Atmospheric response to a mid-latitude sea surface temperature (SST) front is studied, while emphasizing low-frequency modes induced by the presence of such a front. An idealized atmospheric quasi-geostrophic (QG) model is forced by the SST field of an idealized oceanic QG model. First, the equilibria of the oceanic model and the associated SST fronts are computed. Next, these equilibria are used to force the atmospheric model and compute its equilibria when varying the strength of the oceanic forcing.Low-frequency modes of atmospheric variability are identified and associated with successive Hopf bifurcations. The origin of these Hopf bifurcations is studied in detail, and connected to barotropic instability. Finally, a link is established between the model's time integrations and the previously obtained equilibria.

The goal of this project was to obtain a predictive understanding of a major component of the climate system's interdecadal variability: the oceans' wind-driven circulation. To do so, we developed and applied advanced computational and statistical methods to the problem of climate variability and climate change. The methodology was developed first for models of intermediate complexity, such as the quasi-geostrophic and the primitive equations, which describe the wind-driven, near-surface flow in mid-latitude ocean basins. Our computational work consisted in developing efficient multi-level methods to simulate this flow and study its dependence on physically relevant parameters. Our oceanographic and climate work consisted in applying these methods to study the bifurcations in the wind-driven circulation and their relevance to the flows observed at present and those that might occur in a warmer climate. Both aspects of the work are crucial for the efficient treatment of large-scale, eddy-resolving numerical simulations of the oceans and an increased understanding and better prediction of climate change. Considerable progress has been achieved in understanding ocean-atmosphere interaction in the mid-latitudes. An important by-product of this research is a novel approach to explaining the North Atlantic Oscillation.

The goal of our work is to study the most consolidated items of semantic memory in normal subjects and in patients with Alzheimer's disease (AD). Patients and method. The first test is based on automatic recall of didactic knowledge. This test is made of 250 automatic verbal expressions exploring general knowledge. It as been validated according to age and cultural levels in 219 normal subjects (20-90 years old). Another simplified test called EVA including only 50 of the 250 previously chosen items was also used. The EVA scores found in a normal population have been classified by centilages according to age and cultural levels. The EVA was also tested in 20 patients with AD and the results compared with MMSE and "Pyramids and Palm Trees Test" (semantic memory testing). Results. The results reveal that the scores observed with the first test in a normal population with comparable cultural levels are correlated with age. EVA test scores found in control subjects show that the median value, for a same age group, is positively correlated with cultural levels. In patients with AD, scores for EVA test and MMSE are associated, the low results being linked to the severity of dementia. In addition, scores for EVA test and "Pyramids and Palm Trees Test" are also significantly correlated. Seven patients with mild dementia (MMSE > 20) have abnormal scores for the "Pyramids and Palm Trees Test", Conclusion. Our study confirms that changes linked to aging do not involve all aspects of cognition. The most consolidated items of semantic memory assessed by EVA test seem to resist at the beginning of AD but later decline similarly to the other items of semantic memory. Normal results for EVA tests do not imply that semantic memory is not affected in the early phases of AD. We propose this new test which assesses the semantic memory stock without involving an active process of recuperation. This test is not suitable for an early diagnosis of AD but could help to evaluate the severity of the disease during the evolution.

The goal of our work is to study the most consolidated items of semantic memory in normal subjects and in patients with Alzheimer's disease (AD).The first test is based on automatic recall of didactic knowledge. This test is made of 250 automatic verbal expressions exploring general knowledge. It as been validated according to age and cultural levels in 219 normal subjects (20-90 years old). Another simplified test called EVA including only 50 of the 250 previously chosen items was also used. The EVA scores found in a normal population have been classified by centilages according to age and cultural levels. The EVA was also tested in 20 patients with AD and the results compared with MMSE and "Pyramids and Palm Trees Test" (semantic memory testing).The results reveal that the scores observed with the first test in a normal population with comparable cultural levels are correlated with age. EVA test scores found in control subjects show that the median value, for a same age group, is positively correlated with cultural levels. In patients with AD, scores for EVA test and MMSE are associated, the low results being linked to the severity of dementia. In addition, scores for EVA test and "Pyramids and Palm Trees Test" are also significantly correlated. Seven patients with mild dementia (MMSE>20) have abnormal scores for the "Pyramids and Palm Trees Test".Our study confirms that changes linked to aging do not involve all aspects of cognition. The most consolidated items of semantic memory assessed by EVA test seem to resist at the beginning of AD but later decline similarly to the other items of semantic memory. Normal results for EVA tests do not imply that semantic memory is not affected in the early phases of AD. We propose this new test which assesses the semantic memory stock without involving an active process of recuperation. This test is not suitable for an early diagnosis of AD but could help to evaluate the severity of the disease during the evolution.

