### Abstract

In classical work, Mathéron and the Marsilly showed that superdiffusive scaling of mean-square displacements occurs in transport diffusion for stratified flows with steady simple shear layers and long-range spatial correlations. More recently the authors have calculated a formula for the non-Gaussian large-scale long-time renormalized Green function for these problems. Here the scaling laws and renormalized Green functions for diffusion in "nearly stratified" flows are studied; in such flows the simple shear layer with long-range correlations is perturbed by incompressible flows with short-range correlations. Here it is established that these flows belong to the same universality class as the simple shear layers, with a renormalized Green function with a similar structure but reflecting homogenization by the transverse displacements. The tools in the analysis involve a modification of homogenization theory and also rigorous diagrammatic perturbation theory.

Original language | English (US) |
---|---|

Pages (from-to) | 689-729 |

Number of pages | 41 |

Journal | Journal of Statistical Physics |

Volume | 69 |

Issue number | 3-4 |

DOIs | |

State | Published - Nov 1992 |

### Fingerprint

### Keywords

- anomalous transport
- homogenization
- random flows
- Superdiffusion

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Physics and Astronomy(all)
- Mathematical Physics

### Cite this

**Superdiffusion in nearly stratified flows.** / Avellaneda, Marco; Majda, Andrew J.

Research output: Contribution to journal › Article

*Journal of Statistical Physics*, vol. 69, no. 3-4, pp. 689-729. https://doi.org/10.1007/BF01050431

}

TY - JOUR

T1 - Superdiffusion in nearly stratified flows

AU - Avellaneda, Marco

AU - Majda, Andrew J.

PY - 1992/11

Y1 - 1992/11

N2 - In classical work, Mathéron and the Marsilly showed that superdiffusive scaling of mean-square displacements occurs in transport diffusion for stratified flows with steady simple shear layers and long-range spatial correlations. More recently the authors have calculated a formula for the non-Gaussian large-scale long-time renormalized Green function for these problems. Here the scaling laws and renormalized Green functions for diffusion in "nearly stratified" flows are studied; in such flows the simple shear layer with long-range correlations is perturbed by incompressible flows with short-range correlations. Here it is established that these flows belong to the same universality class as the simple shear layers, with a renormalized Green function with a similar structure but reflecting homogenization by the transverse displacements. The tools in the analysis involve a modification of homogenization theory and also rigorous diagrammatic perturbation theory.

AB - In classical work, Mathéron and the Marsilly showed that superdiffusive scaling of mean-square displacements occurs in transport diffusion for stratified flows with steady simple shear layers and long-range spatial correlations. More recently the authors have calculated a formula for the non-Gaussian large-scale long-time renormalized Green function for these problems. Here the scaling laws and renormalized Green functions for diffusion in "nearly stratified" flows are studied; in such flows the simple shear layer with long-range correlations is perturbed by incompressible flows with short-range correlations. Here it is established that these flows belong to the same universality class as the simple shear layers, with a renormalized Green function with a similar structure but reflecting homogenization by the transverse displacements. The tools in the analysis involve a modification of homogenization theory and also rigorous diagrammatic perturbation theory.

KW - anomalous transport

KW - homogenization

KW - random flows

KW - Superdiffusion

UR - http://www.scopus.com/inward/record.url?scp=21144480740&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=21144480740&partnerID=8YFLogxK

U2 - 10.1007/BF01050431

DO - 10.1007/BF01050431

M3 - Article

AN - SCOPUS:21144480740

VL - 69

SP - 689

EP - 729

JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

SN - 0022-4715

IS - 3-4

ER -