80 research outputs found
Chaotic magnetic field reversals in turbulent dynamos
We present direct numerical simulations of reversals of the magnetic field
generated by swirling flows in a spherical domain. In agreement with a recent
model, we observe that coupling dipolar and quadrupolar magnetic modes by an
asymmetric forcing of the flow generates field reversals. In addition, we show
that this mechanism strongly depends on the value of the magnetic Prandtl
number.Comment: 4 pages, 5 figure
Dipolar dynamos in stratified systems
Observations of low-mass stars reveal a variety of magnetic field topologies
ranging from large-scale, axial dipoles to more complex magnetic fields. At the
same time, three-dimensional spherical simulations of convectively driven
dynamos reproduce a similar diversity, which is commonly obtained either with
Boussinesq models or with more realistic models based on the anelastic
approximation, which take into account the variation of the density with depth
throughout the convection zone. Nevertheless, a conclusion from different
anelastic studies is that dipolar solutions seem more difficult to obtain as
soon as substantial stratifications are considered. In this paper, we aim at
clarifying this point by investigating in more detail the influence of the
density stratification on dipolar dynamos. To that end, we rely on a systematic
parameter study that allows us to clearly follow the evolution of the stability
domain of the dipolar branch as the density stratification is increased. The
impact of the density stratification both on the dynamo onset and the dipole
collapse is discussed and compared to previous Boussinesq results. Furthermore,
our study indicates that the loss of the dipolar branch does not ensue from a
specific modification of the dynamo mechanisms related to the background
stratification, but could instead result from a bias as our observations
naturally favour a certain domain in the parameter space characterized by
moderate values of the Ekman number, owing to current computational
limitations. Moreover, we also show that the critical magnetic Reynolds number
of the dipolar branch is scarcely modified by the increase of the density
stratification, which provides an important insight into the global
understanding of the impact of the density stratification on the stability
domain of the dipolar dynamo branch
Topology and field strength in spherical, anelastic dynamo simulations
Numerical modelling of convection driven dynamos in the Boussinesq
approximation revealed fundamental characteristics of the dynamo-generated
magnetic fields and the fluid flow. Because these results were obtained for an
incompressible fluid, their validity for gas planets and stars remains to be
assessed. A common approach is to take some density stratification into account
with the so-called anelastic approximation. The validity of previous results
obtained in the Boussinesq approximation is tested for anelastic models. We
point out and explain specific differences between both types of models, in
particular with respect to the field geometry and the field strength, but we
also compare scaling laws for the velocity amplitude, the magnetic dissipation
time, and the convective heat flux. Our investigation is based on a systematic
parameter study of spherical dynamo models in the anelastic approximation. We
make use of a recently developed numerical solver and provide results for the
test cases of the anelastic dynamo benchmark. The dichotomy of dipolar and
multipolar dynamos identified in Boussinesq simulations is also present in our
sample of anelastic models. Dipolar models require that the typical length
scale of convection is an order of magnitude larger than the Rossby radius.
However, the distinction between both classes of models is somewhat less
explicit than in previous studies. This is mainly due to two reasons: we found
a number of models with a considerable equatorial dipole contribution and an
intermediate overall dipole field strength. Furthermore, a large density
stratification may hamper the generation of dipole dominated magnetic fields.
Previously proposed scaling laws, such as those for the field strength, are
similarly applicable to anelastic models. It is not clear, however, if this
consistency necessarily implies similar dynamo processes in both settings.Comment: 14 pages, 11 figure
A numerical model of the VKS experiment
We present numerical simulations of the magnetic field generated by the flow
of liquid sodium driven by two counter-rotating impellers (VKS experiment).
Using a dynamo kinematic code in cylindrical geometry, it is shown that
different magnetic modes can be generated depending on the flow configuration.
While the time averaged axisymmetric mean flow generates an equatorial dipole,
our simulations show that an axial field of either dipolar or quadrupolar
symmetry can be generated by taking into account non-axisymmetric components of
the flow. Moreover, we show that by breaking a symmetry of the flow, the
magnetic field becomes oscillatory. This leads to reversals of the axial dipole
polarity, involving a competition with the quadrupolar component.Comment: 6 pages, 5 figure
Bistability and hysteresis of dipolar dynamos generated by turbulent convection in rotating spherical shells
Bistability and hysteresis of magnetohydrodynamic dipolar dynamos generated by turbulent convection in rotating spherical fluid shells is demonstrated. Hysteresis appears as a transition between two distinct regimes of dipolar dynamos with rather different properties including a pronounced difference in the amplitude of the axisymmetric poloidal field component and in the form of the differential rotation. The bistability occurs from the onset of dynamo action up to about 9 times the critical value of the Rayleigh number for onset of convection and over a wide range of values of the ordinary and the magnetic Prandtl numbers including the value unity
Formation of eyes in large-scale cyclonic vortices
We present numerical simulations of steady, laminar, axisymmetric convection
of a Boussinesq fluid in a shallow, rotating, cylindrical domain. The flow is
driven by an imposed vertical heat flux and shaped by the background rotation
of the domain. The geometry is inspired by that of tropical cyclones and the
global flow pattern consists of a shallow, swirling vortex combined with a
poloidal flow in the r-z plane which is predominantly inward near the bottom
boundary and outward along the upper surface. Our numerical experiments confirm
that, as suggested by Oruba et al 2017, an eye forms at the centre of the
vortex which is reminiscent of that seen in a tropical cyclone and is
characterised by a local reversal in the direction of the poloidal flow. We
establish scaling laws for the flow and map out the conditions under which an
eye will, or will not, form. We show that, to leading order, the velocity
scales with V=(\alpha g \beta)^{1/2}H, where g is gravity, \alpha the expansion
coefficient, \beta the background temperature gradient, and H is the depth of
the domain. We also show that the two most important parameters controlling the
flow are Re=VH/\nu and Ro=V/\Omega H, where \Omega is the background rotation
rate and \nu the viscosity. The Prandtl number and aspect ratio also play an
important, if secondary, role. Finally, and most importantly, we establish the
criteria required for eye formation. These consist of a lower bound on Re,
upper and lower bounds on Ro, and an upper bound on Ekman number.Comment: 18 pages, 14 figures, 1 tabl
B{\'e}nard convection in a slowly rotating penny shaped cylinder subject to constant heat flux boundary conditions
We consider axisymmetric Boussinesq convection in a shallow cylinder radius,
L, and depth, H (<< L), which rotates with angular velocity about its
axis of symmetry aligned to the vertical. Constant heat flux boundary
conditions, top and bottom, are adopted, for which the onset of instability
occurs on a long horizontal length scale provided that is sufficiently
small. We investigate the nonlinear development by well-established two-scale
asymptotic expansion methods. Comparisons of the results with the direct
numerical simulations (DNS) of the primitive governing equations are good at
sufficiently large Prandtl number, . As is reduced, the finite
amplitude range of applicability of the asymptotics reduces in concert. Though
the large meridional convective cell, predicted by the DNS, is approximated
adequately by the asymptotics, the azimuthal flow fails almost
catastrophically, because of significant angular momentum transport at small
, exacerbated by the cylindrical geometry. To appraise the situation,
we propose hybrid methods that build on the meridional streamfunction
derived from the asymptotics. With given, we solve the now linear
azimuthal equation of motion for the azimuthal velocity v by DNS. Our
''hybrid'' methods enable us to explain features of the flow at large Rayleigh
number, found previously by Oruba, Davidson \& Dormy (J. Fluid Mech.,vol. 812,
2017, pp. 890-904)
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