2,691 research outputs found
The dynamics and excitation of torsional waves in geodynamo simulations
The predominant force balance in rapidly rotating planetary cores is between Coriolis, pressure, buoyancy and Lorentz forces. This magnetostrophic balance leads to a Taylor state where the spatially averaged azimuthal Lorentz force is compelled to vanish on cylinders aligned with the rotation axis. Any deviation from this state leads to a torsional oscillation, signatures of which have been observed in the Earth's secular variation and are thought to influence length of day variations via angular momentum conservation. In order to investigate the dynamics of torsional oscillations (TOs), we perform several 3-D dynamo simulations in a spherical shell. We find TOs, identified by their propagation at the correct AlfvĂ©n speed, in many of our simulations. We find that the frequency, location and direction of propagation of the waves are influenced by the choice of parameters. Torsional waves are observed within the tangent cylinder and also have the ability to pass through it. Several of our simulations display waves with core traveltimes of 4â6âyr. We calculate the driving terms for these waves and find that both the Reynolds force and ageostrophic convection acting through the Lorentz force are important in driving TOs
The Nonlinear Evolution of Instabilities Driven by Magnetic Buoyancy: A New Mechanism for the Formation of Coherent Magnetic Structures
Motivated by the problem of the formation of active regions from a
deep-seated solar magnetic field, we consider the nonlinear three-dimensional
evolution of magnetic buoyancy instabilities resulting from a smoothly
stratified horizontal magnetic field. By exploring the case for which the
instability is continuously driven we have identified a new mechanism for the
formation of concentrations of magnetic flux.Comment: Published in ApJL. Version with colour figure
Transition to chaos and modal structure of magnetized Taylor-Couette flow
Taylor-Couette flow is often used as a simplified model for complex rotating
flows in the interior of stars and accretion disks. The flow dynamics in these
objects is influenced by magnetic fields. For example, quasi-Keplerian flows in
Taylor-Couette geometry become unstable to a travelling or standing wave in an
external magnetic field if the fluid is conducting; there is an instability
even when the flow is hydrodynamically stable. This magnetorotational
instability leads to the development of chaotic states and, eventually,
turbulence, when the cylinder rotation is sufficiently fast. The transition to
turbulence in this flow can be complex, with the coexistence of parameter
regions with spatio-temporal chaos and regions with quasi-periodic behaviour,
involving one or two additional modulating frequencies. Although the unstable
modes of a periodic flow can be identified with Floquet analysis, here we adopt
a more flexible equation-free data-driven approach. We analyse the data from
the transition to chaos in the magnetized Taylor-Couette flow and identify the
flow structures related to the modulating frequencies with Dynamic Mode
Decomposition; this method is based on approximating nonlinear dynamics with a
linear infinite-dimensional Koopman operator. With the use of these structures,
one can construct a nonlinear reduced model for the transition
The magnetic non-hydrostatic shallow-water model
Funding: DGD would like to thank the Leverhulme Trust for support received during a Research Fellowship. SMT was supported by funding from the European Research Council (ERC) under the EU's Horizon 2020 research and innovation programme (grant agreement D5S-DLV-786780).We consider the dynamics of a set of reduced equations describing the evolution of a magnetised, rotating stably stratified fluid layer, atop a stagnant dense, perfectly conducting layer. We consider two closely related models. In the first, the layer has, above it, relatively light fluid where the magnetic pressure is much larger than the gas pressure, and the magnetic field is largely force-free. In the second model, the magnetic field is constrained to lie within the dynamical layer by the implementation of a model diffusion operator for the magnetic field. The model derivation proceeds by assuming that the horizontal velocity and the horizontal magnetic field are independent of the vertical coordinate, whilst the vertical components in the layer have a linear dependence on height. The full system comprises evolution equations for the magnetic field, horizontal velocity and height field together with a linear elliptic equation for the vertically integrated non-hydrostatic pressure. In the magneto-hydrostatic limit, these equations simplify to equations of shallow-water type. Numerical solutions for both models are provided for the fiducial case of a Gaussian vortex interacting with a magnetic field. The solutions are shown to differ negligibly. We investigate how the interaction of the vortex changes in response to the magnetic Reynolds number Rm, the Rossby deformation radius LD, and a Coriolis buoyancy frequency ratio f/N measuring the significance of non-hydrostatic effects. The magneto-hydrostatic limit corresponds to f/Nâ0.Publisher PDFPeer reviewe
On Predicting the Solar Cycle using Mean-Field Models
We discuss the difficulties of predicting the solar cycle using mean-field
models. Here we argue that these difficulties arise owing to the significant
modulation of the solar activity cycle, and that this modulation arises owing
to either stochastic or deterministic processes. We analyse the implications
for predictability in both of these situations by considering two separate
solar dynamo models. The first model represents a stochastically-perturbed flux
transport dynamo. Here even very weak stochastic perturbations can give rise to
significant modulation in the activity cycle. This modulation leads to a loss
of predictability. In the second model, we neglect stochastic effects and
assume that generation of magnetic field in the Sun can be described by a fully
deterministic nonlinear mean-field model -- this is a best case scenario for
prediction. We designate the output from this deterministic model (with
parameters chosen to produce chaotically modulated cycles) as a target
timeseries that subsequent deterministic mean-field models are required to
predict. Long-term prediction is impossible even if a model that is correct in
all details is utilised in the prediction. Furthermore, we show that even
short-term prediction is impossible if there is a small discrepancy in the
input parameters from the fiducial model. This is the case even if the
predicting model has been tuned to reproduce the output of previous cycles.
Given the inherent uncertainties in determining the transport coefficients and
nonlinear responses for mean-field models, we argue that this makes predicting
the solar cycle using the output from such models impossible.Comment: 22 Pages, 5 Figures, Preprint accepted for publication in Ap
Convective dynamo action in a spherical shell: symmetries and modulation
International audienceWe consider dynamo action driven by three-dimensional rotating anelastic convection in a spherical shell. Motivated by the behaviour of the solar dynamo, we examine the interaction of hydromagnetic modes with different symmetries and demonstrate how complicated interactions between convection, differential rotation and magnetic fields may lead to modulation of the basic cycle. For some parameters, Type 1 modulation occurs by the transfer of energy between modes of different symmetries with little change in the overall amplitude; for other parameters, the modulation is of Type 2, where the amplitude is significantly affected (leading to grand minima in activity) without significant changes in symmetry. Most importantly, we identify the presence of 'supermodulation' in the solutions, where the activity switches chaotically between Type 1 and Type 2 modulation; this is believed to be an important process in solar activity
The electromotive force in multi-scale flows at high magnetic Reynolds number
Recent advances in dynamo theory have been made by examining the competition between small and large-scale dynamos at high magnetic Reynolds number Rm. Small-scale dynamos rely on the presence of chaotic stretching whilst the generation of large-scale fields occurs in flows lacking reflectional symmetry via a systematic electromotive force (emf). In this paper we discuss how the statistics of the emf (at high Rm) depend on the properties of the multi-scale velocity that is generating it. In particular, we determine that different scales of flow have different contributions to the statistics of the emf, with smaller-scales contributing to the mean without increasing the variance. Moreover we determine when scales in such a flow act independently in their contribution to the emf. We further examine the role of large-scale shear in modifying the emf. We conjecture that the distribution of the emf, and not simply the mean, largely determines the dominant scale of the magnetic field generated by the flow
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