)

Figure 1 :

 1 Figure 1: Fraction of the dissipated energy that is dissipated under a given height. The height z is normalized by the theoretical height of bottom dissipation hc , and a horizontal black line is drawn at z = hc .

Figure 1 :

 1 Figure 1: Time depth plots of (a) zonal velocity (b) meridional velocity (c) stratification profiles

Figure 1 :

 1 Figure 1: Séries temporelles de température enregistrées par les 103 capteurs NIOZ-HST, exemple représentatif de durée 12h. Chaque ligne horizontale est tracée indépendamment. La couleur représente l'écart de température au gradient adiabatique. Les ondes de grande amplitude (>100m) sont à la période inertielle (f).

Figure 1 :

 1 Figure 1: Champ de vitesse instantanée mesurée par PIV dans la zone stratifiée. Seules les ondes se propageantvers la droite ont été gardées par notre processus de filtrage par Transformée de Hilbert.

  1. F. Bouchet, and A. Venaille, 2012, Statistical mechanics of two-dimensional and geophysical flows, Physics Reports, 515, 5, June 2012, 227-295

Figure 1 :

 1 Figure 1: The small insert is a snapshot of the potential vorticity field showing the tendency of a freely quasi-geostrophic flow to self-organize into a large scale anticyclonic vortex above a topographic bump, which is predicted by equilibriums statistical mechanics. This flow is characterized by its microscopic enstrophy Z0 and its energy Eg. We show that this self-organization phenomenon is robust for shallow water equations, but that some of the energy of the large scale flow is lost into inertial-gravity waves (energy Ew). For an initial entrophy Z0 and a an initialtotal energy E, we predict the ratio Eg/Ew. The two key parameters are the enstrophy Zb of the flow at rest and the total energy E. The inverse temperature associated with the quasi-gesotrophic flow is related to the wwaves through βg=1/Ew. At high temperature, the quasi-geotrophic potential vorticity if fully homogenized. At low temperature, we recover Fofonoff flow that follows topography contours.

Philippe Odier (ENS de Lyon)

  ). B. Voisin et al. and P. Meunier et al. have studied analytically and experimentally the wave pattern emitted by an oscillating torus and an inclined cylinder respectively. M. Bosco et al. have numerically studied the latter problem. The influence of rotation on geophysical flows needs the use of rotating tanks. Mercier et al. have presented amazing laboratory experiments performed in the Coriolis Platform, Grenoble, where a scaled model of the Luzon Strait, reproducing tidal forcing, stratification and rotation was designed. Odier et al. have shown first results from the new rotating tank PERPET at ENS de Lyon, on the influence of rotation on convection. A similar study was presented by Le Gal et al. at the rotating platform of IRPHE, as well as the behaviour of a buoyant jet under the influence of the Coriolis force. Flor et al. have presented results on front instabilities in a rotating-stratified tank. Pierre Labreuche (LEGI) Dissipation of internal waves generated by geostrophic motions over small scale topography ...................................................................................................................................................32 Pascale Bouruet-Aubertot (LOCEAN) Characterization of turbulence from a fine-scale parameterization and microstructure measurements in the Mediterranean Sea during the BOUM experiment.................................33 Louis Gostiaux (LMFA) Observation d'ondes inertielles profondes en Méditerranée : aspects non-traditionnels. ........34 Physique 2 Theo Gerkema (NIOZ, Netherlands) Les courant moyens -quel rôle jouent-ils dans l'effet Doppler ?..............................................36 Alexandre Delache (LMFA) Sur la restauration des caractéristiques isotropes 3D universelles en turbulence de rotation : scénario de Zeman/Ozmidov.....................................................................................................37 Baptiste Bourget (ENS de Lyon) Étude expérimentale de l'instabilité paramétrique subharmonique des ondes internes de gravité........................................................................................................................................38 Patrice Le Gal(Irphe) fluxes and impact on vertical mixing......................................................................................

