Effect of Rossby and Alfv\'{e}n waves on the dynamics of the tachocline

To understand magnetic diffusion, momentum transport, and mixing in the interior of the sun, we consider an idealized model of the tachocline, namely magnetohydrodynamics (MHD) turbulence on a $\beta$ plane subject to a large scale shear (provided by the latitudinal differential rotation). This model enables us to self-consistently derive the influence of shear, Rossby and Alfv\'{e}n waves on the transport properties of turbulence. In the strong magnetic field regime, we find that the turbulent viscosity and diffusivity are reduced by magnetic fields only, similarly to the two-dimensional MHD case (without Rossby waves). In the weak magnetic field regime, we find a crossover scale ($L\_R$) from a Alfv\'{e}n dominated regime (on small scales) to a Rossby dominated regime (on large scales). For parameter values typical of the tachocline, $L\_R$ is larger that the solar radius so that Rossby waves are unlikely to play an important role in the transport of magnetic field and angular momentum. This is mainly due to the enhancement of magnetic back-reaction by shearing which efficiently generates small scales, thus strong currents

Influence of turbulence on the dynamo threshold

We use direct and stochastic numerical simulations of the magnetohydrodynamic equations to explore the influence of turbulence on the dynamo threshold. In the spirit of the Kraichnan-Kazantsev model, we model the turbulence by a noise, with given amplitude, injection scale and correlation time. The addition of a stochastic noise to the mean velocity significantly alters the dynamo threshold. When the noise is at small (resp. large) scale, the dynamo threshold is decreased (resp. increased). For a large scale noise, a finite correlation time reinforces this effect

Global ocean modeling and state estimation in support of climate research

During the last decade it has become obvious that the ocean circulation shows vigorous variability on a wide range of time and space scales and that the concept of a "sluggish" and slowly varying circulation is rather elusive. Increasing emphasis has to be put, therefore, on observing the rapidly changing ocean state on time scales ranging from weeks to decades and beyond, and on understanding the ocean's response to changing atmospheric forcing conditions. As outlined in various strategy and implementation documents (e.g., the implementation plans of WOCE, AMS, CLIVAR, and GODAE) a combination of the global ocean data sets with a state-of-the-art numerical circulation model is required to interpret the various diverse data sets and to produce the best possible estimates of the time-varying ocean circulation. The mechanism of ocean state estimates is a powerful tool for such a "synthesis" of observations, obtained on very complex space-time pattern, into one dynamically consistent picture of the global time-evolving ocean circulation. This process has much in common with ongoing analysis and reanalysis activities in the atmospheric community. But because the ocean is, and will remain for the foreseeable future, substantially under-sampled, the burden put on the modeling and estimations components is substantially larger than in the atmosphere. Moreover, the smaller dynamical eddy scales which need to be properly parameterized or resolved in ocean model simulations, put stringent requirements on computational resources for ongoing and participated climate research

