Weakly non-Boussinesq convection in a gaseous spherical shell

We examine the dynamics associated with weakly compressible convection in a spherical shell by running 3D direct numerical simulations using the Boussinesq formalism [1]. Motivated by problems in astrophysics, we assume the existence of a finite adiabatic temperature gradient $\nabla T_{\rm{ad}}$ and use mixed boundary conditions for the temperature with fixed flux at the inner boundary and fixed temperature at the outer boundary. This setup is intrinsically more asymmetric than the more standard case of Rayleigh-B\'{e}nard convection in liquids between parallel plates with fixed temperature boundary conditions. Conditions where there is substantial asymmetry can cause a dramatic change in the nature of convection and we demonstrate that this is the case here. The flows can become pressure- rather than buoyancy- dominated leading to anomalous heat transport by upflows. Counter-intuitively, the background temperature gradient $\nabla\bar{T}$ can develop a subadiabatic layer (where $\boldsymbol{g}\cdot\nabla\bar{T}<\boldsymbol{g}\cdot\nabla T_{\rm{ad}}$, where $\boldsymbol{g}$ is gravity) although convection remains vigorous at every point across the shell. This indicates a high degree of non-locality.Comment: 19 figure

Convective overshooting and penetration in a Boussinesq spherical shell

We study the dynamics associated with the extension of turbulent convective motions from a convection zone (CZ) into a stable region (RZ) that lies below the latter. For that purpose, we have run a series of three-dimensional direct numerical simulations solving the Navier-Stokes equations under the Boussinesq approximation in a spherical shell geometry. We observe that the overshooting of the turbulent motions into the stably stratified region depends on three different parameters: the relative stability of the RZ, the transition width between the two, and the intensity of the turbulence. In the cases studied, these motions manage to partially alter the thermal stratification and induce thermal mixing, but not so efficiently as to extend the nominal CZ further down into the stable region. We find that the kinetic energy below the convection zone can be modeled by a half-Gaussian profile whose amplitude and width can be predicted a priori for all of our simulations. We examine different dynamical lengthscales related to the depth of the extension of the motions into the RZ, and we find that they all scale remarkably well with a lengthscale that stems from a simple energetic argument. We discuss the implications of our findings for 1D stellar evolution calculations

On the dynamical interaction between overshooting convection and an underlying dipole magnetic field -- I. The non-dynamo regime

Motivated by the dynamics in the deep interiors of many stars, we study the interaction between overshooting convection and the large-scale poloidal fields residing in radiative zones. We have run a suite of 3D Boussinesq numerical calculations in a spherical shell that consists of a convection zone with an underlying stable region that initially compactly contains a dipole field. By varying the strength of the convective driving, we find that, in the less turbulent regime, convection acts as turbulent diffusion that removes the field faster than solely molecular diffusion would do. However, in the more turbulent regime, turbulent pumping becomes more efficient and partially counteracts turbulent diffusion, leading to a local accumulation of the field below the overshoot region. These simulations suggest that dipole fields might be confined in underlying stable regions by highly turbulent convective motions at stellar parameters. The confinement is of large-scale field in an average sense and we show that it is reasonably modeled by mean-field ideas. Our findings are particularly interesting for certain models of the Sun, which require a large-scale, poloidal magnetic field to be confined in the solar radiative zone in order to explain simultaneously the uniform rotation of the latter and the thinness of the solar tachocline.Comment: Accepted to MNRAS, 14 figure

Systematic Bias in Helioseismic Measurements of Meridional Circulation Arising from Nonlocal Averaging Kernels