In this article, we present a family of models which approximate the full primitive equations (PEs) of the ocean, with temperature and salinity, as introduced in [9]. We consider asymptotic expansions of the PEs to all orders with respect to the aspect ratio delta. At first order, we recover the well-known barotropic quasi-geostrophic (QG) equations of the ocean. At higher orders, we obtain simple linear models that share the same mathematical structure but different right-hand sides. From the computational point of view, there are two advantages. Firstly, all the higher-order expansions are linear so that they are easy to implement. Secondly, the same numerical code can be used to compute all of them. From the physical viewpoint, we expect that higher-order corrections to the first-order barotropic QG equations will capture the vertical dynamics and the thermiodynamics correctly. We will address these delicate physical issues as well as the convergence of the asymptotics in a forthcoming work.

The low-frequency dynamics of the double-gyre wind-driven circulation in large midlatitude oceanic basins is investigated. It is shown that for quasigeostrophic models linear (Rayleigh) friction is necessary to obtain realistic recirculation gyres and elongated jet streams with small meridional-to-zonal aspect ratio. It is also found that the use of either no-slip or free-slip boundary conditions does not change the drastic effects of bottom drag on the large scales. These long oceanic jets are alternatively destabilized and restabilized through successive (subcritical) supercritical symmetry-breaking bifurcations that are linked to the (non) existence of stationary Rossby waves. These waves are strongly localized along the oceanic front and are thus hardly affected by the basin geometry. Numerical and analytical results show that these waves are “quantized” with respect to the length of the jet, and an explicit dispersion relation is given. Numerical computations of branches of steady states, together with linear and nonlinear analysis, indicate that two classes of regimes characterize the low-frequency dynamics of the flow. The first class corresponds to supercritical regimes, which are associated with oceanic jets that have been destabilized by undamped stationary Rossby waves. In particular, these regimes allow the formation of gyre modes responsible for low-frequency relaxation oscillations of the jet. The second class corresponds to subcritical regimes, which are either quiescent or dominated by high-frequency instabilities and are characterized by jets that do not allow the formation of both stationary Rossby waves and gyre modes. Each of these regimes is characterized by typical spatial and time scales that are both quantized. The number n of “bumps” of the jet, which is related to the zonal wavenumber of the stationary Rossby waves, is used to distinguish between these regimes either in their supercritical or subcritical phase. For instance, the supercritical n = 2 regime is associated with a class of interdecadal gyre modes that extend up to 3000 km in the zonal direction. The quantization of the low-frequency dynamics and the existence of these regimes are also found to survive severe modifications of the basin geometry. These quantized regimes suggest that the low-frequency dynamics in turbulent regimes is likely to be autosimilar to the low-frequency dynamics found in a weakly nonlinear “ground” regime corresponding to n = 0.

The wind-driven double-gyre circulation in a rectangular basin goes through several dynamical regimes as the amount of lateral friction is decreased. This paper studies the transition to irregular flow in the double-gyre circulation by applying dynamical systems methodology to a quasigeostrophic, equivalent-barotropic model with a 10-km resolution. The origin of the irregularities, in space and time, is the occurrence of homoclinic bifurcations that involve phase-space behavior far from stationary solutions. The connection between these homoclinic bifurcations and earlier transitions, which occur at larger lateral friction, is explained. The earlier transitions, such as pitchfork and asymmetric Hopf bifurcation, only involve the nonlinear saturation of linear instabilities, while the homoclinic bifurcations are associated with genuinely nonlinear behavior. The sequence of bifurcations—pitchfork, Hopf, and homoclinic—is independent of the lateral friction and may be described as the unfolding of a singularity that occurs in the frictionless, Hamiltonian limit of the governing equations. Two distinct chaotic regimes are identified: Lorenz chaos at relatively large lateral friction versus Shilnikov chaos at relatively small lateral friction. Both types of homoclinic bifurcations induce chaotic behavior of the recirculation gyres that is dominated by relaxation oscillations with a well-defined period. The relevance of these results to the mid-latitude oceans’ observed low-frequency variations is discussed. A previously documented 7-year peak in observed North-Atlantic variability is shown to exist across a hierarchy of models that share the gyre modes and homoclinic bifurcations discussed herein.

