Advection of a passive scalar near two dimensions

摘要

The model of advection of a passive scalar in turbulent velocity field generated by the stochastically forced Navier-Stokes equation has been studied by means of the quantum field theoretical renormalization group near two dimensions. A perturbative two-parameter expansion scheme, the parameters of which are the deviation of the spatial dimension and the deviation of the exponent of the powerlike correlation function of the random force from their critical values, has been used in one-loop approximation. It is shown that the fixed points of the renormalization group are independent of the parameters of random injection of the passive scalar. The asymptotic behavior of velocity-velocity and scalar-scalar correlation functions has been calculated at leading order in the two-parameter expansion at the kinetic fixed point associated with the Kolmogorov scaling regime. In this regime the values of the inverse Prandtl number, the Kolmogorov constant, and the Obukhov-Corrsin constant have been calculated at leading order in the double expansion for d greater than or equal to 2. [References: 37]