263 research outputs found
On the relation between viscoelastic and magnetohydrodynamic flows and their instabilities
We demonstrate a close analogy between a viscoelastic medium and an
electrically conducting fluid containing a magnetic field. Specifically, the
dynamics of the Oldroyd-B fluid in the limit of large Deborah number
corresponds to that of a magnetohydrodynamic (MHD) fluid in the limit of large
magnetic Reynolds number. As a definite example of this analogy, we compare the
stability properties of differentially rotating viscoelastic and MHD flows. We
show that there is an instability of the Oldroyd-B fluid that is physically
distinct from both the inertial and elastic instabilities described previously
in the literature, but is directly equivalent to the magnetorotational
instability in MHD. It occurs even when the specific angular momentum increases
outwards, provided that the angular velocity decreases outwards; it derives
from the kinetic energy of the shear flow and does not depend on the curvature
of the streamlines. However, we argue that the elastic instability of
viscoelastic Couette flow has no direct equivalent in MHD.Comment: 21 pages, 3 figures, to be published in J. Fluid Mec
Effects of fluctuation on alpha-omega dynamo models
We analyse the role of a fluctuating alpha-effect in alpha-omega dynamo
models, and show that there is a mechanism for magnetic field generation, valid
at large scale separation, deriving from the interaction of mean shear and a
fluctuating alpha-effect. It is shown that this effect can act as a dynamo even
in the absence of a mean alpha-effect, and that the timescale for dynamo waves
is strongly affected by the presence of fluctuations.Comment: 4 pages, 3 figure
Double-diffusive instabilities of a shear-generated magnetic layer
Previous theoretical work has speculated about the existence of
double-diffusive magnetic buoyancy instabilities of a dynamically evolving
horizontal magnetic layer generated by the interaction of forced vertically
sheared velocity and a background vertical magnetic field. Here we confirm
numerically that if the ratio of the magnetic to thermal diffusivities is
sufficiently low then such instabilities can indeed exist, even for high
Richardson number shear flows. Magnetic buoyancy may therefore occur via this
mechanism for parameters that are likely to be relevant to the solar
tachocline, where regular magnetic buoyancy instabilities are unlikely.Comment: Submitted to ApJ
The Evolution of a Double Diffusive Magnetic Buoyancy Instability
Recently, Silvers, Vasil, Brummell, & Proctor (2009), using numerical
simulations, confirmed the existence of a double diffusive magnetic buoyancy
instability of a layer of horizontal magnetic field produced by the interaction
of a shear velocity field with a weak vertical field. Here, we demonstrate the
longer term nonlinear evolution of such an instability in the simulations. We
find that a quasi two-dimensional interchange instability rides (or "surfs") on
the growing shear-induced background downstream field gradients. The region of
activity expands since three-dimensional perturbations remain unstable in the
wake of this upward-moving activity front, and so the three-dimensional nature
becomes more noticeable with time.Comment: 9 pages; 3 figures; accepted to appear in IAU symposium 27
Nonlinear Competition Between Small and Large Hexagonal Patterns
Recent experiments by Kudrolli, Pier and Gollub on surface waves,
parametrically excited by two-frequency forcing, show a transition from a small
hexagonal standing wave pattern to a triangular ``superlattice'' pattern. We
show that generically the hexagons and the superlattice wave patterns bifurcate
simultaneously from the flat surface state as the forcing amplitude is
increased, and that the experimentally-observed transition can be described by
considering a low-dimensional bifurcation problem. A number of predictions come
out of this general analysis.Comment: 4 pages, RevTex, revised, to appear in Phys. Rev. Let
Large-scale Dynamo Action Driven by Velocity Shear and Rotating Convection
By incorporating a large-scale shear flow into turbulent rotating convection,
we show that a sufficiently strong shear can promote dynamo action in flows
that in the absence of shear do not act as dynamos. Our results are consistent
with a dynamo driven by either the shear-current effect or by the interaction
between a fluctuating -effect and the velocity shear; they are though
inconsistent with either a classical or mean field
dynamo.Comment: 4 pages, 4 fig
A novel type of intermittency in a nonlinear dynamo in a compressible flow
The transition to intermittent mean--field dynamos is studied using numerical
simulations of isotropic magnetohydrodynamic turbulence driven by a helical
flow. The low-Prandtl number regime is investigated by keeping the kinematic
viscosity fixed while the magnetic diffusivity is varied. Just below the
critical parameter value for the onset of dynamo action, a transient
mean--field with low magnetic energy is observed. After the transition to a
sustained dynamo, the system is shown to evolve through different types of
intermittency until a large--scale coherent field with small--scale turbulent
fluctuations is formed. Prior to this coherent field stage, a new type of
intermittency is detected, where the magnetic field randomly alternates between
phases of coherent and incoherent large--scale spatial structures. The
relevance of these findings to the understanding of the physics of mean--field
dynamo and the physical mechanisms behind intermittent behavior observed in
stellar magnetic field variability are discussed.Comment: 19 pages, 13 figure
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 ‘shear dynamo’ 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
- …