Meridional circulation in the solar convection zone plays a profound role in regulating the interior dynamics of the Sun and its magnetism. While it is well accepted that meridional flows move from the equator towards the poles at the Sun's surface, helioseismic observations have yet to provide a definitive answer for the depth at which those flows return to the equator, or the number of circulation cells in depth. In this work, we investigate whether the discrepancies regarding the nature of the return flow are intrinsic to how helioseismic observations are made. We examine the seismic signature of possible meridional flow profiles by convolving time-distance averaging kernels with the mean flows obtained from 3-D hydrodynamic simulations of the solar convection zone. At mid and high latitudes, we find that weak flow structures in the deeper regions of the convection zone can be strongly obscured by signal from the much stronger surface flows. This contamination is the result of extended side lobes in the averaging kernels and generates a spurious equatorward signal of 2--3 m s$^{-1}$ at those latitudes, and at $\approx 70~\mathrm{Mm}$ depth. At low latitudes, however, the flows in the simulations tend to be stronger and multiple cells across the shell depth can produce a sufficiently strong seismic signal to survive the convolution process. The signal associated with the deep equatorward return flow in the Sun is expected to be weak and in the same sense as the contamination from the surface. Hence, the return flow needs to exceed $\sim 2$--$3~ \mathrm{m~s^{-1}}$ in magnitude for reported detections to be considered significant.Comment: Submitted to AAS Journal

Dynamics of weakly non-Boussinesq convection, convective overshooting and magnetic field confinement in a spherical shell

This doctoral work is motivated by the Sun and solar-type stars, which consist of an unstable convection zone (CZ) that lies on top of a stably stratified radiative zone (RZ). The dynamics occurring at the CZ-RZ interface are not well understood, and yet they are known to play a significant role in processes such as transport of chemical species, angular momentum and magnetic fields. To shed some new light on this complicated problem, we have compartmentalized this work into three main chapters. In the first part, in order to mimic stellar-like conditions, we study convection in a weakly non-Boussinesq gaseous spherical shell in the low-Prandtl number regime assuming a constant adiabatic temperature gradient and employing fixed flux at the inner boundary. We find the remarkable emergence of a subadiabatic layer within the domain for sufficiently turbulent flows enhanced by large variations in the superadiabaticity across the shell. However, convection remains vigorous everywhere across the shell thus indicating that it is a highly non-local process. In the second part, we further extend our study to include a stable region below the convective zone and we investigate the dynamics of overshooting/penetrative convection. We observe that the overshooting of the turbulent motions into the RZ depends on three different parameters: the relative stability of the stable zone, the transition width between the two, and the intensity of the turbulence. We find that, in the parameter regime studied, these overshooting motions manage to partially alter the thermal stratification, but not so efficiently as to create a fully mixed adiabatic region. We have built a model of these processes that could be useful for stellar evolution codes. In the third and final part, we also add a poloidal dipole magnetic field initially contained in the stable zone and study its interaction with the turbulent motions. Our numerical results are categorized into non-dynamo and dynamo cases. In the non-dynamo cases, the field diffuses outward, and its field lines open up and penetrate in the CZ. At the same time, a large fraction of its energy is removed due to the turbulent diffusion by the convective motions. In the dynamo cases, the field starts diffusing outward but its interaction with the turbulent motions leads to a small-scale essentially kinematic dynamo within the CZ and the overshoot region. In both of these cases, we find that the dipole field cannot remain confined in the RZ by the turbulent motions

Αριθμητικές Μέθοδοι στις Παραβολικές Μερικές Διαφορικές Εξισώσεις

81 σ.Μελέτη της εξίσωσης της θερμότητας στη μία και στις δύο διαστάσεις και εκτιμήσεις σφαλμάτων που προκύπτουν από τις αριθμητικές προσεγγιστικές λύσεις της εξίσωσης της θερμότητας. Βασικά θεωρήματα και ορισμοί για τους χώρους Hilbert. Μελέτη παραβολικών εξισώσεων. Χρήση μεθόδου πεπερασμένων στοιχείων (Galerkin) για την προς τα πίσω μέθοδο Euler και για τη μέθοδο Crank-Nicolson, μέθοδος πεπερασμένων διαφορών και χωροχρονική μέθοδος πεπερασμένων στοιχείων. Υπολογιστικά παραδείγματα και εκτίμηση σφαλμάτων στις L2 και H1 νόρμες με χρήση αλγορίθμου στο MATLAB(μονοδιάστατη περίπτωση) και στο λογισμικό FreeFem++(δισδιάστατη περίπτωση). Γραφήματα της θερμότητας για διαφορετικά χωροχρονικά βήματα.Study of the heat equation in one and two dimensions and error estimates resulting from the approximate numerical solution of the heat equation. Basic definitions and theorems for Hilbert spaces. Study of the parabolic equations. Use of finite elements method (Galerkin) for the backward Euler method and the Crank-Nicolson method, finite differences and space-time finite elements method. Computational examples and error estimates in L2 and H1 norms using MATLAB (1D case) and software FreeFem + + (2D case). Graphs of heat for different space and time steps.Λυδία Γ. Κορρ

