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Anisotropic diffusion and shear instabilities
S. Talon,J. -P. Zahn
Physics , 1996,
Abstract: We examine the role of anisotropic turbulence on the shear instabilities in a stratified flow. Such turbulence is expected to occur in the radiative interiors of stars, due to their differential rotation and their strong stratification, and the turbulent transport associated with it will be much stronger in the horizontal than in the vertical direction. It will thus weaken the restoring force which is caused by the gradient of mean molecular weight ($\mu$). We find that the critical shear which is able to overcome the $\mu$-gradient is substantially reduced by this anisotropic turbulence, and we derive an estimate for the resulting turbulent diffusivity in the vertical direction.
Shear turbulence beneath the solar tachocline
E. Schatzman,J. -P. Zahn,P. Morel
Physics , 2000,
Abstract: Helioseismic inversions of the Sun's internal angular velocity profile show that the rotation changes from differential in latitude in the convection zone to almost uniform in the radiative region below. The transition occurs in a thin layer, the tachocline, which is the seat of strong shear in the vertical direction. In this Note we examine whether this rotation profile can lead to shear turbulence at the top of the radiation zone. By using the standard solar model, we show that such turbulence can be generated only in a narrow region 0.695R_sun < r < 0.713R_sun at the equator and even in narrower layers at higher latitudes. We conclude that the turbulence generated by this vertical shear is unlikely to play a significant role in the transport of matter and angular momentum, and that other mechanisms must be invoked to achieve this.
The equilibrium tide in stars and giant planets: I - the coplanar case
F. Remus,S. Mathis,J. -P. Zahn
Physics , 2012, DOI: 10.1051/0004-6361/201118160
Abstract: Since 1995, more than 500 extrasolar planets have been discovered orbiting very close to their parent star, where they experience strong tidal interactions. Their orbital evolution depends on the physical mechanisms that cause tidal dissipation, and these are still not well understood. We refine the theory of the equilibrium tide in fluid bodies that are partly or entirely convective, to predict the dynamical evolution of the systems. In particular, we examine the validity of modeling the tidal dissipation by the quality factor Q, as is commonly done. We consider here the simplest case where the considered star or planet rotates uniformly, all spins are aligned, and the companion is reduced to a point-mass. The first manifestation of the tide is to distort the shape of the star or planet adiabatically along the line of centers. This generates the divergence-free velocity field of the adiabatic equilibrium tide which is decoupled from the dynamical tide. The tidal kinetic energy is dissipated into heat through turbulent friction, which is modeled here as an eddy-viscosity acting on the adiabatic tidal flow. This dissipation induces a second velocity field, the dissipative equilibrium tide, which is in quadrature with the exciting potential; it is responsible for the imaginary part of the disturbing function, which is implemented in the dynamical evolution equations, from which one derives characteristic evolution times. The rate at which the system evolves depends on the physical properties of tidal dissipation, and specifically on how the eddy viscosity varies with tidal frequency and on the thickness of the convective envelope for the fluid equilibrium tide. At low frequency, this tide retards by a constant time delay, whereas it lags by a constant angle when the tidal frequency exceeds the convective turnover rate.
Influence of the Tachocline on Solar Evolution
A. S. Brun,J. P. Zahn
Physics , 2000, DOI: 10.1111/j.1749-6632.2000.tb06167.x
Abstract: Recently helioseismic observations have revealed the presence of a shear layer at the base of the convective zone related to the transition from differential rotation in the convection zone to almost uniform rotation in the radiative interior, the tachocline. At present, this layer extends only over a few percent of the solar radius and no definitive explanations have been given for this thiness. Following Spiegel and Zahn (1992, Astron. Astrophys.), who invoke anisotropic turbulence to stop the spread of the tachocline deeper in the radiative zone as the Sun evolves, we give some justifications for their hypothesis by taking into account recent results on rotating shear instability (Richard and Zahn 1999, Astron. Astrophys.). We study the impact of the macroscopic motions present in this layer on the Sun's structure and evolution by introducing a macroscopic diffusivity $D_T$ in updated solar models. We find that a time dependent treatment of the tachocline significantly improves the agreement between computed and observed surface chemical species, such as the $^7$Li and modify the internal structure of the Sun (Brun, Turck-Chi\`eze and Zahn, 1999, in Astrophys. J.).
Tailoring tunnel magnetoresistance by ultrathin Cr and Co interlayers: A first-principles investigation of Fe/MgO/Fe junctions
P. Bose,P. Zahn,J. Henk,I. Mertig
Physics , 2010, DOI: 10.1103/PhysRevB.82.014412
Abstract: We report on systematic ab-initio investigations of Co and Cr interlayers embedded in Fe(001)/MgO/Fe(001) magnetic tunnel junctions, focusing on the changes of the electronic structure and the transport properties with interlayer thickness. The results of spin-dependent ballistic transport calculations reveal options to specifically manipulate the tunnel magnetoresistance ratio. The resistance area products and the tunnel magnetoresistance ratios show a monotonous trend with distinct oscillations as a function of the Cr thickness. These modulations are directly addressed and interpreted by means of magnetic structures in the Cr films and by complex band structure effects. The characteristics for embedded Co interlayers are considerably influenced by interface resonances which are analyzed by the local electronic structure.
