DISSIPATION FLUCTUATIONS OF A PASSIVE SCALAR ADVECTED BY A RANDOM VELOCITY-FIELD

The dynamics of fluctuations of the dissipation rate of a passive scal ar advected by a rapidly changing in time Gaussian random velocity fie ld with the variance [v(i)(x)-v(i)(x+r)](2) proportional to r(xi) is c onsidered. It is shown that when xi/d-->0 the dissipation correlation function [epsilon(x)epsilon(x+r)]proportional to r(gamma) with gamma=- 4 xi/(d+2) in agreement with the recent works of Gawedzkii and Kupiane n [Phys. Rev. Lett, 75, 3608 (1995)], and Chertkov er al. [Phys. Rev. E 52, 4924 (1995)]. It is shown that in this limit the fourth-order mo ment of the scalar difference is completely described in terms of the second-order moment and the scalar dissipation rate correlation functi on.