2,348 research outputs found
On knotted streamtubes in incompressible hydrodynamical flow and a restricted conserved quantity
For certain families of fluid flow, a new conserved quantity --
stream-helicity -- has been established.Using examples of linked and knotted
streamtubes, it has been shown that stream-helicity does, in certain cases,
entertain itself with a very precise topological meaning viz, measure of the
degree of knottedness or linkage of streamtubes.As a consequence,
stream-helicity emerges as a robust topological invariant.Comment: This extended version is the basically a more clarified version of
the previous submission physics/0611166v
Decay of helical and non-helical magnetic knots
We present calculations of the relaxation of magnetic field structures that
have the shape of particular knots and links. A set of helical magnetic flux
configurations is considered, which we call -foil knots of which the trefoil
knot is the most primitive member. We also consider two nonhelical knots;
namely, the Borromean rings as well as a single interlocked flux rope that also
serves as the logo of the Inter-University Centre for Astronomy and
Astrophysics in Pune, India. The field decay characteristics of both
configurations is investigated and compared with previous calculations of
helical and nonhelical triple-ring configurations. Unlike earlier nonhelical
configurations, the present ones cannot trivially be reduced via flux
annihilation to a single ring. For the -foil knots the decay is described by
power laws that range form to , which can be as slow as
the behavior for helical triple-ring structures that were seen in
earlier work. The two nonhelical configurations decay like , which is
somewhat slower than the previously obtained behavior in the decay
of interlocked rings with zero magnetic helicity. We attribute the difference
to the creation of local structures that contain magnetic helicity which
inhibits the field decay due to the existence of a lower bound imposed by the
realizability condition. We show that net magnetic helicity can be produced
resistively as a result of a slight imbalance between mutually canceling
helical pieces as they are being driven apart. We speculate that higher order
topological invariants beyond magnetic helicity may also be responsible for
slowing down the decay of the two more complicated nonhelical structures
mentioned above.Comment: 11 pages, 27 figures, submitted to Phys. Rev.
Optimization of the magnetic dynamo
In stars and planets, magnetic fields are believed to originate from the
motion of electrically conducting fluids in their interior, through a process
known as the dynamo mechanism. In this Letter, an optimization procedure is
used to simultaneously address two fundamental questions of dynamo theory:
"Which velocity field leads to the most magnetic energy growth?" and "How large
does the velocity need to be relative to magnetic diffusion?" In general, this
requires optimization over the full space of continuous solenoidal velocity
fields possible within the geometry. Here the case of a periodic box is
considered. Measuring the strength of the flow with the root-mean-square
amplitude, an optimal velocity field is shown to exist, but without limitation
on the strain rate, optimization is prone to divergence. Measuring the flow in
terms of its associated dissipation leads to the identification of a single
optimal at the critical magnetic Reynolds number necessary for a dynamo. This
magnetic Reynolds number is found to be only 15% higher than that necessary for
transient growth of the magnetic field.Comment: Optimal velocity field given approximate analytic form. 4 pages, 4
figure
Transport coefficients for the shear dynamo problem at small Reynolds numbers
We build on the formulation developed in Sridhar & Singh (JFM, 664, 265,
2010), and present a theory of the \emph{shear dynamo problem} for small
magnetic and fluid Reynolds numbers, but for arbitrary values of the shear
parameter. Specializing to the case of a mean magnetic field that is slowly
varying in time, explicit expressions for the transport coefficients,
and , are derived. We prove that, when the velocity
field is non helical, the transport coefficient vanishes. We then
consider forced, stochastic dynamics for the incompressible velocity field at
low Reynolds number. An exact, explicit solution for the velocity field is
derived, and the velocity spectrum tensor is calculated in terms of the
Galilean--invariant forcing statistics. We consider forcing statistics that is
non helical, isotropic and delta-correlated-in-time, and specialize to the case
when the mean-field is a function only of the spatial coordinate and time
; this reduction is necessary for comparison with the numerical
experiments of Brandenburg, R{\"a}dler, Rheinhardt & K\"apyl\"a (ApJ, 676, 740,
2008). Explicit expressions are derived for all four components of the magnetic
