306 research outputs found
Linking dissipation-induced instabilities with nonmodal growth: the case of helical magnetorotational instability
The helical magnetorotational instability is known to work for resistive
rotational flows with comparably steep negative or extremely steep positive
shear. The corresponding lower and upper Liu limits of the shear are
continuously connected when some axial electrical current is allowed to flow
through the rotating fluid. Using a local approximation we demonstrate that the
magnetohydrodynamic behavior of this dissipation-induced instability is
intimately connected with the nonmodal growth and the pseudospectrum of the
underlying purely hydrodynamic problem.Comment: 5 pages, 4 figure
Continuation and stability of rotating waves in the magnetized spherical Couette system: Secondary transitions and multistability
Rotating waves (RW) bifurcating from the axisymmetric basic magnetized
spherical Couette (MSC) flow are computed by means of Newton-Krylov
continuation techniques for periodic orbits. In addition, their stability is
analysed in the framework of Floquet theory. The inner sphere rotates whilst
the outer is kept at rest and the fluid is subjected to an axial magnetic
field. For a moderate Reynolds number (measuring inner
rotation) the effect of increasing the magnetic field strength (measured by the
Hartmann number ) is addressed in the range
corresponding to the working conditions of the HEDGEHOG experiment at
Helmholtz-Zentrum Dresden-Rossendorf. The study reveals several regions of
multistability of waves with azimuthal wave number , and several
transitions to quasiperiodic flows, i.e modulated rotating waves (MRW). These
nonlinear flows can be classified as the three different instabilities of the
radial jet, the return flow and the shear-layer, as found in previous studies.
These two flows are continuously linked, and part of the same branch, as the
magnetic forcing is increased. Midway between the two instabilities, at a
certain critical , the nonaxisymmetric component of the flow is
maximum.Comment: Published in the Proceedings of the Royal Society A journal. Contains
3 tables and 12 figure
Destabilization of rotating flows with positive shear by azimuthal magnetic fields
According to Rayleigh's criterion, rotating flows are linearly stable when
their specific angular momentum increases radially outward. The celebrated
magnetorotational instability opens a way to destabilize those flows, as long
as the angular velocity is decreasing outward. Using a short-wavelength
approximation we demonstrate that even flows with very steep positive shear can
be destabilized by azimuthal magnetic fields which are current-free within the
fluid. We illustrate the transition of this instability to a rotationally
enhanced kink-type instability in case of a homogeneous current in the fluid,
and discuss the prospects for observing it in a magnetized Taylor-Couette flow.Comment: 4 pages, 4 figur
Standard and helical magnetorotational instability: How singularities create paradoxal phenomena in MHD
The magnetorotational instability (MRI) triggers turbulence and enables
outward transport of angular momentum in hydrodynamically stable rotating shear
flows, e.g., in accretion disks. What laws of differential rotation are
susceptible to the destabilization by axial, azimuthal, or helical magnetic
field? The answer to this question, which is vital for astrophysical and
experimental applications, inevitably leads to the study of spectral and
geometrical singularities on the instability threshold. The singularities
provide a connection between seemingly discontinuous stability criteria and
thus explain several paradoxes in the theory of MRI that were poorly understood
since the 1950s.Comment: 25 pages, 10 figures. A tutorial paper. Invited talk at SPT 2011,
Symmetry and Perturbation Theory, 5 - 12 June 2011, Otranto near Lecce
(Italy
Extending the range of the inductionless magnetorotational instability
The magnetorotational instability (MRI) can destabilize hydrodynamically
stable rotational flows, thereby allowing angular momentum transport in
accretion disks. A notorious problem for MRI is its questionable applicability
in regions with low magnetic Prandtl number, as they are typical for
protoplanetary disks and the outer parts of accretion disks around black holes.
Using the WKB method, we extend the range of applicability of MRI by showing
that the inductionless versions of MRI, such as the helical MRI and the
azimuthal MRI, can easily destabilize Keplerian profiles ~ 1/r^(3/2) if the
radial profile of the azimuthal magnetic field is only slightly modified from
the current-free profile ~ 1/r. This way we further show how the formerly known
lower Liu limit of the critical Rossby number, Ro=-0.828, connects naturally
with the upper Liu limit, Ro=+4.828.Comment: Growth rates added, references modified; submitted to Physical Review
Letter
Parametric instability in periodically perturbed dynamos
We examine kinematic dynamo action driven by an axisymmetric large scale flow
that is superimposed with an azimuthally propagating non-axisymmetric
perturbation with a frequency . Although we apply a rather simple large
scale velocity field, our simulations exhibit a complex behavior with
oscillating and azimuthally drifting eigenmodes as well as stationary regimes.
Within these non-oscillating regimes we find parametric resonances
characterized by a considerable enhancement of dynamo action and by a locking
of the phase of the magnetic field to the pattern of the perturbation. We find
an approximate fulfillment of the relationship between the resonant frequency
of the disturbed system and the eigenfrequency
of the undisturbed system given by which is known
from paradigmatic rotating mechanical systems and our prior study [Giesecke et
al., Phys. Rev. E, 86, 066303 (2012)]. We find further -- broader -- regimes
with weaker enhancement of the growth rates but without phase locking. However,
this amplification regime arises only in case of a basic (i.e. unperturbed)
state consisting of several different eigenmodes with rather close growth
rates. Qualitatively, these observations can be explained in terms of a simple
low dimensional model for the magnetic field amplitude that is derived using
Floquet theory. The observed phenomena may be of fundamental importance in
planetary dynamo models with the base flow being disturbed by periodic external
forces like precession or tides and for the realization of dynamo action under
laboratory conditions where imposed perturbations with the appropriate
frequency might facilitate the occurrence of dynamo action.Comment: 25 pages, 19 Figures, minor corrections to match the published
version published in Phys. Rev. Fluids 2, 053701 (2017
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