Stability of scaling regimes in $d\geq 2$ developed turbulence with weak anisotropy

Details Stability of scaling regimes in $d\geq 2$ developed turbulence with weak anisotropy Stability of scaling regimes in $d\geq 2$ developed turbulence with weak anisotropy

2001-01-29

arxiv.org/abs/nlin/0101050v1

Phys.Rev. E64 (2001) 016312

Nonlinear Sciences

Chaotic Dynamics

23 pages, 2 figures

Scientific paper

10.1103/PhysRevE.64.016312

The fully developed turbulence with weak anisotropy is investigated by means of renormalization group approach (RG) and double expansion regularization for dimensions $d\ge 2$. Some modification of the standard minimal substraction scheme has been used to analyze stability of the Kolmogorov scaling regime which is governed by the renormalization group fixed point. This fixed point is unstable at $d=2$; thus, the infinitesimally weak anisotropy destroyes above scaling regime in two-dimensional space. The restoration of the stability of this fixed point, under transition from $d=2$ to $d=3,$ has been demonstrated at borderline dimension $ 2

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