Logarithmic correlation functions in two-dimensional turbulence |
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| Institution: | 1. Institute for Studies in Theoretical Physics and Mathematics, P.O. Box 19395-5531, Tehran, Iran;2. Department of Physics, Iran University of Science and Technology, Narmak, Tehran 16844, Iran;3. Department of Physics, Sharif University of Technology, P.O. Box 11365-9161, Tehran, Iran;1. Division of Biomedical & Life Sciences, Faculty of Health & Medicine, Lancaster University, Lancaster LA1 4YW, UK;2. Department of Management Science, Management School, Lancaster University, Lancaster LA1 4YW, UK;1. Aix Marseille Univ, CNRS, BIP, IMM, Marseille, France;2. Department of Molecular Biosciences, University of Kansas, Lawrence, KS 66045, USA |
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| Abstract: | 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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