Convection patterns in a spherical fluid shell

Feudel, Fred; Bergemann, Kay; Tuckerman, Laurette S.; Egbers, Christoph; Futterer, Birgit; Gellert, M.; Hollerbach, Rainer

doi:10.1103/physreve.83.046304

Cited by 36 publications

(27 citation statements)

References 23 publications

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“…This observation along with the fact that the convective regions of descending motion are defined by both the vertices of a triangle in the polar regions (the case for the tetrahedral pattern) and those of a square in the equatorial regions (the case for the cubic pattern) leads us consider a mixed-mode interaction between the = 3 and an = 4 modes for an initial condition. Previous studies of mixed-mode patterns bifurcating from spherically symmetric ones have been predicted in Busse and Riahi (1988) and numerically observed in Feudel et al (2011). However, these studied reported a seven cell pattern resulting from an interaction of a = 4 and = 5 modes.…”

Section: A New Convection Mode: Five Cellsmentioning

confidence: 85%

On the sensitivity of 3-D thermal convection codes to numerical discretization: a model intercomparison

et al. 2014

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Abstract. Fully 3-D numerical simulations of thermal convection in a spherical shell have become a standard for studying the dynamics of pattern formation and its stability under perturbations to various parameter values. The question arises as to how the discretization of the governing equations affects the outcome and thus any physical interpretation. This work demonstrates the impact of numerical discretization on the observed patterns, the value at which symmetry is broken, and how stability and stationary behavior is dependent upon it. Motivated by numerical simulations of convection in the Earth's mantle, we consider isoviscous Rayleigh-Bénard convection at infinite Prandtl number, where the aspect ratio between the inner and outer shell is 0.55. We show that the subtleties involved in developing mantle convection models are considerably more delicate than has been previously appreciated, due to the rich dynamical behavior of the system. Two codes with different numerical discretization schemes -an established, communitydeveloped, and benchmarked finite-element code (CitcomS) and a novel spectral method that combines Chebyshev polynomials with radial basis functions (RBFs) -are compared. A full numerical study is investigated for the following three cases. The first case is based on the cubic (or octahedral) initial condition (spherical harmonics of degree = 4). How this pattern varies to perturbations in the initial condition and Rayleigh number is studied. The second case investigates the stability of the dodecahedral (or icosahedral) initial condition (spherical harmonics of degree = 6). Although both methods first converge to the same pattern, this structure is ultimately unstable and systematically degenerates to cubic or tetrahedral symmetries, depending on the code used. Lastly, a new steady-state pattern is presented as a combination of third-and fourth-order spherical harmonics leading to a fivecell or hexahedral pattern and stable up to 70 times the critical Rayleigh number. This pattern can provide the basis for a new accuracy benchmark for 3-D spherical mantle convection codes.

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Section: A New Convection Mode: Five Cellsmentioning

confidence: 85%

On the sensitivity of 3-D thermal convection codes to numerical discretization: a model intercomparison

et al. 2014

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“…All those patterns of convection are comparable to that in the case of absence of rotation and are characterized by symmetry-breaking bifurcations as described in Feudel et al (2011). So we have in the middle and right half of the illustration in Fig.…”

Section: Numerical Simulation Of Traveling Waves In Lower Rotating Spmentioning

confidence: 84%

Traveling waves in low and intermediate rotating spherical shell convection

Futterer¹,

Koch

Egbers

2011

J. Phys.: Conf. Ser.

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Abstract. The spherical shell convection in the lower rotational regime is discussed with numerical simulation by the use of a pseudo-spectral code and experimental observation by the use of a microgravity experiment in self-gravitating force field. While a low Coriolis force produces traveling waves of cubic, five-fold and frozen tetrahedral symmetry with a prograde drift, in the transition zone to chaos an axisymmetric flow is visible. The chaotic fluid flow does neither show a specific drift nor a dominating pattern of convection. Numerical and experimental data are in a good agreement.

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“…The Newton solver uses Stokes preconditioning and the matrix-free biconjugate gradient stabilized (BiCGSTAB) algorithm [35] to solve the linear systems. This approach of using a standard time-stepping code and adapting it to carry out Newton's method was originally developed by Mamun and Tuckerman [36] and has been successfully applied to a variety of fluid problems [22,25,37]. See these references for more a detailed exposition.…”

Section: Governing Equations and Numerical Methodsmentioning

confidence: 99%

“…Path-following techniques have already been applied to nonmagnetic spherical shell convection in different parameter regimes, see e.g. [22][23][24][25][26].…”

Section: Introductionmentioning

confidence: 99%

Hysteresis of dynamos in rotating spherical shell convection

et al. 2017

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Bifurcations of dynamos in rotating and buoyancy-driven spherical Rayleigh-Bénard convection in an electrically conducting fluid are investigated numerically. Both nonmagnetic and magnetic solution branches comprised of rotating waves (RWs) are traced by path-following techniques, and their bifurcations and interconnections for different Ekman numbers are determined. In particular the question of whether the dynamo branches bifurcate super-or subcritically and whether a direct link to the primary pure convective states exists is answered.

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Convection patterns in a spherical fluid shell

Cited by 36 publications

References 23 publications

On the sensitivity of 3-D thermal convection codes to numerical discretization: a model intercomparison

On the sensitivity of 3-D thermal convection codes to numerical discretization: a model intercomparison

Traveling waves in low and intermediate rotating spherical shell convection

Hysteresis of dynamos in rotating spherical shell convection

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