15,187 research outputs found
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
Grothendieck-Serre formula and bigraded Cohen-Macaulay Rees algebras
The Grothendieck-Serre formula for the difference between the Hilbert
function and Hilbert polynomial of a graded algebra is generalized for bigraded
standard algebras. This is used to get a similar formula for the difference
between the Bhattacharya function and Bhattacharya polynomial of two m-primary
ideals I and J in a local ring (A,m) in terms of local cohomology modules of
Rees algebras of I and J. The cohomology of a variation of the Kirby-Mehran
complex for bigraded Rees algebras is studied which is used to characterize the
Cohen-Macaulay property of bigraded Rees algebra of I and J for two dimensional
Cohen-Macaulay local rings.Comment: 23 page
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
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
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