## Abstract

The anomalous scaling behavior of the nth-order correlation functions F_{n} of the Kraichnan model of turbulent passive scalar advection is believed to be dominated by the homogeneous solutions (zero modes) of the Kraichnan equation B_{n}F_{n} = 0. In this paper we present an extensive analysis of the simplest (nontrivial) case of n = 3 in the isotropic sector. The main parameter of the model, denoted as ζ_{h}, characterizes the eddy diffusivity and can take values in the interval 0≤ζ_{h}≤2. After choosing appropriate variables we can present nonperturbative numerical calculations of the zero modes in a projective two dimensional circle. In this presentation it is also very easy to perform perturbative calculations of the scaling exponent ζ_{3} of the zero modes in the limit ζ_{h}→0, and we display quantitative agreement with the nonperturbative calculations in this limit. Another interesting limit is ζ_{h}→2. This second limit is singular, and calls for a study of a boundary layer using techniques of singular perturbation theory. Our analysis of this limit shows that the scaling exponent ζ_{3} vanishes as √ζ_{2}/|Inζ_{2}, where ζ_{2} is the scaling exponent of the second-order correlation function. In this limit as well, perturbative calculations are consistent with the nonperturbative calculations.

Original language | American English |
---|---|

Pages (from-to) | 406-416 |

Number of pages | 11 |

Journal | Physical Review E |

Volume | 56 |

Issue number | 1 SUPPL. A |

DOIs | |

State | Published - 1997 |

Externally published | Yes |