	Réunion OGOA, 23-24 mai 2013, session : Physique 1 Réunion OGOA, 23-24 mai 2013, session : Physique 1
	Première expérience sur la plateforme tournante PERPET :
	convection pénétrative en rotation
	P. Odier, S. Joubaud, Laboratoire de Physique, ENS Lyon
	T. Alboussiere, S. Labrosse, Laboratoire de Géologie de Lyon
	Notre laboratoire s'est doté récemment d'une plate-forme tournante de 2 m de diamètre (PERPET,
	Plate-forme d'Études en Rotation des Phénomènes et Écoulements de la Terre), pouvant tourner
	jusqu'à 1 tour/s tout en portant une charge utile de 750 kg. Elle est équipée d'un contacteur tournant
	permettant à la fois la transmission de la puissance électrique nécessaire aux expériences
	embarquées et la transmission des signaux mesurés. Cette plate-forme a été conçue en concertation
	avec plusieurs équipes sur la région lyonnaise, afin qu'elle puisse servir non seulement aux desseins
	des équipes de notre Laboratoire mais aussi à d'autres projets. En collaboration avec Thierry
	Alboussière et Stéphane Labrosse, du Laboratoire de Géologie de Lyon, une première campagne
	d'expériences a déjà été effectuée sur la plate-forme, depuis son installation en janvier 2013. Elle
	concerne une étude de l'influence de la rotation sur le phénomène de convection pénétrante, qui
	existe probablement dans le noyau liquide terrestre et que l'on peut reproduire en refroidissant de
	l'eau par le bas en-dessous de 4°C. En effet l'eau présente un maximum de densité à cette
	température et par conséquent, la région entre 0 et 4°C sera convective, alors que la région au-Physique 1 dessus de 4°C sera stratifiée de manière stable. Dans un tel dispositif, on peut donc étudier la
	pénétration de la région convective dans la région stratifiée.	..42
	F. Lott (LMD)
	Equatorial waves in some CMIP5 coupled models (with stratosphere) ..................................43

Génération d'ondes gravito-inertielles par la turbulence...........................................................39 Freddy Bouchet (ENS de Lyon) Mécanique statistiques des équations de Saint Venant et dissipation d'énergie par les modes agéostrophiques.........................................................................................................................40 Posters Yannis Cuypers (LOCEAN) Tropical storm-induced near-inertial internal waves during the Cirene experiment: energy

Hélène Scolan (ENS de Lyon)

  Dans le cas d'un domaine confiné, les réflexions successives des faisceaux d'ondes internes sur les limites rigides peuvent converger vers une trajectoire fermée : un attracteur d'ondes internes[START_REF] Mercier | Large-scale, realistic laboratory modeling of M2 internal tide generation at the Luzon Strait[END_REF]. Les trajectoires pour un domaine de forme arbitraire ne sont en général pas fermées et l'énergie injectée dans le domaine est répartie uniformément. Au contraire, quand un attracteur est présent, l'énergie est concentrée essentiellement sur les quelques faisceaux associés au cycle limite où on peut s'attendre au développement d'instabilités non-linéaires.

	Réunion OGOA, 23-24 mai 2013, session : Physique 1
	Attracteurs d'ondes internes: génération et instabilité
	Hélène Scolan (Laboratoire de Physique de l'Ecole Normale Supérieure de Lyon, Lyon, France)
	Eugeny Ermanyuk (Lavrentyev Institute of Hydrodynamics, Novosibirsk State University,
	Novosibirsk )
	Thierry Dauxois (Laboratoire de Physique de l'Ecole Normale Supérieure de Lyon, Lyon, France)
	helene.scolan@ens-lyon.fr
	Jusqu'à présent, les attracteurs observés expérimentalement
	[2, 4, 5] ont relativement peu d'énergie injectée et leur
	comportement a été expliqué par des mécanismes linéaires
	étudiés aussi numériquement [3]. Nous présentons une étude
	en laboratoire de l'instabilité d'un attracteur d'ondes internes

de gravité dans un domaine trapézoïdal rempli de fluide uniformément stratifié. L'attracteur d'ondes internes est obtenu selon une nouvelle méthode d'injection d'énergie dans le système avec un générateur d'ondes internes [6] par l'intermédiaire d'ondes stationnaires de type mouvement d'une paroi verticale. En outre, nous montrerons que les attracteurs deviennent instables au dessus d'un certain seuil d'amplitude du générateur ce qui fournit une explication possible à la difficulté d'observer les attracteurs dans les océans. 1. L.R.M. Maas and F.-P.A. Lam, J. Fluid Mech. 300, 1 (1995).

