Instanton for the Kraichnan Passive Scalar Problem

Details Instanton for the Kraichnan Passive Scalar Problem Instanton for the Kraichnan Passive Scalar Problem

1998-03-12

arxiv.org/abs/chao-dyn/9803018v2

Phys. Rev. E, 58, 5776, (1998)

Nonlinear Sciences

Chaotic Dynamics

20 pages, RevTex

Scientific paper

10.1103/PhysRevE.58.5776

We consider high-order correlation functions of the passive scalar in the Kraichnan model. Using the instanton formalism we find the scaling exponents $\zeta_n$ of the structure functions $S_n$ for $n\gg1$ under the additional condition $d\zeta_2\gg1$ (where $d$ is the dimensionality of space). At $nn_c$ they are $n$-independent: $\zeta_n=\zeta_2 n_c/4$. We also estimate $n$-dependent factors in $S_n$, particularly their behavior at $n$ close to $n_c$.

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