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 $E^u(k)/E^b(k)$, i.e., fluid to magnetic energy ratios when the normalized cross helicity is zero. We find that $K$ increases from 1.47 to 4.12 as we go from fully fluid case $(E^b=0)$ to a situation when $E^u/E^b=0.5$, then it decreases to 3.55 in a fully magnetic limit $(E^u=0)$. When $E^u/E^b=1$, we find that $K=3.43$.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 $\sigma_c =0$ and $\sigma_c \to 1$. 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 $d \ge d_c \approx 2.2$. The renormalized viscosity $\nu^*$ and resistivity $\eta^*$ have been calculated, and they are found to be positive for all parameter regimes. For $\sigma_c=0$ and large Alfv\'{e}n ratio (ratio of kinetic and magnetic energies) $r_A$, $\nu^*=0.36$ and $\eta^*=0.85$. As $r_A$ is decreased, $\nu^*$ increases and $\eta^*$ decreases, untill $r_A \approx 0.25$ where both $\nu^*$ and $\eta^*$ are approximately zero. For large $d$, both $\nu^*$ and $\eta^*$ vary as $d^{-1/2}$. The renormalized parameters for the case $\sigma_c \to 1$ 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 $10^8$ 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 $d^{1/3}$.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 $64^3$ grid. These results match quite well with direct numerical simulations of $128^3$. We show that proper choice of parameter is necessary in LES.Comment: 12 pages, 4 figures: Proper figures inserte