## Abstract

We study analytically and numerically structure functions S_{q}(r) in the one-dimensional Burgers equation, driven by noise with variance ∞|k|^{β} in Fourier space, (a) when the noise is cut off at some length l_{∞} and (b) when it is not. We present exact relations satisfied by S_{3}(r) (the von Karman-Howarth relation) and S_{4}(r) that form the basis of our analysis. When there is a cutoff length, shocks occur and S_{q}(r) ∞r for q≥2 for δ<r <l_{c} where δ is the shock thickness for all β between -1 and 2. We deduce this behavior from the exact relations along with an ansatz that is verified numerically. When there is no cutoff length, multifractal behavior is known to occur only when β<0. Through a study of exact expression S_{3} we highlight the difference between ltifractality in this case as compared to the case with a cutoff.

Original language | English |
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Pages (from-to) | 227-234 |

Number of pages | 8 |

Journal | Physical Review E |

Volume | 56 |

Issue number | 1 SUPPL. A |

DOIs | |

State | Published - 1997 |

Externally published | Yes |