107 research outputs found
Statistics of active vs. passive advections in magnetohydrodynamic turbulence
Active turbulent advection is considered in the context of
magneto-hydrodynamics. In this case, an auxiliary passive field bears no
apparent connection to the active field. The scaling properties of the two
fields are different. In the framework of a shell model, we show that the
two-point structure function of the passive field has a unique zero mode,
characterizing the scaling of this field only. In other words, the existence of
statistical invariants for the decaying passive field carries no information on
the scaling properties of the active field.Comment: 4 pages, 2 figure
Magnetic waves in a stratified medium: dispersion relations and exact solutions
We solve for waves in an isothermal, stratified medium with a magnetic field
that points along a direction perpendicular to that of gravity and varies
exponentially in the direction of gravity. For waves propagating along the
magnetic field, we calculate approximate dispersion relation as a function of
the magnetic field strength. We also find exact solutions for two different
cases: (a) waves propagating along the direction of the magnetic field and (b)
waves propagating along the direction of gravity. In each of these cases, we
find solutions in terms of either confluent hypergeometric functions or Gauss
hypergeometric functions depending on whether the ratio of the scale height of
the magnetic field over the density scale height is equal to two or not.Comment: 9 pages, 4 figures, Submitte
A mean field dynamo from negative eddy diffusivity
Using direct numerical simulations, we verify that "flow IV" of Roberts
(1972) exhibits dynamo action dominated by horizontally averaged large-scale
magnetic field. With the test-field method we compute the turbulent magnetic
diffusivity and find that it is negative and overcomes the molecular
diffusivity, thus explaining quantitatively the large-scale dynamo for magnetic
Reynolds numbers above . As expected for a dynamo of this type, but
contrary to -effect dynamos, the two horizontal field components grow
independently of each other and have arbitrary amplitude ratios and phase
differences. Small length scales of the mean magnetic field are shown to be
stabilized by the turbulent magnetic diffusivity becoming positive at larger
wavenumbers. Oscillatory decaying or growing solutions have also been found in
certain wavenumber intervals and sufficiently large values of the magnetic
Reynolds number. For magnetic Reynolds numbers below the turbulent
magnetic diffusivity is confirmed to be positive, as expected for all
incompressible flows. Earlier claims of a dynamo driven by a modified
Taylor-Green flow through negative eddy diffusivity could not be confirmed.Comment: 7 pages, 9 figures, accepted to MNRA
Can planetesimals form by collisional fusion?
As a test bed for the growth of protoplanetary bodies in a turbulent
circumstellar disk we examine the fate of a boulder using direct numerical
simulations of particle seeded gas flowing around it. We provide an accurate
description of the flow by imposing no-slip and non-penetrating boundary
conditions on the boulder surface using the immersed boundary method pioneered
by Peskin (2002). Advected by the turbulent disk flow, the dust grains collide
with the boulder and we compute the probability density function (PDF) of the
normal component of the collisional velocity. Through this examination of the
statistics of collisional velocities we test the recently developed concept of
collisional fusion which provides a physical basis for a range of collisional
velocities exhibiting perfect sticking. A boulder can then grow sufficiently
rapidly to settle into a Keplerian orbit on disk evolution time scales.Comment: Astrophysical Journal, in pres
Kazantsev dynamo in turbulent compressible flows
We consider the kinematic fluctuation dynamo problem in a flow that is
random, white-in-time, with both solenoidal and potential components. This
model is a generalization of the well-studied Kazantsev model. If both the
solenoidal and potential parts have the same scaling exponent, then, as the
compressibility of the flow increases, the growth rate decreases but remains
positive. If the scaling exponents for the solenoidal and potential parts
differ, in particular if they correspond to typical Kolmogorov and Burgers
values, we again find that an increase in compressibility slows down the growth
rate but does not turn it off. The slow down is, however, weaker and the
critical magnetic Reynolds number is lower than when both the solenoidal and
potential components display the Kolmogorov scaling. Intriguingly, we find that
there exist cases, when the potential part is smoother than the solenoidal
part, for which an increase in compressibility increases the growth rate. We
also find that the critical value of the scaling exponent above which a dynamo
is seen is unity irrespective of the compressibility. Finally, we realize that
the dimension is special, since for all other values of the
critical exponent is higher and depends on the compressibility.Comment: 12 pages, 6 figure
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