Analytical theory of forced rotating sheared turbulence: The perpendicular case

Rotation and shear flows are ubiquitous features of many astrophysical and geophysical bodies. To understand their origin and effect on turbulent transport in these systems, we consider a forced turbulence and investigate the combined effect of rotation and shear flow on the turbulence properties. Specifically, we study how rotation and flow shear influence the generation of shear flow (e.g., the direction of energy cascade), turbulence level, transport of particles and momentum, and the anisotropy in these quantities. In all the cases considered, turbulence amplitude is always quenched due to strong shear (ξ=νky2/A⪡1, where A is the shearing rate, ν is the molecular viscosity, and ky is a characteristic wave number of small-scale turbulence), with stronger reduction in the direction of the shear than those in the perpendicular directions. Specifically, in the large rotation limit (Ω⪢A), they scale as A−1 and A−1|ln ξ|, respectively, while in the weak rotation limit (Ω⪡A), they scale as A−1 and A−2/3, respectively. Thus, flow shear always leads to weak turbulence with an effectively stronger turbulence in the plane perpendicular to shear than in the shear direction, regardless of rotation rate. The anisotropy in turbulence amplitude is, however, weaker by a factor of ξ1/3|ln ξ| (∝A−1/3|ln ξ|) in the rapid rotation limit (Ω⪢A) than that in the weak rotation limit (Ω⪡A) since rotation favors almost-isotropic turbulence. Compared to turbulence amplitude, particle transport is found to crucially depend on whether rotation is stronger or weaker than flow shear. When rotation is stronger than flow shear (Ω⪢A), the transport is inhibited by inertial waves, being quenched inversely proportional to the rotation rate (i.e., ∝Ω−1) while in the opposite case, it is reduced by shearing as A−1. Furthermore, the anisotropy is found to be very weak in the strong rotation limit (by a factor of 2) while significant in the strong shear limit. The turbulent viscosity is found to be negative with inverse cascade of energy as long as rotation is sufficiently strong compared to flow shear (Ω⪢A) while positive in the opposite limit of weak rotation (Ω⪡A). Even if the eddy viscosity is negative for strong rotation (Ω⪢A), flow shear, which transfers energy to small scales, has an interesting effect by slowing down the rate of inverse cascade with the value of negative eddy viscosity decreasing as |νT|∝A−2 for strong shear. Furthermore, the interaction between the shear and the rotation is shown to give rise to a nondiffusive flux of angular momentum (Λ effect), even in the absence of external sources of anisotropy. This effect provides a mechanism for the existence of shearing structures in astrophysical and geophysical systems

Dynamics and thermodynamics of axisymmetric flows: I. Theory

We develop new variational principles to study stability and equilibrium of axisymmetric flows. We show that there is an infinite number of steady state solutions. We show that these steady states maximize a (non-universal) $H$-function. We derive relaxation equations which can be used as numerical algorithm to construct stable stationary solutions of axisymmetric flows. In a second part, we develop a thermodynamical approach to the equilibrium states at some fixed coarse-grained scale. We show that the resulting distribution can be divided in a universal part coming from the conservation of robust invariants and one non-universal determined by the initial conditions through the fragile invariants (for freely evolving systems) or by a prior distribution encoding non-ideal effects such as viscosity, small-scale forcing and dissipation (for forced systems). Finally, we derive a parameterization of inviscid mixing to describe the dynamics of the system at the coarse-grained scale

Dynamical model for spindown of solar-type stars

After their formation, stars slow down their rotation rates by the removal of angular momentum from their surfaces, e.g., via stellar winds. Explaining how this rotation of solar-type stars evolves in time is currently an interesting but difficult problem in astrophysics. Despite the complexity of the processes involved, a traditional model, where the removal of angular momentum by magnetic fields is prescribed, has provided a useful framework to understand observational relations between stellar rotation, age, and magnetic field strength. Here, for the first time, a spindown model is proposed where loss of angular momentum by magnetic fields evolves dynamically, instead of being prescibed kinematically. To this end, we evolve the stellar rotation and magnetic field simultaneously over stellar evolution time by extending our previous work on a dynamo model which incorporates nonlinear feedback mechanisms on rotation and magnetic fields. We show that our extended model reproduces key observations and is capable of explaining the presence of the two branches of (fast and slow rotating) stars which have different relations between rotation rate Ω versus time (age), magnetic field strength $| B|$ versus rotation rate, and frequency of magnetic field ${\omega }_{\mathrm{cyc}}$ versus rotation rate. For fast rotating stars we find that: (i) there is an exponential spindown ${\rm{\Omega }}\propto {e}^{-1.35t}$, with t measured in Gyr; (ii) magnetic activity saturates for higher rotation rate; (iii) ${\omega }_{\mathrm{cyc}}\propto {{\rm{\Omega }}}^{0.83}$. For slow rotating stars we find: (i) a power-law spindown ${\rm{\Omega }}\propto {t}^{-0.52}$; (ii) that magnetic activity scales roughly linearly with rotation rate; (iii) ${\omega }_{\mathrm{cyc}}\propto {{\rm{\Omega }}}^{1.16}$. The results obtained from our investigations are in good agreement with observations. The Vaughan–Preston gap is consistently explained in our model by the shortest spindown timescale in this transition from fast to slow rotators. Our results highlight the importance of self-regulation of magnetic fields and rotation by direct and indirect interactions involving nonlinear feedback in stellar evolution

