### Abstract

We provide mathematical justification of the emergence of large-scale coherent structure in a two-dimensional fluid system under small-scale random bombardments with small forcing and appropriate scaling assumptions. The analysis shows that the large-scale structure emerging out of the small-scale random forcing is not the one predicted by equilibrium statistical mechanics. But the error is very small, which explains earlier successful prediction of the large-scale structure based on equilibrium statistical mechanics.

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

Pages (from-to) | 467-500 |

Number of pages | 34 |

Journal | Communications on Pure and Applied Mathematics |

Volume | 59 |

Issue number | 4 |

State | Published - Apr 2006 |

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### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

*Communications on Pure and Applied Mathematics*,

*59*(4), 467-500.

**The emergence of large-scale coherent structure under small-scale random bombardments.** / Majda, Andrew; Wang, Xiaoming.

Research output: Contribution to journal › Article

*Communications on Pure and Applied Mathematics*, vol. 59, no. 4, pp. 467-500.

}

TY - JOUR

T1 - The emergence of large-scale coherent structure under small-scale random bombardments

AU - Majda, Andrew

AU - Wang, Xiaoming

PY - 2006/4

Y1 - 2006/4

N2 - We provide mathematical justification of the emergence of large-scale coherent structure in a two-dimensional fluid system under small-scale random bombardments with small forcing and appropriate scaling assumptions. The analysis shows that the large-scale structure emerging out of the small-scale random forcing is not the one predicted by equilibrium statistical mechanics. But the error is very small, which explains earlier successful prediction of the large-scale structure based on equilibrium statistical mechanics.

AB - We provide mathematical justification of the emergence of large-scale coherent structure in a two-dimensional fluid system under small-scale random bombardments with small forcing and appropriate scaling assumptions. The analysis shows that the large-scale structure emerging out of the small-scale random forcing is not the one predicted by equilibrium statistical mechanics. But the error is very small, which explains earlier successful prediction of the large-scale structure based on equilibrium statistical mechanics.

UR - http://www.scopus.com/inward/record.url?scp=33644998524&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33644998524&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:33644998524

VL - 59

SP - 467

EP - 500

JO - Communications on Pure and Applied Mathematics

JF - Communications on Pure and Applied Mathematics

SN - 0010-3640

IS - 4

ER -