The Instanton Solution of Forced Burgers Equation in Polyakov's Approach

Details The Instanton Solution of Forced Burgers Equation in Polyakov's Approach The Instanton Solution of Forced Burgers Equation in Polyakov's Approach

1997-07-14

arxiv.org/abs/hep-th/9707127v1

Physics

High Energy Physics

High Energy Physics - Theory

10 pages, latex, no figures

Scientific paper

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 generalized 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 left-tail 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)\sim u^{-7/2}$. Finally we calculate the assymptotic behaviour of the N-point generating function of the velocity field, using the new OPE.

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