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Dynamical scaling and the finite-capacity anomaly in three-wave turbulence
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Connaughton, Colm and Newell, Alan C., 1941-. (2010) Dynamical scaling and the finite-capacity anomaly in three-wave turbulence. Physical Review E (Statistical, Nonlinear, and Soft Matter Physics), Vol.81 (No.3). Article no. 036303. ISSN 1539-3755
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Official URL: http://dx.doi.org/10.1103/PhysRevE.81.036303
Abstract
We present a systematic study of the dynamical scaling process leading to the establishment of the Kolmogorov-Zakharov (KZ) spectrum in weak three-wave turbulence. In the finite-capacity case, in which the transient spectrum reaches infinite frequency in finite time, the dynamical scaling exponent is anomalous in the sense that it cannot be determined from dimensional considerations. As a consequence, the transient spectrum preceding the establishment of the steady state is steeper than the KZ spectrum. Constant energy flux is actually established from right to left in frequency space after the singularity of the transient solution. From arguments based on entropy production, a steeper transient spectrum is heuristically plausible.
| Item Type: | Journal Article |
|---|---|
| Subjects: | Q Science > QC Physics |
| Divisions: | Faculty of Science > Centre for Complexity Science Faculty of Science > Mathematics |
| Library of Congress Subject Headings (LCSH): | Turbulence, Waves -- