38 research outputs found
Rossby waves and -effect
Rossby waves drifting in the azimuthal direction are a common feature at the
onset of thermal convective instability in a rapidly rotating spherical shell.
They can also result from the destabilization of a Stewartson shear layer
produced by differential rotation as expected in the liquid sodium experiment
(DTS) working in Grenoble, France. A usual way to explain why Rossby waves can
participate to the dynamo process goes back to Busse (1975). In his picture,
the flow geometry is a cylindrical array of parallel rolls aligned with the
rotation axis. The axial flow component (the component parallel to the rotation
axis) is (i) maximum in the middle of each roll and changes its sign from one
roll to the next. It is produced by the Ekman pumping at the fluid containing
shell boundary. The corresponding dynamo mechanism can be explained in terms of
an -tensor with non-zero coefficients on the diagonal. In rapidly
rotating objects like the Earth's core (or in a fast rotating experiment),
Rossby waves occur in the limit of small Ekman number (). In
that case, the main source of the axial flow component is not the Ekman pumping
but rather the ``geometrical slope effect'' due to the spherical shape of the
fluid containing shell. This implies that the axial flow component is (ii)
maximum at the borders of the rolls and not at the centers. If assumed to be
stationary, such rolls would lead to zero coefficients on the diagonal of the
-tensor, making the dynamo probably less efficient if possible at all.
Actually, the rolls are drifting as a wave, and we show that this drift implies
non--zero coefficients on the diagonal of the -tensor. These new
coefficients are in essence very different from the ones obtained in case (i)
and cannot be interpreted in terms of the heuristic picture of Busse (1975)
Dissipation scales of kinetic helicities in turbulence
A systematic study of the influence of the viscous effect on both the spectra
and the nonlinear fluxes of conserved as well as non conserved quantities in
Navier-Stokes turbulence is proposed. This analysis is used to estimate the
helicity dissipation scale which is shown to coincide with the energy
dissipation scale. However, it is shown using the decomposition of helicity
into eigen modes of the curl operator, that viscous effects have to be taken
into account for wave vector smaller than the Kolomogorov wave number in the
evolution of these eigen components of the helicity.Comment: 6 pages, 2 figures, submited to Po
Dynamo effect in parity-invariant flow with large and moderate separation of scales
It is shown that non-helical (more precisely, parity-invariant) flows capable
of sustaining a large-scale dynamo by the negative magnetic eddy diffusivity
effect are quite common. This conclusion is based on numerical examination of a
large number of randomly selected flows. Few outliers with strongly negative
eddy diffusivities are also found, and they are interpreted in terms of the
closeness of the control parameter to a critical value for generation of a
small-scale magnetic field. Furthermore, it is shown that, for parity-invariant
flows, a moderate separation of scales between the basic flow and the magnetic
field often significantly reduces the critical magnetic Reynolds number for the
onset of dynamo action.Comment: 44 pages,11 figures, significantly revised versio
Cylindrical anisotropic dynamos
We explore the influence of geometry variations on the structure and the
time-dependence of the magnetic field that is induced by kinematic
dynamos in a finite cylinder. The dynamo action is due to an anisotropic
effect which can be derived from an underlying columnar flow. The
investigated geometry variations concern, in particular, the aspect ratio of
height to radius of the cylinder, and the thickness of the annular space to
which the columnar flow is restricted. Motivated by the quest for laboratory
dynamos which exhibit Earth-like features, we start with modifications of the
Karlsruhe dynamo facility. Its dynamo action is reasonably described by an
mechanism with anisotropic tensor. We find a critical
aspect ratio below which the dominant magnetic field structure changes from an
equatorial dipole to an axial dipole. Similar results are found for
dynamos working in an annular space when a radial dependence of
is assumed. Finally, we study the effect of varying aspect ratios of
dynamos with an tensor depending both on radial and axial coordinates.
In this case only dominant equatorial dipoles are found and most of the
solutions are oscillatory, contrary to all previous cases where the resulting
fields are steady.Comment: 15 pages, 8 figure
Asymmetric polarity reversals, bimodal field distribution, and coherence resonance in a spherically symmetric mean-field dynamo model
Using a mean-field dynamo model with a spherically symmetric helical
turbulence parameter alpha which is dynamically quenched and disturbed by
additional noise, the basic features of geomagnetic polarity reversals are
shown to be generic consequences of the dynamo action in the vicinity of
exceptional points of the spectrum. This simple paradigmatic model yields long
periods of constant polarity which are interrupted by self-accelerating field
decays leading to asymmetric polarity reversals. It shows the recently
discovered bimodal field distribution, and it gives a natural explanation of
the correlation between polarity persistence time and field strength. In
addition, we find typical features of coherence resonance in the dependence of
the persistence time on the noise.Comment: 5 pages, 7 figure
Deciphering solar turbulence from sunspots records
It is generally believed that sunspots are the emergent part of magnetic flux
tubes in the solar interior. These tubes are created at the base of the
convection zone and rise to the surface due to their magnetic buoyancy. The
motion of plasma in the convection zone being highly turbulent, the surface
manifestation of sunspots may retain the signature of this turbulence,
including its intermittency. From direct observations of sunspots, and indirect
observations of the concentration of cosmogenic isotopes C in tree rings
or Be in polar ice, power spectral densities in frequency are plotted.
Two different frequency scalings emerge, depending on whether the Sun is
quiescent or active. %magnetic activity is maximum or minimum. From direct
observations we can also calculate scaling exponents. These testify to a strong
intermittency, comparable with that observed in the solar wind.Comment: 5 pages, 6 figures, accepted for publication in MNRAS Letter
Why dynamos are prone to reversals
In a recent paper (Phys. Rev. Lett. 94 (2005), 184506; physics/0411050) it
was shown that a simple mean-field dynamo model with a spherically symmetric
helical turbulence parameter alpha can exhibit a number of features which are
typical for Earth's magnetic field reversals. In particular, the model produces
asymmetric reversals, a positive correlation of field strength and interval
length, and a bimodal field distribution. All these features are attributable
to the magnetic field dynamics in the vicinity of an exceptional point of the
spectrum of the non-selfadjoint dynamo operator. The negative slope of the
growth rate curve between the nearby local maximum and the exceptional point
makes the system unstable and drives it to the exceptional point and beyond
into the oscillatory branch where the sign change happens. A weakness of this
reversal model is the apparent necessity to fine-tune the magnetic Reynolds
number and/or the radial profile of alpha. In the present paper, it is shown
that this fine-tuning is not necessary in the case of higher supercriticality
of the dynamo. Numerical examples and physical arguments are compiled to show
that, with increasing magnetic Reynolds number, there is strong tendency for
the exceptional point and the associated local maximum to move close to the
zero growth rate line. Although exemplified again by the spherically symmetric
alpha^2 dynamo model, the main idea of this ''self-tuning'' mechanism of
saturated dynamos into a reversal-prone state seems well transferable to other
dynamos. As a consequence, reversing dynamos might be much more typical and may
occur much more frequently in nature than what could be expected from a purely
kinematic perspective.Comment: 11 pages, 10 figure