2,390 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
Bipartite partial duals and circuits in medial graphs
It is well known that a plane graph is Eulerian if and only if its geometric
dual is bipartite. We extend this result to partial duals of plane graphs. We
then characterize all bipartite partial duals of a plane graph in terms of
oriented circuits in its medial graph.Comment: v2: minor changes. To appear in Combinatoric
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
Rotary Honing: a Variant of the Taylor Paint-Scraper Problem
The three-dimensional Row in a corner of fixed angle α induced by the rotation in its plane of one of the boundaries is considered. A local similarity solution valid in a neighbourhood of the centre of rotation is obtained and the streamlines are shown to be closed curves. The effects of inertia are considered and are shown to be significant in a small neighbourhood of the plane of symmetry of the flow. A simple experiment confirms that the streamlines are indeed nearly closed; their projections on planes normal to the line of intersection of the boundaries are precisely the \u27Taylor\u27 streamlines of the well-known \u27paint-scraper\u27 problem. Three geometrical variants are considered: (i) when the centre of rotation of the lower plate is offset from the contact line; (ii) when both planes rotate with different angular velocities about a vertical axis and Coriolis effects are retained in the analysis; and (iii) when two vertical planes intersecting at an angle 2β are honed by a rotating conical boundary. The last is described by a similarity solution of the first kind (in the terminology of Barenblatt) which incorporates within its structure a similarity solution of the second kind involving corner eddies of a type familiar in two-dimensional corner flows
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