  The numerical study by Chemel et al.(Meteorol Atmos Phys 203:187-194, 2009) showed that, in the stable atmosphere of a deep valley, the oscillatory motions associated with the IGWs generated by katabatic winds are distinct from those of the katabatic winds. The IGW frequency was found to be independent of α and about 0.8N.

	Their study did not consider the effects of
	the background stratification and valley
	geometry on these results. These effects
	are investigated in the present study for a
	wide range of stratification and slope
	angles, through numerical simulations for
	a deep valley. The two oscillatory
	systems are reproduced in the
	simulations. The frequency of the
	oscillations of the katabatic winds is
	found to be equal to N times the sine of
	the maximum slope angle. Remarkably,
	the IGW frequency is found to also vary
	as CwN, with Cw in the range 0.7 -0.95.
	These values for C w are similar to those
	reported for IGWs radiated by any
	turbulent field with no dominant
	frequency component. Results suggest
	that the IGW wavelength is controlled by
	the valley depth.

  Alexandre Paci (CNRM-GAME, Météo-France & CNRS) Le laboratoire de mécanique des fluides géophysiques du CNRM-GAME (UMR3589 CNRS et Météo-France) dispose d'un ensemble expérimental unique pour l'étude des écoulements stratifiés en densité et cisaillés (une veine hydraulique, deux canaux hydrauliques et une table tournante). Les activités de l'équipe se concentrent sur les interactions écoulement/topographie dans l'atmosphère et dans l'océan (couche limite atmosphérique, ondes de gravité internes générées sur une topographie). La veine hydraulique est en particulier reconnue comme une installation hydraulique majeure en Europe à travers son insertion, en partenariat avec la plaque tournante Coriolis du LEGI, dans le réseau du programme européen HYDRALAB. Cette veine hydraulique de 30 m de long peut aussi être utilisée en mode canal fermé. Elle a été conçue pour produire en laboratoire, donc dans des conditions parfaitement contrôlées, des jeux de données précis et complets sur des écoulements semblables à ceux d'un certain nombre de processus de l'atmosphère et de l'océan. Elle permet donc de compléter les observations du milieu naturel, limitées par leur dispersion et l'impossibilité de contrôler les conditions de l'écoulement.

	Cette installation fut initialement conçue
	pour l'étude du vent à petite échelle sur
	des structures ou des topographies
	complexes. Elle est maintenant largement
	utilisée pour mener des travaux de
	recherche sur des thématiques océan-
	atmosphère. Des expériences y sont
	conduites depuis quelques années pour
	étudier différents aspects des ondes de
	gravité internes générées sur une
	topographie dans l'atmosphère et dans
	l'océan. Un aperçu des expériences
	menées dans le contexte atmosphérique
	(rotors en aval d'une chaîne de montagne,
	ondes piégées au dessus d'un mont isolé,
	déferlement...) sera donné.

  Pour ce faire, une cartographie des zones d'instabilités sera étudiée. Létude se limite tout d'abord au cas idéalisé d'un domaine 2D dans lequel on considère la génération des ondes internes induites par la marée barotrope. Ce domaine, périodique dans la direction zonale, est composé d'une topographie aléatoire aux petites échelles au niveau du sol marin. Le travail est alors de mener une étude d'instabilité afin de déterminer les zones instables. Ensuite, l'étude de leurs causes sera abordée. Le travail sera mener à la fois sur un modèle numérique DNS (le code MITgcm) et à la fois sur un modèle analytique dans le but de pouvoir comparer les résultats du modèle analytique avec le modèle numérique.

Réunion OGOA, 23-24 mai 2013, session : Posters

Physique 2

Réunion OGOA, 23-24 mai 2013, session : Physique 2

Theo Gerkema (NIOZ, Netherlands)

Les courant moyens -quel rôle jouent-ils dans l'effet Doppler ?

