Critical dimensions and perturbation theory for randomly stirred fluids.

Abstract

The randomly stirred model of DeDominicis and Martin [Phys. Rev. A 19, 419 (1979)] is studied. It is shown from considerations of energy transfer that y=4 corresponds to the Kolmogorov model, when the wave-number (k) dependence of the stirring force is ${k}^{\mathrm{\ensuremath{-}}D+4\mathrm{\ensuremath{-}}y}$, D being the dimensionality of space. It is seen that the correlation function has to be non-Lorentzian for y\ensuremath{\ne}2-D, and hence the perturbation theory has to be a double-power series in y and D-2, in accordance with the recent calculation [Phys. Rev. A 36, 3322 (1987)] using the field-theoretic renormalization group. Amplitude ratios are calculated to the lowest order.