1998/03/31 by E. Balkovsky, V. Lebedev, В. В. Лебедев · 2 citations
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Quantum chaos and dynamical systems #chao-dyn #nlin.CD
paper · pdf · doi:10.1103/physreve.58.5776
published as Phys. Rev. E, 58, 5776, (1998) · 20 pages, RevTex
arxiv created 1998/09/10 · openalex publication_date 1998/11/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider high-order correlation functions of the passive scalar in the Kraichnan model. Using the instanton formalism we find the scaling exponents \ensuremathζn of the structure functions Sn for n\ensuremath≫1 under the additional condition d\ensuremathζ2\ensuremath≫1 (where d is the dimensionality of space). At n<nc [where nc=d\ensuremathζ2/2(2\ensuremath-\ensuremathζ2)] the exponents are \ensuremathζn=(\ensuremathζ2/4)(2n\ensuremath-n2/nc), while at n>nc they are n independent: \ensuremathζn=\ensuremathζ2nc/4. We also estimate n-dependent factors in Sn, particularly their behavior at n close to nc.