The Cultural Project : Formal Chronological Modelling of the Early and Middle Neolithic Sequence in Lower Alsace

Starting from questions about the nature of cultural diversity, this paper examines the pace and tempo of change and the relative importance of continuity and discontinuity. To unravel the cultural project of the past, we apply chronological modelling of radiocarbon dates within a Bayesian statistical framework, to interrogate the Neolithic cultural sequence in Lower Alsace, in the upper Rhine valley, in broad terms from the later sixth to the end of the fifth millennium cal BC. Detailed formal estimates are provided for the long succession of cultural groups, from the early Neolithic Linear Pottery culture (LBK) to the Bischheim Occidental du Rhin Supérieur (BORS) groups at the end of the Middle Neolithic, using seriation and typology of pottery as the starting point in modelling. The rate of ceramic change, as well as frequent shifts in the nature, location and density of settlements, are documented in detail, down to lifetime and generational timescales. This reveals a Neolithic world in Lower Alsace busy with comings and goings, tinkerings and adjustments, and relocations and realignments. A significant hiatus is identified between the end of the LBK and the start of the Hinkelstein group, in the early part of the fifth millennium cal BC. On the basis of modelling of existing dates for other parts of the Rhineland, this appears to be a wider phenomenon, and possible explanations are discussed; full reoccupation of the landscape is only seen in the Grossgartach phase. Radical shifts are also proposed at the end of the Middle Neolithic

Détection des radionucléides artificiels dans les produits laitiers après l’accident de Tchernobyl

Dès les premiers jours du mois de mai 1986, le contrôle du niveau de radioactivité artificielle dans les denrées alimentaires a été intensifié et de nombreuses mesures d’activité ont été réalisées dans les laboratoires des services vétérinaires. Une évaluation des activités en iode a été faite à partir de 6 prélèvements de lait fournis par chaque département. Les activités moyennes en iode 131 sont restées inférieures à 30 Bq/kg dans toute la moitié Ouest de la France. Des niveaux plus élevés ont été détectés dans l’Est. Les valeurs maximales enregistrées ont été de 700 Bq/kg dans des échantillons du Nord-Est de la France, au cours de la première semaine du mois de mai 1986. Les valeurs les plus élevées en césium 137 et 134 ont été mises en évidence dans le Sud-Est où des pluies diluviennes sont survenues au début du mois de mai. Ces précipitations ont entraîné des dépôts d’isotopes radioactifs plus importants dans ces régions. Cependant, une très grande hétérogénéité des activités a été observée dans des zones très proches. Les valeurs moyennes ont toujours été très inférieures aux niveaux de tolérance maximale fixées par la CEE. Aucun produit animal ou d’origine animale n’a été retiré à la consommation

Assimilation of Altimetric Data into an Eddy-Permitting Model of the North Atlantic

This paper shows that the mean flow of an eddy-permitting model can be altered by assimilation of surface height variability, providing that information about the mean sea surface is included, using an adaption of a statistical–dynamical method devised by Oschlies and Willebrand. We show that for a restricted depth range (about 1000 m), dynamical knowledge can make up for the null space present in surface data whose temporal extent may be too short to distinguish between vertical modes. The lack of an accurate geoid has meant that most assimilation methods, while representing variability well, have been unable to modify the mean flow to any extent. However, we show that by including several approximate forms for the mean sea surface, the mean interior flow in the upper kilometer can be rapidly adjusted towards reality by the assimilation, with the location of major current systems moved by hundreds of kilometers