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.
In: Studies in Applied Mathematics, Vol. 108, No. 1, 01.2002, p. 39-64.Research output: Contribution to journal › Article
}
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.
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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 -