In this article, we study the baroclinic flow in the primitive equations (PEs) of the ocean, which are known to be the fundamental equations of the ocean, [4]–[8]. We prove that the magnitude of the baroclinic flow in the L2-norm is of order O(δ), where δ is the aspect ratio of the ocean. Some numerical simulations of the PEs of the ocean consistent with these estimates are also presented.

This study examines the flow induced in a highly idealized atmospheric model by an east-west-oriented oceanic thermal front. The model has a linear marine boundary layer coupled to a quasigeostrophic, equivalent-barotropic free atmosphere. The vertical velocity at the top of the boundary layer drives the flow in the free atmosphere and produces an eastward jet, parallel to the oceanic front's isotherms. A large gyre develops on either side of this jet, cyclonic to the north and anticyclonic to the south of it. As the jet intensifies during spinup from rest, it becomes unstable. The most unstable wave has a length of about 500 km, it evolves into a meander, and eddies detach from the eastern edge of each gyre.The dependence of the atmospheric dynamics on the strength T-* of the oceanic front is studied. The Gulf Stream and Kuroshio fronts correspond roughly, in the scaling used here, to T (*)congruent to 7degreesC. For weak fronts, T-* less than or equal to 4degreesC, the circulation is steady and exhibits two large, antisymmetric gyres separated by a westerly zonal jet. As the front strengthens, 4, T-*< 5, the solution undergoes Hopf bifurcation to become periodic in time, with a period of 30 days, and spatially asymmetric. The bifurcation is due to the westerly jet's barotropic instability, which has a symmetric spatial pattern. The addition of this pattern to the antisymmetric mean results in the overall asymmetry of the full solution. The spatial scale and amplitude of the symmetric, internally generated, and antisymmetric, forced mode increase with the strength T-* of the oceanic front. For T-* >= 5 degrees C, the solution becomes chaotic, but a dominant period still stands out above the broadband noise. This dominant period increases with T-* overall, but the increase is not monotonic.The oceanic front's intensity dictates the mean speed of the atmospheric jet. Two energy regimes are obtained. 1) In the low-energy regime, the SST front, and hence the atmospheric jet, are weak; in this regime, small meanders develop along the jet axis, and the dominant period is about 25 days. 2) In the high-energy regime, the SST front and the jet are strong; in it, large meanders and eddies develop along the jet, and the dominant oscillation has a period of about 70 days. The physical nature of the two types of oscillations is discussed, as are possible transitions between them when T-* changes on very long time scales. The results are placed in the context of previous theories of ocean front effects on atmospheric flows, in which baroclinic phenomena are dominant.

The temporal variability of the midlatitude double-gyre wind-driven ocean circulation is studied in a three-layer quasi-geostrophic model over a broad range in parameter space. Four different types of flow regimes are found, each characterized by a specific time-mean state and spatio-temporal variability. As the lateral friction is decreased, these regimes are encountered in the following order: the viscous antisymmetric regime, the asymmetric regime, the quasi-homoclinic regime and the inertial antisymmetric regime. The variability in the viscous and the inertial antisymmetric regimes (at high and low lateral friction, respectively) is mainly caused by Rossby basin modes. Lowfrequency variability, i.e. on interannual to decadal time-scales, is present in the asymmetric and quasi-homoclinic regime and can be related to relaxation oscillations originating from low-frequency gyre modes. The focus of this paper is on the mechanisms of the transitions between the different regimes. The transition from the viscous antisymmetric regime to the asymmetric regime occurs through a symmetry-breaking pitchfork bifurcation. There are strong indications that the quasihomoclinic regime is introduced through the existence of a homoclinic orbit. The transition to the inertial antisymmetric regime is due to the symmetrization of the time-mean state zonal velocity field through rectification effects.

