Stability of scaling regimes in d >= 2 developed turbulence with weak anisotropy - art. no. 016312

Fully developed turbulence with weak anisotropy is investigated by means of the renormalization group approach and double expansion regularization for dimensions d greater than or equal to 2. Some modification of the standard minimal subtraction scheme has been used to analyze the stability of the K olmogorov scaling regime which is governed by the renormalization group fix ed point. This fixed point is unstable at d = 2; thus the infinitesimally w eak anisotropy destroys the above scaling regime in two-dimensional space. The restoration of the stability of this fixed point, under a transition fr om d = 2 to 3, is demonstrated at a borderline dimension 2 < d(c) < 3. The results are in qualitative agreement with results recently obtained in the framework of a typical analytical regularization scheme.