In the ocean, internal waves commonly occur together with other, large-scale (mean) flows. How are the wave properties affected by such mean flows? In the oceanographic literature, mean flows are often said to create a "Doppler shift". It has passed unnoticed, however, that the term "Doppler shift" is being employed in an ambiguous way. Upon closer examination, it appears that two quite distinct concepts of ''Doppler shifts'' feature in the literature; they are sometimes conflated, resulting in erroneous interpretations. One concept refers to the difference in frequencies measured by two observers, one at a fixed position and one moving with the mean flow-here referred to as ''quasi-Doppler shifts.'' The other concept is the one used in physics, where the frequency measured by an observer is compared to that of the source. In the latter sense, Doppler shifts occur only if the source and observer move with respect to each other; a steady mean flow alone cannot create a Doppler shift. This talk rehashes the classical theory to straighten out some misconceptions. It is also discussed how wave dispersion affects the classical relations and their application. Comme l'échelle d' Ozmidov (1965) en turbulence stratifié stablement, l'échelle de Zeman (1994) a été introduite en turbulence de rotation afin de quantifier le caractère isotropes ou anisotrope de l'écoulement pour différentes échelles: à grandes échelles, l'anisotropie créée par la rotation est dominant, alors qu'à petites échelles, les caractéristiques isotropes 3D universelles de turbulences semblent être restauré. Je présenterai des résultats confirmant ce scénario à partir de simulations numériques directes et pour différente vitesse de rotation. Nous confirmons le retour à l'isotropie des petites échelles par l'analyse du spectres angulaire, par l'analyse du transfert d'énergie et par la décompostion des modes d'énergie poloïdal / toroïdal. L'universalité est rétablie à petite échelle, mais pour des vitesses de rotation élevée. Réunion OGOA, 23-24 mai 2013, session : Physique 2

Baptiste Bourget (ENS de Lyon)

Étude expérimentale de l'instabilité paramétrique subharmonique des ondes internes de gravité.

Baptiste Bourget, Thierry Dauxois, Philippe Odier, Sylvain Joubaud. Laboratoire de Physique de l'ENS de Lyon. Near-inertial Internal Waves (NIW) excited by storms and cyclones play an essential role in driving turbulent mixing in the thermocline and interior ocean. Storm-induced mixing may be climatically relevant in regions like the thermocline ridge in the southwestern Indian Ocean, where a shallow thermocline and strong high frequency wind activity enhance the impact of internal gravity waveinduced mixing on sea surface temperature. The Cirene research cruise in early 2007 collected shipborne and mooring vertical profiles in this region under the effect of a developing tropical cyclone. In this paper, we characterize the NIW field and the impact of these waves on turbulent mixing in the upper ocean. NIW packets were identified down to 1000 m, the maximum depth of the measurements. We estimated a NIW vertical energy flux of up to 2.5 mW m-2 within the pycnocline, which represents about 10% of the maximum local wind power input. A nonnegligible fraction of the wind power input is hence potentially available for subsurface mixing. The impact of mixing by internal waves on the upper ocean heat budget was estimated from a fine-scale mixing parameterization. During the first leg of the cruise (characterized by little NIW activity), the average heating rate due to mixing was ~0.06°C month-1 in the thermocline (23-24 kg m-3 isopycnals). During the second leg, characterized by strong NIW energy in the thermocline and below, this heating rate increased to 0.42°C month-1, indicative of increased shear instability along near inertial wave energy pathways. Cuypers, Y., Le Vaillant, X., Bouruet-Aubertot, P., Vialard, J., McPhaden, M.. «Generation and propagation of near-inertial baroclinic waves during Cirene experiment: energy fluxes and impact on vertical mixing", J. Geophys. Res., 118, 358-380 Réunion OGOA, 23-24 mai 2013, session : Posters

F. Lott (LMD)

Equatorial waves in some CMIP5 coupled models (with stratosphere) F. Lott , P. Maury (LMD, Paris)

The Kelvin and the Rossby Gravity Waves (RGWs) packets that dominate the day to day variability in the low equatorial stratosphere (50hPa) are analyzed in 7 ESMs that participate to CMIP5 and that include a well resolved stratosphere. The results are compared to ERAI. Two models are also used to quantify better (i) the impact of the QBO on these waves (MPI-P and MPI-MR), and (ii) the impact of convection (IPSL-CM5A and CM5B).

