### Abstract

The asymptotic expansions for (1) the slow changes in particle number/energy density; namely, the kinetic equation, (2) frequency renormalization; and (3) the nth-order structure functions for wave turbulence systems are almost always nonuniform at either small or large length scales. The manifestation of this nonuniformity is fully nonlinear behavior either in the form of localized structures (coherent structures, shocks) or condensates (nonzero mean over large distances). The result is intermittent behavior dominated by large fluctuation events, anomolous scaling, and far from joint Gaussian statistics. Despite this unexpected surprise, and it is a surprise considering that wave turbulence has been the subject of continuous and intense investigation for several decades, wave turbulence still offers an advantage over systems that are nonlinear over all scales. The advantage is that the nature of the fully nonlinear behavior often can be identified, which gives us reasonable hope that wave turbulent systems may be treated as a two species gas of random wavetrains and randomly occurring coherent structures.

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

Pages (from-to) | 39-64 |

Number of pages | 26 |

Journal | Studies in Applied Mathematics |

Volume | 108 |

Issue number | 1 |

DOIs | |

State | Published - Jan 2002 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

**Wave turbulence is almost always intermittent at either small or large scales.** / Newell, Alan C.

Research output: Contribution to journal › Article

*Studies in Applied Mathematics*, vol. 108, no. 1, pp. 39-64. https://doi.org/10.1111/1467-9590.01422

}

TY - JOUR

T1 - Wave turbulence is almost always intermittent at either small or large scales

AU - Newell, Alan C

PY - 2002/1

Y1 - 2002/1

N2 - The asymptotic expansions for (1) the slow changes in particle number/energy density; namely, the kinetic equation, (2) frequency renormalization; and (3) the nth-order structure functions for wave turbulence systems are almost always nonuniform at either small or large length scales. The manifestation of this nonuniformity is fully nonlinear behavior either in the form of localized structures (coherent structures, shocks) or condensates (nonzero mean over large distances). The result is intermittent behavior dominated by large fluctuation events, anomolous scaling, and far from joint Gaussian statistics. Despite this unexpected surprise, and it is a surprise considering that wave turbulence has been the subject of continuous and intense investigation for several decades, wave turbulence still offers an advantage over systems that are nonlinear over all scales. The advantage is that the nature of the fully nonlinear behavior often can be identified, which gives us reasonable hope that wave turbulent systems may be treated as a two species gas of random wavetrains and randomly occurring coherent structures.

AB - The asymptotic expansions for (1) the slow changes in particle number/energy density; namely, the kinetic equation, (2) frequency renormalization; and (3) the nth-order structure functions for wave turbulence systems are almost always nonuniform at either small or large length scales. The manifestation of this nonuniformity is fully nonlinear behavior either in the form of localized structures (coherent structures, shocks) or condensates (nonzero mean over large distances). The result is intermittent behavior dominated by large fluctuation events, anomolous scaling, and far from joint Gaussian statistics. Despite this unexpected surprise, and it is a surprise considering that wave turbulence has been the subject of continuous and intense investigation for several decades, wave turbulence still offers an advantage over systems that are nonlinear over all scales. The advantage is that the nature of the fully nonlinear behavior often can be identified, which gives us reasonable hope that wave turbulent systems may be treated as a two species gas of random wavetrains and randomly occurring coherent structures.

UR - http://www.scopus.com/inward/record.url?scp=0036420714&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0036420714&partnerID=8YFLogxK

U2 - 10.1111/1467-9590.01422

DO - 10.1111/1467-9590.01422

M3 - Article

VL - 108

SP - 39

EP - 64

JO - Studies in Applied Mathematics

JF - Studies in Applied Mathematics

SN - 0022-2526

IS - 1

ER -