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Paper   IPM / Physic / 6556
School of Physics
  Title:   Logarithmic Correlation Functions in Two-Dimensional Turbulence
1.  S. Rouhani
2.  M.R. Rahimi Tabar
  Status:   Published
  Journal: Phys. Lett. A
  No.:  52
  Vol.:  224
  Year:  1997
  Pages:   331-336
  Supported by:  IPM
We consider the correlation functions of two-dimensional turbulence in the presence and absence of a three-dimensional perturbation, by means of conformal field theory. In the presence of three-dimensional perturbation, we show that in the strong coupling limit of a small scale random force, there is some logarithmic factor in the correlation functions of velocity stream functions. We show that the logarithmic conformal field theory c8,1 describes the 2D-turbulence both in the absence and in the presence of the perturbation. We obtain the energy spectrum E(k) ∼ k−5.125 ln (k) for perturbed 2D-turbulence and E(k) ∼ k−5 ln (k) for unperturbed turbulence. Recent numerical simulation and experimental results confirm our prediction.

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