Phys. Rev. E 58, 5776–5795 (1998)Instanton for the Kraichnan passive scalar problemReceived 2 June 1998; published in the issue dated November 1998 We consider high-order correlation functions of the passive scalar in the Kraichnan model. Using the instanton formalism we find the scaling exponents ζn of the structure functions Sn for n≫1 under the additional condition dζ2≫1 (where d is the dimensionality of space). At n<nc [where nc=dζ2/2(2-ζ2)] the exponents are ζn=(ζ2/4)(2n-n2/nc), while at n>nc they are n independent: ζn=ζ2nc/4. We also estimate n-dependent factors in Sn, particularly their behavior at n close to nc. © 1998 The American Physical Society URL:
http://link.aps.org/doi/10.1103/PhysRevE.58.5776
DOI:
10.1103/PhysRevE.58.5776
PACS:
47.27.Ak, 05.20.-y, 05.40.+j, 47.10.+g
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