The Instanton Solution of Forced Burgers Equation in Polyakov’s Approach
نویسنده
چکیده
We calculate the coefficients of the operator product expansion (OPE), in Polyakov’s approach for Burgers turbulence. We show that the OPE has to be generelized and it is shown that the extra term gives us the instanton solution (shock solution) of Burgers equation. We consider the effect of the new-term in the OPE, on the right and lefttail of probability distribution function (PDF). It is shown that the left-tail of PDF, where is dominated by the well-separated shocks behaves as W (u) ∼ u−7/2. Finally we calculate the assymptotic behaviour of the N-point generating function of the velocity field, using the new OPE. PACS numbers 47.27.AK, 47.27.Jv
منابع مشابه
The Exact Two–Point Correlation Functions of Forced Burgers Equation in Two and Three–Dimensions
We generelize the Polyakov’s approach for Burgers turbulence in higher dimensions. In this respect, we write the operator product expansion and find the exact two–point functions of the Burgers equation in two and three–dimensions. We show that the angular dependence of the correlation functions satisfy the same equation, which is found in the instanton approach. PACS numbers 47.27.AK, 47.27.Jv
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