Successive bifurcations-from steady states through periodic to aperiodic solutions-are studied in a shallow-water, reduced-gravity, 2 1/2-layer model of the midlatitude ocean circulation subject to time-independent wind stress. The bifurcation sequence is studied in detail for a rectangular basin with an idealized spatial pattern of wind stress. The aperiodic behavior is studied also in a North Atlantic-shaped basin with realistic continental contours. The bifurcation sequence in the rectangular basin is studied in Part I, the present article. It follows essentially the one reported for single-layer quasigeostrophic and 1 1/2-layer shallow-water models. As the intensity of the north south-symmetric, zonal wind stress is increased, the nearly symmetric double-gyre circulation is destabilized through a perturbed pitchfork bifurcation. The low-stress steady solution, with its nearly equal subtropical and subpolar gyres, is replaced by an approximately mirror-symmetric pair of stable equilibria. The two solution branches so obtained are named after the inertial recirculation cell that is stronger, subtropical or subpolar, respectively. This perturbed pitchfork bifurcation and the associated Hopf bifurcations are robust to changes in the interface friction between the two active layers and the thickness H-2 of the lower active layer. They persist in the presence of asymmetries in the wind stress and of changes in the model's spatial resolution and finite-difference scheme. Time-dependent model behavior in the rectangular basin, as well as in the more realistic, North Atlantic-shaped one, is studied in Part II.

In this article, we present an equivalent barotropic-baroclinic formulation of the primitive equations (PEs) of the ocean given in [J.L. Lions, R. Temam and S. Wang (1992). On the equations of large-scale ocean. Nonlinearity, 5, 1007-1053.]. From the numerical point of view, the main advantage of this new formulation is that the incompressibility condition appearing in the PEs in [J.L. Lions, R. Temam and S. Wang (1992). On the equations of large-scale ocean. Nonlinearity, 5, 1007-1053.] is automatically satisfied without being explicitly imposed at any stage. Some numerical schemes for the time integration of the PEs are presented and their numerical stability is discussed. These schemes are reminiscent of other schemes that have been used for other equations in particular the Navier-Stokes equations. We end the article by presenting numerical simulations of a wind-driven ocean model using the new formulation. More extensive numerical simulations and physical aspects will be presented elsewhere.

The time-dependent wind-driven ocean circulation is investigated for both a rectangular and a North Atlantic shaped basin. Multiple steady states in a 2 1/2-layer shallow-water model and their dependence on various parameters and other model properties were studied in Part I for the rectangular basin. As the wind stress on the rectangular basin is increased, each steady-state branch is destabilized by a Hopf bifurcation. The periodic solutions that arise off the subpolar branch have a robust subannual periodicity of 4-5 months. For the subtropical branch, the period varies between sub- and interannual, depending on the inverse Froude number F-2 defined with respect to the lower active layer's thickness H-2. As F-2 is lowered, the perturbed-symmetric branch is destabilized baroclinically, before the perturbed pitchfork bifurcation examined in detail in Part I occurs. Transition to aperiodic behavior arises at first by a homoclinic explosion off the isolated branch that exists only for sufficiently high wind stress. Subsequent global and local bifurcations all involve the subpolar branch, which alone exists in the limit of vanishing wind stress. Purely subpolar solutions vary on an interannual scale, whereas combined subpolar and subtropical solutions exhibit complex transitions affected by a second, subpolar homoclinic orbit. In the latter case, the timescale of the variability is interdecadal. The role of the global bifurcations in the interdecadal variability is investigated. Numerical simulations were carried out for the North Atlantic with earth topography-5 minute (ETOPO-5) coastline geometry in the presence of realistic, as well as idealized, wind stress forcing. The simulations exhibit a realistic Gulf Stream at 20-km resolution and with realistic wind stress. The variability at 12-km resolution exhibits spectral peaks at 6 months, 16 months, and 6-7 years. The subannual mode is strongest in the subtropical gyre; the interannual modes are both strongest in the subpolar gyre.

In this article, we conduct a rigorous stability and bifurcation analysis for a highly idealized model of planetary-scale atmospheric and oceanic flows. The model is governed by the two-dimensional, quasi-geostrophic equation for the conservation of vorticity in an east-west oriented, periodic channel. The main result is the existence of Hopf bifurcation of the flow as the Reynolds number crosses a critical value.The key idea in proving this result is translating the eigenvalue problem into a difference equation and treating the latter by continued-fraction methods. Numerical results are obtained by using a finite-difference scheme with high spatial resolution and these results agree closely with the theoretical predictions. The spatio-temporal structure of the limit cycle corresponds to a wave that propagates slowly westward and is symmetric about the midaxis of the channel. For plausible paramater values that correspond to midlatitude atmospheric flows, the period of this wave is 20 - 25 days.