In the stratosphere all models present quite coherent Kelvin waves and RGWs packets, which is good think since these waves dominate the day to day variability in the low stratosphere. The errors on these freely propagating waves seem therefore less pronounced then the differences seen by others on the convectively coupled waves in the troposphere. The difference between the models nevertheless stay very large, the models with a QBO have more pronounced waves, and represent better their life-cycle (this is particularly true for the RGWs). The sensitivity to the convection of the rather slow waves analysed here is not as pronounced as was found in the past for may be faster waves, but is nevertheless confirmed when we look at the same model with two drastically different convection parameterization. In the same spirit, the sensitivity of the RGWs to the QBO is confirmed by comparing almost the same model runs, one with a QBO and one without. Having a QBO nevertheless does not guarantee that the waves are realistic in all respects, as shows for instance the Temperature signature due to the RGWs in the UKMO model. There also seems to have an issue when the resolution changes drastically, the MRI model behaving quite differently from the other models when it comes to the simulations of these equatorial waves.


Debajyoti Upadhyay

Michael Richert

Eric Lacot

Antonello De Martino

Xavier Orlik
email: xavier.orlik@onera.fr

Effect of Speckle on APSCI method and Mueller Imaging

Keywords:

The principle of the polarimetric imaging method called APSCI (Adapted Polarization State Contrast Imaging) is to maximize the polarimetric contrast between an object and its background using specific polarization states of illumination and detection. We perform here a comparative study of the APSCI method with existing Classical Mueller Imaging(CMI) associated with polar decomposition in the presence of fully and partially polarized circular Gaussian speckle. The results show a noticeable increase of the Bhattacharyya distance used as our contrast parameter for the APSCI method, especially when the object and background exhibit several polarimetric properties simultaneously.

Introduction

The polarimetric imaging method APSCI [START_REF] Richert | Adapted Polarization state contrast imaging[END_REF] has been shown to reach beyond the limit of contrast achievable from the Classical Mueller Imaging (CMI) with polar decomposition [START_REF] Lu | Interpretation of Mueller matrices based on polar decomposition[END_REF]. The process utilises a selective polarimetric excitation of the scene in order to provoke a scattering from the object and background characterized by Stokes vectors as far as possible in the Poincaré Sphere [START_REF] Poincaré | Théorie mathématique de la lumière[END_REF]. Then along with an optimal polarimetric detection method specifically adapted to each situation, it has been demonstrated that the contrast between an object and its background could be increased to a higher order of magnitude with respect to the contrast from CMI with polar decomposition [START_REF] Richert | Adapted Polarization state contrast imaging[END_REF].

We propose here to study the performance of the APSCI method taking into account the shot noise of the detector and the speckle noise in the case of a monochromatic illumination giving rise to an additional circular Gaussian speckle noise, where partial depolarization may occur. Moreover, we consider the numerical propagation of errors in the calculation of the polarimetric data from the acquired raw data. For various situations, where the scene exhibits different polarimetric properties such as dichroism, birefringence or depolarization, we perform a comparative study of contrast level, which is quantified by the Bhattacharyya distance [START_REF] Bhattacharyya | On a measure of divergence between two statistical populations defined by probability distributions[END_REF] calculated from the significant parameters of the CMI, the polar decomposition and the APSCI method.

Brief review of the APSCI method

Let us assume a scene with a homogeneous circular object surrounded by a homogeneous background. Then, the scene can be modeled into two mutually exclusive regions O and B having polarimetric properties characterized by their Mueller matrices M O and M B , respectively for the object and the background. As the scene is considered to be a priori unknown, we need an initial estimation of Mueller matrices of the object M O and of the background M B by CMI before implementing APSCI method. During the Mueller imaging process, we consider that each pixel of the detector indexed by (u, v) receives an intensity I(u, v) perturbed by a Poisson distribution in order to take into account the shot noise. The Mueller matrix M(u, v) at each pixel is then calculated from the noisy detected intensities I(u, v).

Let us assume a totally polarized Stokes vector S is used to illuminate the scene after CMI.

The estimations of the Stokes vectors of the field scattered by the object S O and background S B can be expressed as :

S O = S O 0 , S O 1 , S O 2 , S O 3 T = M O S , S B = S B 0 , S B 1 , S B 2 , S B 3 T = M B S (1)
We define the measure of separation of S O and S B in the Poincaré sphere by the Euclidean distance D between their last three parameters. Then, we determine numerically using a simplex search algorithm the specific incident Stokes vector S in that maximizes this Euclidean distance.

It is worthy to emphasize that the Stokes vectors S O and S B are not normalized and can exhibit different rate of depolarization. As a consequence, the maximization of the Euclidean distance mentioned above takes into account two physical entities : the polarization state and the intensity of the polarized part of the scattered field.

