Renormalization group in the theory of two-dimensional turbulence: Instability of the fixed point with respect to weak anisotropy

A statistical model of fully developed turbulence in two-dimensional space is considered by means of the renormalization group method in the weak anisotropy approximation. It is shown that the corresponding fixed point of the renormalization group equations is not infrared stable. Hence, the weak, anisotropy approximation is not valid for describing two-dimensional turbulence. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 112, No. 3, pp. 417–427, September, 1997.