The difficulty to recall proper nouns is often something elderly people complain about. Thus, we tried to build and standardize a tool that could allow a quantified estimation of the naming and recognition abilities about famous people faces, specifying the part of gender, age and cultural level for each kind of test. The performances of 542 subjects divided in 3 age brackets and 3 academic knowledge levels were analysed. To carry out the test material, the artistic team of the Grevin Museum (Paris) was called upon. Their work offers a homogeneous way to shape famous people faces. One same person thus photographed 75 characters from different social categories with the same conditions of light, during only one day. The results of the study show that men perform better than women as concerns naming task, but that there's no difference between genders as concerns recognition task. Recognition performances are significantly better whatever the age, the gender and the cultural level may be. Generally, performances are all the more better since subjects are younger and have a higher cultural level. Our study then confirms the fact that normal aging goes hand in hand with rising difficulties to name faces. Moreover, results tend to show that recognition of faces remains better preserved and that the greater disability to recall a name is linked to difficulties in lexical accessing.

In idealized models that aim to understand the temporal variability of the wind-driven ocean circulation, low-frequency instabilities associated with so-called oscillatory gyre modes have been found. For the double-gyre case, the spectral origin of these modes as well as the physical mechanism of the instability is explained. In a barotropic quasigeostrophic model, the low-frequency modes arise spontaneously from the merging between two nonoscillatory eigenmodes. Of the latter two, one is called here the P-mode and is responsible for the existence of multiple steady states. The other is called the L-mode and it controls the intensity of the gyres. This merging turns out to be robust over a hierarchy of models and can even be found in a low-order truncated quasigeostrophic model. The latter model is used to determine the physical mechanism of the instability. The low-frequency oscillation results from the conjugate effects of shear- and symmetry-breaking instabilities and is free of Rossby wave dynamics.

By applying the dynamical cluster algorithm to large-scale circulation patterns at vari- ous tropospheric levels (Z 700, Z500, and SLP (sea-level pressure)), we obtain the so-called weather regimes (WRs). WRs are the cluster central patterns; there is no subjectivity at all involved in the pro- cedure. A red noise test allows one to select the best number of clusters at each level. A comparison is performed between the different level classifications, and highly significant correlations are found. While previous attempts to classify daily circulations in a fully objective way were concerned with mid-tropospheric levels and could not go further back than 50 yr, here we classify 120 yr of SLP pat- terns. We arrive at the important conclusion that the same 5 WRs are found for the 3 periods 1880-1918, 1919-1957 and 1958-1997. The linkage between these WRs and the local tangible weather is then investigated for both temperatures and precipitation. It is found that the instanta- neous departure of local weather from average climate is highly correlated with the WRs, making this approach a challenging and coherent description of local climates. The atmosphere does not merely evolve around its mean state, but instead spends more time around a few peculiar (large-scale) states with specific consequences for local weather. As a result, the WRs may provide a reliable (and more- over fully objective) framework for building downscaling algorithms appropriate for local climate change studies.

We extract coherent and robust oscillations at the intraseasonal time scale using multichannel singular spectrum analysis (MSSA). Three daily fields are compared, namely sea-level pressure (SLP) and geopotential heights at 500 and 700 hPa (Z500 and Z700). The data set extends from 1958 to 1997 and covers the same North Atlantic-European domain. Three Oscillations stand out with periods of 30-35, 65-70 and 120-130 d respectively. A comparison shows that the same period oscillations at different levels are highly correlated. Moreover, it is shown that these modes are phase-locked and thus should come out from a single limit cycle. When these oscillations are compared with the succession of weather regimes (WRs), it can be shown that WR occurrences are indeed strongly influenced by particular phases of the 30-35 and 65-70 d modes, Transition from one WR to another is also shown to be favored by the life cycle of the previous modes. For instance, zonal regimes are followed preferably by blocking ones, Thus, regime transitions are indeed not random but are somehow steered by the dynamical behavior of a low-dimensional atmospheric attractor. We then explore the links between the intraseasonal modes and the local temperatures over France and Western Europe as well as precipitations over France. Once again, we conclude that bursts of low-frequency oscillations, such as the ones detected, significantly influence local surface weather conditions.

We study here the finite element approximation of the vector Laplace-Beltrami Equation on the sphere \(S^2\). Because of the lack of a smooth parametrization of the whole sphere (the so-called “poles problem”), we construct a finite element basis using two different coordinate systems, thus avoiding the introduction of artificial poles. One of the difficulties when discretizing the Laplace operator on the sphere, is then to recover the optimal order error. This is achieved here by a suitable perturbation of the vector field basis, locally, near the matching region of the coordinate systems.