Antoine Venaille

Baroclinic Turbulence in the Ocean: Analysis with Primitive Equation and Quasigeostrophic Simulations

AbstractThis paper examines the factors determining the distribution, length scale, magnitude, and structure of mesoscale oceanic eddies in an eddy-resolving primitive equation simulation of the Southern Ocean [Modeling Eddies in the Southern Ocean (MESO)]. In particular, the authors investigate the hypothesis that the primary source of mesoscale eddies is baroclinic instability acting locally on the mean state. Using local mean vertical profiles of shear and stratification from an eddying primitive equation simulation, the forced–dissipated quasigeostrophic equations are integrated in a doubly periodic domain at various locations. The scales, energy levels, and structure of the eddies found in the MESO simulation are compared to those predicted by linear stability analysis, as well as to the eddying structure of the quasigeostrophic simulations. This allows the authors to quantitatively estimate the role of local nonlinear effects and cascade phenomena in the generation of the eddy field.There is a modes...

Statistical Ensemble Inequivalence and Bicritical Points for Two-Dimensional Flows and Geophysical Flows

X iv :0 71 0. 56 06 v1 [ co nd -m at .s ta tm ec h] 3 0 O ct 2 00 7 Ensemble inequivalen e, bi riti al points and azeotropy for generalized Fofono ows Antoine Venaille and Freddy Bou het∗ Laboratoire des É oulements Géophysiques et Industriels, UJF, INPG, CNRS ; BP 53, 38041 Grenoble, Fran e and Institut Non Linéaire de Ni e , CNRS, UNSA, 1361 route des lu ioles, 06 560 Valbonne Sophia Antipolis, Fran e (Dated: February 2, 2008) We present a theoreti al des ription for the equilibrium states of a large lass of models of twodimensional and geophysi al ows, in arbitrary domains. We a ount for the existen e of ensemble inequivalen e and negative spe i heat in those models, for the rst time using expli it omputations. We give exa t theoreti al omputation of a riteria to determine phase transition lo ation and type. Strikingly, this riteria does not depend on the model, but only on the domain geometry. We report the rst example of bi riti al points and se ond order azeotropy in the ontext of systems with long range intera tions. PACS numbers: 05.20.-y, 05.70.Fh, 47.32.-y. In many elds of physi s, the parti le or elds dynami s is not governed by lo al intera tions. For instan e for self gravitating stars in astrophysi s [1, 2℄, for vorti es in two dimensional and geophysi al ows [3, 4, 5℄, for uns reened plasma or models des ribing intera tions between waves and parti les [6℄, the intera tion potential is not integrable [7℄. Re ently, a new light was shed on the equilibrium statisti al me hani s of su h systems with long range intera tions : there has been a mathemati al hara terization of ensemble inequivalen e [8℄, a study of several simple models [9, 10℄, and a full lassi ation of phase transitions and of ensemble inequivalen e [11℄ . One of the promising eld of appli ation for the statisti al me hani s of systems with long range intera tions, is the statisti al predi tion of large s ale geophysi al ows. For instan e, the stru ture of Jupiters troposphere has been su essfully explained using the Robert-SommeriaMiller (RSM) equilibrium theory [12℄ [13℄. One of the major s ope of this eld is to go towards earth o ean appli ations. All textbook in o eanography present the Fofono ows whi h have played an important histori al role in that eld [14℄. In this letter, we propose a theoreti al des ription of su h ows in the ontext of the statistial theories whi h, for the rst time, relates its properties to phase transitions (see Fig. 1), negative spe i heat and ensemble inequivalen e. One of the striking features of the equilibrium theory of systems with long range intera tions is the generi existen e of negative spe i heat. This strange phenomena is possible as a onsequen e of the la k of additivity of the energy and is related to the inequivalen e between the mi ro anoni al and anoni al ensemble of statistial physi s. This was rst predi ted in the ontext of astrophysi s [15℄. For two dimensional ows, existen e of su h inequivalen e has been matemati ally proven for point vorti es [16℄ (without expli it omputation), and numeri ally observed in a parti ular situation of a QuasiGeostrophi (QG) model [17℄, and in a Monte Carlo study of points vorti es in a disk [18℄. One of the novelty 0 0

