17 research outputs found
Large-to small-scale dynamo in domains of large aspect ratio: kinematic regime
The Sunâs magnetic field exhibits coherence in space and time on much larger scales than
the turbulent convection that ultimately powers the dynamo. In this work, we look for numerical
evidence of a large-scale magnetic field as the magnetic Reynolds number, Rm, is
increased. The investigation is based on the simulations of the induction equation in elongated
periodic boxes. The imposed flows considered are the standard ABC flow (named after
Arnold, Beltrami & Childress) with wavenumber ku = 1 (small-scale) and a modulated ABC
flow with wavenumbers ku = m, 1, 1 ± m, where m is the wavenumber corresponding to
the long-wavelength perturbation on the scale of the box. The critical magnetic Reynolds
number Rcrit
m decreases as the permitted scale separation in the system increases, such that
Rcrit
m â [Lx /Lz]
â1/2. The results show that the α-effect derived from the mean-field theory
ansatz is valid for a small range of Rm after which small scale dynamo instability occurs and the
mean-field approximation is no longer valid. The transition from large- to small-scale dynamo
is smooth and takes place in two stages: a fast transition into a predominantly small-scale
magnetic energy state and a slower transition into even smaller scales. In the range of Rm
considered, the most energetic Fourier component corresponding to the structure in the long
x-direction has twice the length-scale of the forcing scale. The long-wavelength perturbation
imposed on the ABC flow in the modulated case is not preserved in the eigenmodes of the
magnetic field
On the necessary conditions for bursts of convection within the rapidly rotating cylindrical annulus
Zonal flows are often found in rotating convective systems. Not only are
these jet-flows driven by the convection, they can also have a profound effect
on the nature of the convection. In this work the cylindrical annulus geometry
is exploited in order to perform nonlinear simulations seeking to produce
strong zonal flows and multiple jets. The parameter regime is extended to
Prandtl numbers that are not unity. Multiple jets are found to be spaced
according to a Rhines scaling based on the zonal flow speed, not the convective
velocity speed. Under certain conditions the nonlinear convection appears in
quasi-periodic bursts. A mean field stability analysis is performed around a
basic state containing both the zonal flow and the mean temperature gradient
found from the nonlinear simulations. The convective growth rates are found to
fluctuate with both of these mean quantities suggesting that both are necessary
in order for the bursting phenomenon to occur
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
Solenoidal force balances in numerical dynamos
Numerical simulations of the geodynamo (and other planetary dynamos) have
made significant progress in recent years. As computing power has advanced,
some new models claim to be ever more appropriate for understanding Earth's
core dynamics. One measure of the success of such models is the ability to
replicate the expected balance between forces operating within the core;
Coriolis and Lorentz forces are predicted to be most important. The picture is
complicated for an incompressible flow by the existence of the pressure
gradient force which renders the gradient parts of all other forces dynamically
unimportant. This can confuse the situation, especially when the scale
dependence of forces are considered. In this work we investigate force balances
through the alternative approach of eliminating gradient parts of each force to
form `solenoidal force balances'. We perform a lengthscale dependent analysis
for several spherical simulations and find that removal of gradient parts
offers an alternative picture of the force balance compared to looking at
traditional forces alone. Solenoidal force balances provide some agreement with
the results of previous studies but also significant differences. They offer a
cleaner overall picture of the dynamics and introduce differences at smaller
scales. This has implications for geodynamo models purporting to have reached
Earth-like regimes: in order to achieve a meaningful comparison of forces, only
the solenoidal part of forces should be considered.Comment: 12 pages, 4 figures, 1 tabl
Rapidly rotating plane layer convection with zonal flow
The onset of convection in a rapidly rotating layer in which a thermal wind
is present is studied. Diffusive effects are included. The main motivation is
from convection in planetary interiors, where thermal winds are expected due to
temperature variations on the core-mantle boundary. The system admits both
convective instability and baroclinic instability. We find a smooth transition
between the two types of modes, and investigate where the transition region
between the two types of instability occurs in parameter space. The thermal
wind helps to destabilise the convective modes. Baroclinic instability can
occur when the applied vertical temperature gradient is stable, and the
critical Rayleigh number is then negative. Long wavelength modes are the first
to become unstable. Asymptotic analysis is possible for the transition region
and also for long wavelength instabilities, and the results agree well with our
numerical solutions. We also investigate how the instabilities in this system
relate to the classical baroclinic instability in the Eady problem. We conclude
by noting that baroclinic instabilities in the Earth's core arising from
heterogeneity in the lower mantle could possibly drive a dynamo even if the
Earth's core were stably stratified and so not convecting.Comment: 20 pages, 7 figure
The transition to Earth-like torsional oscillations in magnetoconvection simulations
Evidence for torsional oscillations (TOs) operating within the Earth's fluid outer core has been found in the secular variation of the geomagnetic field. These waves arise via disturbances to the predominant (magnetostrophic) force balance believed to exist in the core. The coupling of the core and mantle allow TOs to affect the length-of-day of the Earth via angular momentum conservation. Encouraged by previous work, where we were able to observe TOs in geodynamo simulations, we perform 3-D magnetoconvection simulations in a spherical shell in order to reach more Earth-like parameter regimes that proved hitherto elusive. At large Ekman numbers we find that TOs can be present but are typically only a small fraction of the overall dynamics and are often driven by Reynolds forcing at various locations throughout the domain. However, as the Ekman number is reduced to more Earth-like values, TOs become more apparent and can make up the dominant portion of the short timescale flow. This coincides with a transition to regimes where excitation is found only at the tangent cylinder, is delivered by the Lorentz force and gives rise to a periodic Earth-like wave pattern, approximately operating on a 4 to 5 year timescale. The core travel times of our waves also become independent of rotation at low Ekman number with many converging to Earth-like values of around 4 years
Destruction of large-scale magnetic field in non-linear simulations of the shear dynamo
The Sun's magnetic field exhibits coherence in space and time on much larger scales than the turbulent convection that ultimately powers the dynamo. In the past the α-effect (mean-field) concept has been used to model the solar cycle, but recent work has cast doubt on the validity of the mean-field ansatz under solar conditions. This indicates that one should seek an alternative mechanism for generating large-scale structure. One possibility is the recently proposed âshear dynamoâ mechanism where large-scale magnetic fields are generated in the presence of a simple shear. Further investigation of this proposition is required, however, because work has been focused on the linear regime with a uniform shear profile thus far. In this paper we report results of the extension of the original shear dynamo model into the nonlinear regime. We find that whilst large-scale structure can initially persist into the saturated regime, in several of our simulations it is destroyed via large increase in kinetic energy. This result casts doubt on the ability of the simple uniform shear dynamo mechanism to act as an alternative to the α-effect in solar conditions.This work was supported by the Science and Technology Facilities Council, grant ST/L000636/1.This is the author accepted manuscript. The final version is available from Oxford University Press via http://dx.doi.org/10.1093/mnras/stw49