14,994 research outputs found
Computation of Kolmogorov's Constant in Magnetohydrodynamic Turbulence
In this paper we calculate Kolmogorov's constant for magnetohydrodynamic
turbulence to one loop order in perturbation theory using the direct
interaction approximation technique of Kraichnan. We have computed the
constants for various , i.e., fluid to magnetic energy ratios
when the normalized cross helicity is zero. We find that increases from
1.47 to 4.12 as we go from fully fluid case to a situation when , then it decreases to 3.55 in a fully magnetic limit .
When , we find that .Comment: Latex, 10 pages, no figures, To appear in Euro. Phys. Lett., 199
Incompressible Turbulence as Nonlocal Field Theory
It is well known that incompressible turbulence is nonlocal in real space
because sound speed is infinite in incompressible fluids. The equation in
Fourier space indicates that it is nonlocal in Fourier space as well. Contrast
this with Burgers equation which is local in real space. Note that the sound
speed in Burgers equation is zero. In our presentation we will contrast these
two equations using nonlocal field theory. Energy spectrum and renormalized
parameters will be discussed.Comment: 7 pages; Talk presented in Conference on "Perspectives in Nonlinear
Dynamics (PNLD 2004)" held in Chennai, 200
Calculation of renormalized viscosity and resistivity in magnetohydrodynamic turbulence
A self-consistent renormalization (RG) scheme has been applied to nonhelical
magnetohydrodynamic turbulence with normalized cross helicity and
. Kolmogorov's 5/3 powerlaw is assumed in order to compute the
renormalized parameters. It has been shown that the RG fixed point is stable
for . The renormalized viscosity and resistivity
have been calculated, and they are found to be positive for all
parameter regimes. For and large Alfv\'{e}n ratio (ratio of
kinetic and magnetic energies) , and . As
is decreased, increases and decreases, untill where both and are approximately zero. For large ,
both and vary as . The renormalized parameters for
the case are also reported.Comment: 19 pages REVTEX, 3 ps files (Phys. Plasmas, v8, 3945, 2001
Energy fluxes in helical magnetohydrodynamics and dynamo action
Renormalized viscosity, renormalized resistivity, and various energy fluxes
are calculated for helical magnetohydrodynamics using perturbative field
theory. The calculation is to first-order in perturbation. Kinetic and magnetic
helicities do not affect the renormalized parameters, but they induce an
inverse cascade of magnetic energy. The sources for the the large-scale
magnetic field have been shown to be (1) energy flux from large-scale velocity
field to large-scale magnetic field arising due to nonhelical interactions, and
(2) inverse energy flux of magnetic energy caused by helical interactions.
Based on our flux results, a premitive model for galactic dynamo has been
constructed. Our calculations yields dynamo time-scale for a typical galaxy to
be of the order of years. Our field-theoretic calculations also reveal
that the flux of magnetic helicity is backward, consistent with the earlier
observations based on absolute equilibrium theory.Comment: REVTEX4; A factor of 2 corrected in helicit
Initial Condition Sensitivity of Global Quantities in Magnetohydrodynamic Turbulence
In this paper we study the effect of subtle changes in initial conditions on
the evolution of global quantities in two-dimensional Magnetohydrodynamic (MHD)
turbulence. We find that a change in the initial phases of complex Fourier
modes of the Els\"{a}sser variables, while keeping the initial values of total
energy, cross helicity and Alfv\'{e}n ratio unchanged, has a significant effect
on the evolution of cross helicity. On the contrary, the total energy and
Alfv\'{e}n ratio are insensitive to the initial phases. Our simulations are
based on direct numerical simulation using the pseudo-spectral method.Comment: 12 pages LateX, 11 ps figures. Accepted for publication by Physics of
Plasma
Field theoretic calculation of scalar turbulence
The cascade rate of passive scalar and Bachelor's constant in scalar
turbulence are calculated using the flux formula. This calculation is done to
first order in perturbation series. Batchelor's constant in three dimension is
found to be approximately 1.25. In higher dimension, the constant increases as
.Comment: RevTex4, publ. in Int. J. Mod. Phy. B, v.15, p.3419, 200
Local shell-to-shell energy transfer via nonlocal Interactions in fluid turbulence
In this paper we analytically compute the strength of nonlinear interactions
in a triad, and the energy exchanges between wavenumber shells in
incompressible fluid turbulence. The computation has been done using
first-order perturbative field theory. In three dimension, magnitude of triad
interactions is large for nonlocal triads, and small for local triads. However,
the shell-to-shell energy transfer rate is found to be local and forward. This
result is due to the fact that the nonlocal triads occupy much less Fourier
space volume than the local ones. The analytical results on three-dimensional
shell-to-shell energy transfer match with their numerical counterparts. In
two-dimensional turbulence, the energy transfer rates to the near-by shells are
forward, but to the distant shells are backward; the cumulative effect is an
inverse cascade of energy.Comment: 10 pages, Revtex
Large-Eddy Simulations of Fluid and Magnetohydrodynamic Turbulence Using Renormalized Parameters
In this paper a procedure for large-eddy simulation (LES) has been devised
for fluid and magnetohydrodynamic turbulence in Fourier space using the
renormalized parameters. The parameters calculated using field theory have been
taken from recent papers by Verma [Phys. Rev. E, 2001; Phys. Plasmas, 2001]. We
have carried out LES on grid. These results match quite well with direct
numerical simulations of . We show that proper choice of parameter is
necessary in LES.Comment: 12 pages, 4 figures: Proper figures inserte
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