Finally, we utilize a Two Channel Imaging (TCI) system that projects the scattered field resulting from the selective excitation S in , into 2 states of polarization S out1 and S out2 , that are defined to maximize respectively ( I O -I B ) and ( I B -I O ), where I O and I B are the evaluations of the mean intensity detected respectively from the object and background scattering. From simple calculation it can be shown that:

S out1 = 1, ∆ S T / ∆ S T , S out2 = 1, -∆ S T / ∆ S T (2)
where

∆ S = S out O 1 -S out B 1 , S out O 2 -S out B 2 , S out O 3 -S out B 3 T , (3)
with

S out O 0 , S out O 1 , S out O 2 , S out O 3 T = S out O = M O S in , S out B 0 , S out B 1 , S out B 2 , S out B 3 T = S out B = M B S in . (4)
The APSCI parameter is then defined for each pixel of the detector indexed by the coordinates (u, v) as :

APSCI(u, v) = I 1 (u, v) -I 2 (u, v) I 1 (u, v) + I 2 (u, v) , (5)
where I 1 (u, v) and I 2 (u, v) are the detected intensity after projection respectively on the 2 states of polarization S out1 and S out2 .

In this study, we use the Bhattacharyya distance as a contrast parameter for each physical quantity under investigation that can be, for comparison purposes, either the APSCI parameter as defined above, either the more pertinent parameters extracted from the polar decomposition of the Mueller matrices of the object and background. A more detailed discussion of the APSCI method is proposed in [START_REF] Richert | Adapted Polarization state contrast imaging[END_REF].

Characteristics of the Speckle noise

We have chosen to study an unfavourable situation of imaging regarding both the speckle grain size and its contrast. Thus, we assume a speckle grain with a size similar to that of the pixel of the detector. On the experimental point of view, this situation corresponds to a contrast that is not decreased by the integration of several grains into a single pixel. Moreover, we choose to study the effect of a completely polarized and developed circular Gaussian speckle because it exhibits a strong contrast and so is susceptible to decrease the performance of the APSCI method. As will be pointed out later in this article, biological applications of the APSCI method seem very promising. So, in order to take into account some possible movement of the object, we consider a dynamical speckle: each intensity acquisition is then submitted to a different speckle pattern.

The effect of a partially polarized speckle is also of interest regarding the APSCI method because it combines 2 antagonist effects : a decrease of the speckle contrast that increases the Bhattacharyya distance of the APSCI parameter and a lower amount of polarized light usable by the APSCI method for the optimization that, on the contrary, is expected to decrease signal to noise ratio and hence this distance. In our simulations, the speckle is taken into account by a modulation of intensity at the image plane that is considered independent of the state of polarization scattered by the object and background. This modulation of intensity is performed according to the probability density function of intensity p I (I) of a completely developed cir- cular Gaussian speckle that depends on the degree of polarization P [START_REF] Goodman | Speckle Phenomena in optics[END_REF]:

p I (I) = 1 PI exp - 2 1 + P I I -exp - 2 1 -P I I ( 6
)
where I is the average intensity.

Results and analysis

We have chosen to study in Fig. 1 the effect of a completely developed circular Gaussian speckle on three different situations where the object and background are defined to have a difference of 10% in one polarimetric property : the cases (a) and (b) exhibit this difference in the scalar birefringence, the cases (c) and (d) in the scalar dichroism and the cases (e) and (f) in the degree of linear polarization. The situations (a), (c) and (e) consider only the shot noise whereas (b), (d) and (f) take into account an additional speckle noise. For each of these situations, we calculate between the object and background region, the Bhattacharyya distance of the AP-SCI parameter and of the other pertinent parameters extracted from the polar decomposition. For comparison purposes, the Bhattacharyya distances are plotted versus the signal to noise ratio (SNR) for a same number of intensity acquisition. We would like to point out that, due to their different dichroism, the energy scattered by the object and background and focalized by imaging elements towards the detector can be different, and hence their corresponding classical SNR's. Thus, we choose to define here a global SNR by considering the shot noise generated by the amount of energy received by the detector without the use of any polarizer and after the back-scattering on a virtual perfectly lambertian and non absorbing object, whose size and position are similar to that of the scene under investigation. In Fig. 1 B(M) is defined to be the selected element between M O and M B that provides the best Bhattacharyya distance over the 16 possible elements. In a similar way, B(M R ), B(M D ) and B(M ∆ ) represent respectively the best Bhattacharyya distance obtained from the selected element of the birefringence, the dichroism and the depolarization matrices extracted from M O and M B using the forward polar decomposition. The Bhattacharyya distances corresponding to scenes exhibiting a difference of scalar birefringence, scalar dichroism and in their ability to depolarize linear polarized light are plotted respectively as B(R), B(D) and B(DOP L ). Finally, B APSCI represents the Bhattacharyya distance of the APSCI parameter as defined in section 2.