Correlating transmission and local electronic structure in planar junctions: A tool for analyzing spin-dependent transport calculations
P. Bose,P. Zahn,I. Mertig,J. Henk
Physics , 2010, DOI: 10.1103/PhysRevB.83.174451
Abstract: We propose to correlate transmittance maps and spectral-density maps of planar junctions, in order to analyze quantitatively and in detail spin-dependent transport calculations. Since spectral-density maps can be resolved with respect to atom, angular momentum, and spin, the resulting correlation coefficients reveal unequivocally, e.g., which layers or which orbitals determine the tunnel conductances. Our method can be used for transport calculations within the Landauer-B\"uttiker formalism. Its properties and features will be discussed by means of a pure bcc Fe(001) lead as well as an extensively studied Fe(001)/MgO/Fe(001) planar tunnel junction.
Noctilucent clouds and the mesospheric water vapour: the past decade
U. von Zahn,U. Berger,J. Fiedler,P. Hartogh
Atmospheric Chemistry and Physics Discussions , 2004,
Abstract: The topic of this paper is the expected (from modelling) and observed sensitivity of the brightness β of noctilucent clouds (NLC) on the ambient water vapour mixing ratio f(H2O). Firstly, we show that state-of-the-art models of NLC layer formation predict that in the Arctic summer, a 10% increase of f(H2O) in the upper mesosphere should lead to a 22% increase in β. Secondly, we review observations of episodic changes in f(H2O) and those in β, the former being available since 1992, the latter since 1979. We also add a new series of observations of f(H2O) in the Arctic summer, performed at the ALOMAR observatory (69° N). Thirdly, we show that an increase in daily averaged f(H2O) observed in the Arctic summer since 1996, when introduced into the NLC models, comes close to explaining the observed increase in β. In contrast to this gratifying situation for the summer means of f(H2O) and β (the latter being available only in summer anyway), the behaviour of annual means of f(H2O) is quite different. Those indicate that since 1996 significant decreases of annually averaged upper mesospheric water vapour have occurred at low, mid, and high latitude which can not be used to explain the observed near-stability in NLC brightness over this time period. We close with comments on the very different character of decadal variations in NLC brightness and occurrence rate.
Macroscopic Processes in the Solar Interior
A. S. Brun,S. Turck-Chieze,J. P. Zahn
Physics , 1998,
Abstract: With the recent results of helioseismology aboard SOHO, solar models are more and more constrained (Brun, Turck-Chieze and Morel 1998 (astro-ph/9806272)). New physical processes, mainly connected to macroscopic motions, must be introduced to understand these new observations. In this poster, we present solar models including a turbulent pressure in the outer layers and mixing due to the tachocline (Spiegel and Zahn 1992). Our results lead us to conclude that: - Turbulent pressure improves the absolute value of the acoustic mode frequencies (~ 10 microHz at 4mHz), - Mixing in a tachocline thickness of 0.05 +/- 0.03 Ro (Corbard et al. 1997) looks promising.
Anelastic tidal dissipation in multi-layer planets
F. Remus,S. Mathis,J. -P. Zahn,V. Lainey
Physics , 2012, DOI: 10.1051/0004-6361/201118595
Abstract: Earth-like planets have viscoelastic mantles, whereas giant planets may have viscoelastic cores. The tidal dissipation of such solid regions, gravitationally perturbed by a companion body, highly depends on their rheology and on the tidal frequency. Therefore, modelling tidal interactions presents a high interest to provide constraints on planets' properties and to understand their history and their evolution, in our Solar System or in exoplanetary systems. We examine the equilibrium tide in the anelastic parts of a planet whatever the rheology, taking into account the presence of a fluid envelope of constant density. We show how to obtain the different Love numbers that describe its tidal deformation. Thus, we discuss how the tidal dissipation in solid parts depends on the planet's internal structure and rheology. Finally, we show how the results may be implemented to describe the dynamical evolution of planetary systems. The first manifestation of the tide is to distort the shape of the planet adiabatically along the line of centers. Then, the response potential of the body to the tidal potential defines the complex Love numbers whose real part corresponds to the purely adiabatic elastic deformation, while its imaginary part accounts for dissipation. This dissipation is responsible for the imaginary part of the disturbing function, which is implemented in the dynamical evolution equations, from which we derive the characteristic evolution times. The rate at which the system evolves depends on the physical properties of tidal dissipation, and specifically on how the shear modulus varies with tidal frequency, on the radius and also the rheological properties of the solid core. The quantification of the tidal dissipation in solid cores of giant planets reveals a possible high dissipation which may compete with dissipation in fluid layers.
Magnetic confinement of the solar tachocline: II. Coupling to a convection zone
A. Strugarek,A. S. Brun,J. -P. Zahn
Physics , 2011, DOI: 10.1051/0004-6361/201116518
Abstract: The reason for the observed thinness of the solar tachocline is still not well understood. One of the explanations that have been proposed is that a primordial magnetic field renders the rotation uniform in the radiation zone. We test here the validity of this magnetic scenario through 3D numerical MHD simulations that encompass both the radiation zone and the convection zone. The numerical simulations are performed with the anelastic spherical harmonics (ASH) code. The computational domain extends from $0.07\;R_\odot$ to $0.97\;R_\odot$. In the parameter regime we explored, a dipolar fossil field aligned with the rotation axis can not remain confined in the radiation zone. When the field lines are allowed to interact with turbulent unstationary convective motions at the base of the convection zone, 3D effects prevent the field confinement. In agreement with previous work, we find that a dipolar fossil field, even when it is initially buried deep inside the radiation zone, will spread into the convective zone. According to Ferraro's law of iso-rotation, it then imprints on the radiation zone the latitudinal differential rotation of the convection zone, which is not observed.
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