diffusivity tensor, . These are used to prove that the
shear-current effect cannot be responsible for dynamo action at small \re and
\rem, but for all values of the shear parameter.Comment: 27 pages, 5 figures, Published in Physical Review
Supercriticality to subcriticality in dynamo transitions
Evidence from numerical simulations suggest that the nature of dynamo
transition changes from supercritical to subcritical as the magnetic Prandtl
number is decreased. To explore this interesting crossover we first use direct
numerical simulations to investigate the hysteresis zone of a subcritical
Taylor-Green dynamo. We establish that a well defined boundary exists in this
hysteresis region which separates dynamo states from the purely hydrodynamic
solution. We then propose simple dynamo models which show similar crossover
from supercritical to subcritical dynamo transition as a function of the
magnetic Prandtl number. Our models show that the change in the nature of
dynamo transition is connected to the stabilizing or de-stabilizing influence
of governing non-linearities.Comment: Version 3 note: Found a sign-error in an equation which propagated
further. Section 4 and Fig. 3,4,5 are updated in Version 3 (final form
Geometrical statistics and vortex structures in helical and nonhelical turbulences
In this paper we conduct an analysis of the geometrical and vortical statistics in the small scales of helical and nonhelical turbulences generated with direct numerical simulations. Using a filtering approach, the helicity flux from large scales to small scales is represented by the subgrid-scale (SGS) helicity dissipation. The SGS helicity dissipation is proportional to the product between the SGS stress tensor and the symmetric part of the filtered vorticity gradient, a tensor we refer to as the vorticity strain rate. We document the statistics of the vorticity strain rate, the vorticity gradient, and the dual vector corresponding to the antisymmetric part of the vorticity gradient. These results provide new insights into the local structures of the vorticity field. We also study the relations between these quantities and vorticity, SGS helicity dissipation, SGS stress tensor, and other quantities. We observe the following in both helical and nonhelical turbulences: (1) there is a high probability to find the dual vector aligned with the intermediate eigenvector of the vorticity strain rate tensor; (2) vorticity tends to make an angle of 45 with both the most contractive and the most extensive eigendirections of the vorticity strain rate tensor; (3) the vorticity strain rate shows a preferred alignment configuration with the SGS stress tensor; (4) in regions with strong straining of the vortex lines, there is a negative correlation between the third order invariant of the vorticity gradient tensor and SGS helicity dissipation fluctuations. The correlation is qualitatively explained in terms of the self-induced motions of local vortex structures, which tend to wind up the vortex lines and generate SGS helicity dissipation. In helical turbulence, we observe that the joint probability density function of the second and third tensor invariants of the vorticity gradient displays skewed distributions, with the direction of skewness depending on the sign of helicity input. We also observe that the intermediate eigenvalue of the vorticity strain rate tensor is more probable to take negative values. These interesting observations, reported for the first time, call for further studies into their dynamical origins and implications. (C) 2010 American Institute of Physics. [doi: 10.1063/1.3336012
Turbulent transport and dynamo in sheared MHD turbulence with a non-uniform magnetic field
We investigate three-dimensional magnetohydrodynamics turbulence in the presence of velocity and magnetic shear (i.e., with both a large-scale shear flow and a nonuniform magnetic field). By assuming a turbulence driven by an external forcing with both helical and nonhelical spectra, we investigate the combined effect of these two shears on turbulence intensity and turbulent transport represented by turbulent diffusivities (turbulent viscosity, α and β effect) in Reynolds-averaged equations. We show that turbulent transport (turbulent viscosity and diffusivity) is quenched by a strong flow shear and a strong magnetic field. For a weak flow shear, we further show that the magnetic shear increases the turbulence intensity while decreasing the turbulent transport. In the presence of a strong flow shear, the effect of the magnetic shear is found to oppose the effect of flow shear (which reduces turbulence due to shear stabilization) by enhancing turbulence and transport, thereby weakening the strong quenching by flow shear stabilization. In the case of a strong magnetic field (compared to flow shear), magnetic shear increases turbulence intensity and quenches turbulent transport
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