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

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