Solvable Phase Diagrams and Ensemble Inequivalence for Two-Dimensional and Geophysical Turbulent Flows

Using explicit analytical computations, generic occurrence of inequivalence between two or more statistical ensembles is obtained for a large class of equilibrium states of two-dimensional and geophysical turbulent flows. The occurrence of statistical ensemble inequivalence is shown to be related to previously observed phase transitions in the equilibrium flow topology. We find in these turbulent flow equilibria, two mechanisms for the appearance of ensemble equivalences, that were not observed in any physical systems before. These mechanisms are associated respectively with second-order azeotropy (simultaneous appearance of two second-order phase transitions), and with bicritical points (bifurcation from a first-order to two second-order phase transition lines). The important roles of domain geometry, of topography, and of a screening length scale (the Rossby radius of deformation) are discussed. It is found that decreasing the screening length scale (making interactions more local) surprisingly widens the range of parameters associated with ensemble inequivalence. These results are then generalized to a larger class of models, and applied to a complete description of an academic model for inertial oceanic circulation, the Fofonoff flow.

Bottom-trapped currents as statistical equilibrium states above topographic anomalies

Oceanic geostrophic turbulence is mostly forced at the surface, yet strong bottom-trapped flows are commonly observed along topographic anomalies. Here we consider the case of a freely evolving, initially surface-intensified velocity field above a topographic bump, and show that the self-organization into a bottom-trapped current can result from its turbulent dynamics. Using equilibrium statistical mechanics, we explain this phenomenon as the most probable outcome of turbulent stirring. We compute explicitly a class of solutions characterized by a linear relation between potential vorticity and streamfunction, and predict when the bottom intensification is expected. Using direct numerical simulations, we provide an illustration of this phenomenon that agrees qualitatively with theory, although the ergodicity hypothesis is not strictly fulfilled.

Oceanic Rings and Jets as Statistical Equilibrium States

AbstractEquilibrium statistical mechanics of two-dimensional flows provides an explanation and a prediction for the self-organization of large-scale coherent structures. This theory is applied in this paper to the description of oceanic rings and jets, in the framework of a 1.5-layer quasigeostrophic model. The theory predicts the spontaneous formation of regions where the potential vorticity is homogenized, with strong and localized jets at their interface. Mesoscale rings are shown to be close to a statistical equilibrium: the theory accounts for their shape, drift, and ubiquity in the ocean, independently of the underlying generation mechanism. At basin scale, inertial states presenting midbasin eastward jets (and then different from the classical Fofonoff solution) are described as marginally unstable states. In that case, considering a purely inertial limit is a first step toward more comprehensive out-of-equilibrium studies that would take into account other essential aspects, such as wind forcing.

Experimental observation of a strong mean flow induced by internal gravity waves

We report the experimental observation of a robust horizontal mean flow induced by internal gravity waves. A wave beam is forced at the lateral boundary of a tank filled with a linearly stratified fluid initially at rest. After a transient regime, a strong jet appears in the wave beam, with horizontal recirculations outside the wave beam. Using multiple scale analysis, we present a simple physical mechanism predicting the growth rate of the mean flow and its initial spatial structure. We find good agreement with experimental results. These results show that a mean flow with non-zero vertical vorticity can be generated by Reynolds stresses if the wave fulfils two conditions: (1) the wave amplitude must vary along its propagation direction, which is the case in the presence of viscosity; (2) the wave amplitude must vary in the lateral direction, which is the case when the wave generator is localized in space.

The catalytic role of the beta effect in barotropization processes

The vertical structure of freely evolving, continuously stratified, quasi-geo\-strophic flow is investigated. We predict the final state organization, and in particular its vertical structure, using statistical mechanics and these predictions are tested against numerical simulations. The key role played by conservation laws in each layer, including the fine-grained enstrophy, is discussed. In general, the conservation laws, and in particular that enstrophy is conserved layer-wise, prevent complete barotropization, i.e., the tendency to reach the gravest vertical mode. The peculiar role of the

Instabilities of Internal Gravity Wave Beams

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Topological origin of equatorial waves

-effect, i.e. of the existence of planetary vorticity gradients, is discussed. In particular, it is shown that increasing

Is Turbulent Mixing a Self-Convolution Process?

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