Considering the situations (a), (c) and (e) that take into account only the shot noise, we observe that from a SNR threshold, the polar decomposition that isolates the property of interest (red and black curves) brings always better Bhattacharyya distances than B(M) (green curve) selected from the raw data of M O and M B . Below this threshold, the noise introduced by this decomposition worsen the situation (as can be seen in case (a)) because M O and M B are insufficiently determined. Secondly, we observe that the parameter B APSCI (blue curve) exhibits the highest Bhattacharyya distances for all the SNR studied in (a) (c) and (e). However, for the case (c), we notice that it exhibits also higher uncertainty bars associated to lower mean values of Bhattacharyya distances compared to cases (a) and (e). This lower performance of the AP-SCI method in the case of dichroism is coming from 2 phenomena : the absorption of energy due to the dichroism effect and the cartesian distance between the matrices of the object and background defined here as the square root of the sum of the square of the element-wise differences. Indeed, as previously discussed in [START_REF] Richert | Adapted Polarization state contrast imaging[END_REF], a 10% difference in one polarimetric property between the object and background gives rise to various cartesian distances in function of the scene studied. For cases (a), (c) and (e), the cartesian distances are respectively : 0.44, 0.09 and 0.14. The lowest value corresponds to the dichroism case and explains the lower performance of the APSCI method in that case. When adding the speckle noise, we observe in (b) compared to (a), a strong degradation of all the Bhattacharyya distances under study. APSCI still remains the more pertinent parameter to distinguish the object from the background even if its standard deviation noticeably increases due to the presence of speckle. The effect of the same speckle noise on situation (c) is plotted on (d). We observe that B(M D ) and B(M) fall to very low values even for high SNR and as a consequence become unusable for imaging. As a result, from the raw data of the Mueller matrices M O and M B associated to the polar decomposition, only B(D) reaches an order of magnitude similar to B APSCI . Moreover, we notice that the standard deviation of B APSCI has considerably increased due to the speckle noise. After a deeper analysis, we have observed that M O and M B are particularly poorly estimated for the case of dichroism (for the 2 reasons mentioned above) and that the addition of speckle noise worsen noticeably this situation. As a consequence, selective states of excitation S in spread near all over the Poincaré sphere, showing only a weak increase of density of probability in the theoretical optimum region.

