What sets the magnetic field strength and cycle period in solar-type stars?

Two fundamental properties of stellar magnetic fields have been determined by observations for solar-like stars with different Rossby numbers (Ro), namely, the magnetic field strength and the magnetic cycle period. The field strength exhibits two regimes: 1) for fast rotation it is independent of Ro, 2) for slow rotation it decays with Ro following a power law. For the magnetic cycle period two regimes of activity, the active and inactive branches, also have been identified. For both of them, the longer the rotation period, the longer the activity cycle. Using global dynamo simulations of solar like stars with Rossby numbers between ~0.4 and ~2, this paper explores the relevance of rotational shear layers in determining these observational properties. Our results, consistent with non-linear alpha^2-Omega dynamos, show that the total magnetic field strength is independent of the rotation period. Yet at surface levels, the origin of the magnetic field is determined by Ro. While for Ro<1 it is generated in the convection zone, for Ro>1 strong toroidal fields are generated at the tachocline and rapidly emerge towards the surface. In agreement with the observations, the magnetic cycle period increases with the rotational period. However, a bifurcation is observed for Ro~1, separating a regime where oscillatory dynamos operate mainly in the convection zone, from the regime where the tachocline has a predominant role. In the latter the cycles are believed to result from the periodic energy exchange between the dynamo and the magneto-shear instabilities developing in the tachocline and the radiative interior.Comment: 43 pages, 14 figures, accepted for publication in The Astrophysical Journa

Multi-scale waves in sound-proof global simulations with EULAG

EULAG is a computational model for simulating flows across a wide range of scales and physical scenarios. A standard option employs an anelastic approximation to capture nonhydrostatic effects and simultaneously filter sound waves from the solution. In this study, we examine a localized gravity wave packet generated by instabilities in Held-Suarez climates. Although still simplified versus the Earth’s atmosphere, a rich set of planetary wave instabilities and ensuing radiated gravity waves can arise. Wave packets are observed that have lifetimes ≤ 2 days, are negligibly impacted by Coriolis force, and do not show the rotational effects of differential jet advection typical of inertia-gravity waves. Linear modal analysis shows that wavelength, period, and phase speed fit the dispersion equation to within a mean difference of ∼ 4%, suggesting an excellent fit. However, the group velocities match poorly even though a propagation of uncertainty analysis indicates that they should be predicted as well as the phase velocities. Theoretical arguments suggest the discrepancy is due to nonlinearity — a strong southerly flow leads to a critical surface forming to the southwest of the wave packet that prevents the expected propagation

Regime of Validity of Sound-Proof Atmospheric Flow Models

Ogura and Phillips (1962) derived their original anelastic model through systematic formal asymptotics using the flow Mach number as the expansion parameter. To arrive at a reduced model which would simultaneously represent internal gravity waves and the effects of advection, they had to adopt a distinguished limit stating that the dimensionless stability of the background state be of the order of the Mach number squared. For typical flow Mach numbers of M = 1/30 this amounts to total variations of potential temperature across the troposphere of less than one Kelvin, i.e., to unrealistically weak stratication. Various generalizations of Ogura and Phillips' anelastic model have been proposed to remedy this issue, e.g., by Dutton & Fichtl (1969), and Lipps & Hemler (1982). Following the same goals, but a somewhat different route of argumentation, Durran proposed the pseudoincompressible model in 1989. The present paper provides a scale analysis showing that the regime of validity of two of these extended models covers stratification strengths of order of the Mach number to the power 2/3, which corresponds to realistic variations of potential temperature across the pressure scale height of about 30 K

A finite-volume module for simulating global all-scale atmospheric flows

This paper was accepted for publication in the Journal of Computational Physics and the definitive published version is available at http://dx.doi.org/10.1016/j.jcp.2016.03.015.The paper documents the development of a global nonhydrostatic finite-volume module designed to enhance an established spectral-transform based numerical weather prediction (NWP) model. The module adheres to NWP standards, with formulation of the governing equations based on the classical meteorological latitude-longitude spherical framework. In the horizontal, a bespoke unstructured mesh with finite-volumes built about the reduced Gaussian grid of the existing NWP model circumvents the notorious stiffness in the polar regions of the spherical framework. All dependent variables are co-located, accommodating both spectral-transform and grid-point solutions at the same physical locations. In the vertical, a uniform finite-difference discretisation facilitates the solution of intricate elliptic problems in thin spherical shells, while the pliancy of the physical vertical coordinate is delegated to generalised continuous transformations between computational and physical space. The newly developed module assumes the compressible Euler equations as default, but includes reduced soundproof PDEs as an option. Furthermore, it employs semi-implicit forward-in-time integrators of the governing PDE systems, akin to but more general than those used in the NWP model. The module shares the equal regions parallelisation scheme with the NWP model, with multiple layers of parallelism hybridising MPI tasks and OpenMP threads. The efficacy of the developed nonhydrostatic module is illustrated with benchmarks of idealised global weather

Global simulations of Tayler instability in stellar interiors: a long-time multi-stage evolution of the magnetic field

Magnetic fields have been observed in massive Ap/Bp stars and presumably are also present in the radiative zone of solar-like stars. Yet, to date there is no clear understanding of the dynamics of the magnetic field in stably stratified layers. A purely toroidal magnetic field configuration is known to be unstable, developing mainly non-axisymmetric modes. Rotation and a small poloidal field component may lead to a stable configuration. Here we perform global MHD simulations with the EULAG-MHD code to explore the evolution of a toroidal magnetic field located in a layer whose stratification resembles the solar tachocline. Our numerical experiments allow us to explore the initial unstable phase as well as the long-term evolution of the magnetic field. During the first Alfven cycles, we observe the development of the Tayler instability with the prominent longitudinal wavenumber, $m=1$. Rotation decreases the growth rate of the instability, and eventually suppresses it. However, after a stable phase, sudden energy surges lead to the development of higher order modes even for fast rotation. These modes extract energy from the initial toroidal field. Nevertheless, our results show that sufficiently fast rotation leads to a lower saturation energy of the unstable modes, resulting in a magnetic topology with only a small fraction of poloidal field which remains steady for several hundreds of Alfven travel times. At this stage, the system becomes turbulent and the field is prone to turbulent diffusion. The final toroidal-poloidal configuration of the magnetic field may represent an important aspect of the field generation and evolution in stably-stratified layers.Comment: 15 pages, 16 figures, submitted to MNRA