Weakly non-Boussinesq convection in a gaseous spherical shell.

We examine the dynamics associated with weakly compressible convection in a spherical shell by running 3D direct numerical simulations using the Boussinesq formalism [Spiegel and Veronis, Astrophys. J. 131, 442 (1960)AJLEEY0004-637X10.1086/146849]. Motivated by problems in astrophysics, we assume the existence of a finite adiabatic temperature gradient ∇T_{ad} and use mixed boundary conditions for the temperature with fixed flux at the inner boundary and fixed temperature at the outer boundary. This setup is intrinsically more asymmetric than the more standard case of Rayleigh-Bénard convection in liquids between parallel plates with fixed temperature boundary conditions. Conditions where there is substantial asymmetry can cause a dramatic change in the nature of convection and we demonstrate that this is the case here. The flows can become pressure- rather than buoyancy-dominated, leading to anomalous heat transport by upflows. Counterintuitively, the background temperature gradient ∇T[over ¯] can develop a subadiabatic layer (where g·∇T[over ¯

Can we reveal the core-chemical composition of ultra-massive white dwarfs through their magnetic fields?

Ultra-massive white dwarfs (1.05M⊙ ≲ MWD) are particularly interesting objects that allow us to study extreme astrophysical phenomena such as type Ia supernovae explosions and merger events. Traditionally, ultra-massive white dwarfs are thought to harbour oxygen-neon (ONe) cores. However, recent theoretical studies and new observations suggest that some ultra-massive white dwarfs could harbour carbon-oxygen (CO) cores. Although several studies have attempted to elucidate the core composition of ultra-massive white dwarfs, to date, it has not been possible to distinguish them through their observed properties. Here, we present a new method for revealing the core-chemical composition in ultra-massive white dwarfs that is based on the study of magnetic fields generated by convective mixing induced by the crystallization process. ONe white dwarfs crystallize at higher luminosities than their CO counterparts. Therefore, the study of magnetic ultra-massive white dwarfs in the particular domain where ONe cores have reached the crystallization conditions but CO cores have not, may provide valuable support to their ONe core-chemical composition, since ONe white dwarfs would display signs of magnetic fields and CO would not. We apply our method to eight white dwarfs with magnetic field measurements and we suggest that these stars are candidate ONe white dwarfs.Fil: Camisassa, María Eugenia. State University of Colorado at Boulder; Estados Unidos. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Raddi, Roberto. Universidad Politécnica de Catalunya; EspañaFil: Althaus, Leandro Gabriel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Astrofísica La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Astronómicas y Geofísicas. Instituto de Astrofísica La Plata; Argentina. Universidad Nacional de La Plata. Facultad de Ciencias Astronómicas y Geofísicas; ArgentinaFil: Isern, Jordi. Institute of Space Sciences ; España. Institut d’Estudis Espacials de Catalunya; España. Consejo Superior de Investigaciones Científicas; EspañaFil: Rebassa Mansergas, Alberto. Universidad Politécnica de Catalunya; España. Institut d’Estudis Espacials de Catalunya; EspañaFil: Torres, Santiago. Institut d’Estudis Espacials de Catalunya; España. Universidad Politécnica de Catalunya; EspañaFil: Corsico, Alejandro Hugo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Astrofísica La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Astronómicas y Geofísicas. Instituto de Astrofísica La Plata; Argentina. Universidad Nacional de La Plata. Facultad de Ciencias Astronómicas y Geofísicas; ArgentinaFil: Korre, Lydia. University of Colorado; Estados Unido