We consider now on Fig. 1 (e) and (f) the effect of a partially polarized speckle noise with degrees of polarization being respectively P ob j =0.78 and P back =0.71 for the object and background that exhibit a difference of 10% in their ability to depolarize linear polarized light. We observe only a weak decrease of all the Bhattacharyya distances due to the fact that the speckle, only partially polarized, exhibits a lower contrast (C ob j = 0.90 and C back = 0.87) than in previous situations. Moreover, the APSCI parameter gives rise to Bhattacharyya distances much higher than using the CMI alone or associated with the polar decomposition. In all the previous situations, we have studied scenes that exhibit a difference between the object and background in only one polarimetric property. However, in such pure cases, due to the numerical propagation of errors, the interest of using Mueller Imaging can be inappropriate compared to simpler methods such as ellipsometry [6][7] or polarization difference imaging methods [8][9]. However, Mueller Imaging can be of great interest in the case of scenes exhibiting several polarimetric properties at the same time. Thus, in order to examine the performance of APSCI method in such case, we consider a more complex scene where the object and background have 10% difference in scalar birefringence, scalar dichroism and in the linear degree of polarization simultaneously. In Fig. 2, we show the Bhattacharyya distances of the APSCI parameter compared to the best Bhattacharyya distances obtained from the CMI associated to the polar decomposition that is, in this new situation, the Bhattacharyya distance corresponding to scalar dichroism. We observe that both parameters show only a weak decrease of performance (around 5%) due to the speckle noise because it is only partially polarized and exhibits a contrast significantly inferior to 1. Secondly, we see clearly that the Bhattacharyya distances of the APSCI parameter exhibits much higher values than the ones of the scalar dichroism. A visual comparison for a SNR of 3.2 is proposed in Fig. 2 where the object can clearly be seen only using the APSCI parameter because of having 3.8 times higher Bhattacharyya distances compared to the one of the scalar dichroism. We would like to point out that the APSCI parameter of this complex scene exhibits better Bhattacharyya distances than the pure cases of dichroism and depolarization studied separately in Fig. 1. However, inspite of the same amount of birefringence in the situations of Fig. 2 and Fig. 1(a) and that there are additional properties (dichroism and depolarization) in the mixed case which could help us to differentiate the object from the background, the Bhattacharyya distances obtained in the pure case of birefringence are higher than in the mixed case for a given SNR, even if we correct the SNR value by taking into account absorption that occurs in the latter case. This can be explained by the cartesian distances between the object and background matrices which are respectively 0.44 and 0.13 for the pure birefringent and mixed case. It can appear surprising that adding some polarimetric differences between the object and background can reduce the cartesian distance between their Mueller matrices and so our ability to distinguish them. However, we have to keep in mind that most of the elements of a Mueller matrix describe several properties simultaneously and that from a qualitative point of view, the effects of birefringence and dichroism can produce counter-effects that will decrease the maximum distance achievable between the Stokes vector scattered by the object and background. Such observation is true for all kind of polarimetric measurements, however, as the APSCI method doesn't consider each polarimetric property separately, and rather takes into account the whole Mueller matrices, it is expected to give always the best polarimetric contrast achievable for a 2 channel imaging system.

Conclusion

We have studied in various situations the effect of a completely or partially polarized and fully developed circular Gaussian speckle in presence of shot noise, on the APSCI method compared to the Classical Mueller Imaging associated to the polar decomposition. In spite of the additional high contrast speckle noise, the use of selective polarization states of illumination and detection in the APSCI method improves noticeably the polarimetric contrast between an object and its background with respect to the one achievable from the Classical Mueller imaging, even when pertinent polarimetric data are extracted by the polar decomposition. Moreover, as APSCI optimizes the polarimetric contrast combining dichroism, birefringence and depolarization properties simultaneously, it exhibits remarkably high performance compared to Classical Mueller Imaging when the object and background exhibit multiple polarimetric behaviour. This previous remark makes this technique very promising for medical applications as biological tissues often exhibit several polarimetric properties simultaneously in presence of dynamical speckle noise. Especially, it can represent a powerful and non invasive technique for accurate detection of displasic areas in case of tumour ablation.

Acknowledgement

We would like to thank the region Midi-Pyrénée for providing us financial support for this work.

Fig. 1 .

 1 Fig. 1. Bhattacharyya distances obtained from different SNR levels without (case a, c, e) and with (case b, d, f) speckle noise. The object and background have a difference of 10% only in scalar birefringence, scalar dichroism and linear degree of polarization respectively for the cases a & b, c & d and e & f. In case a & b, (R, λ R , ε R ) represent respectively the scalar birefringence, azimuth and ellipticity of the birefringence vector R. Similarly for case c & d , (D, λ D , ε D ) represent respectively the scalar dichroism, azimuth and ellipticity of the dichroism vector D. For the case e & f, eigen axes of depolarization of the object and background are assumed aligned and ∆DOP L and ∆DOP C represent respectively the difference between the object and background, in their ability to depolarize linear and circular polarized light.

Fig. 2 .

 2 Fig. 2. Comparison of Bhattacharyya distances vs. SNR curves for the best performing parameter of CMI (in this case the scalar dichroism) vs APSCI parameter with (ws) and without speckle noise (wos). The scene is composed of an object and a background exhibiting 10% difference in scalar birefringence R, scalar dichroism D and in the linear degree of polarisation DOP L . At the same SNR level of 3.2, the embedded images (i) and (ii) are obtained respectively using the APSCI parameter and the best parameter of the CMI.