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The fully developed turbulence with weak anisotropy is investigated by meansof renormalization group approach (RG) and double expansion regularization fordimensions $d\ge 2$. Some modification of the standard minimal substractionscheme has been used to analyze stability of the Kolmogorov scaling regimewhich is governed by the renormalization group fixed point. This fixed point isunstable at $d=2$; thus, the infinitesimally weak anisotropy destroyes abovescaling regime in two-dimensional space. The restoration of the stability ofthis fixed point, under transition from $d=2$ to $d=3,$ has been demonstratedat borderline dimension $ 2<d_c<3$. The results are in qualitative agreementwith ones obtained recently in the framework of the usual analyticalregularization scheme.Comment: 23 pages, 2 figure

physical review. e, statistical physics, plasmas, fluids, and related interdisciplinary topics

Stability of scaling regimes in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>d</mml:mi><mml:mo>&gt;~</mml:mo><mml:mn>2</mml:mn></mml:math>developed turbulence with weak anisotropy

Stability of scaling regimes ind>~2developed turbulence with weak anisotropy