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

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

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

Going against the flow: A critical analysis of virtual water trade in the context of India's National River Linking Programme

Virtual water trade has been promoted as a tool to address national and regional water scarcity. In the context of international (food) trade, this concept has been applied with a view to optimize the flow of commodities considering the water endowments of nations. The concept states that water-rich countries should produce and export water intensive commodities (which indirectly carry embedded water needed for producing them) to water-scarce countries, thereby enabling the water-scarce countries to divert their precious water resources to alternative, higher productivity uses.\ud While progress has been made on quantifying virtual water flows between countries, there exists little information on virtual water trade within large countries like India. This report quantifies and critically analyzes inter-state virtual water flows in India in the context of a large inter-basin transfer plan of the Government of India.\ud Our analysis shows that the existing pattern of inter-state virtual water trade is exacerbating scarcities in already water scarce states and that rather than being dictated by water endowments, virtual water flows are influenced by other factors such as "per capita gross cropped area" and "access to secured markets". We therefore argue that in order to have a comprehensive understanding of virtual water trade, non-water factors of production need to be taken into consideration

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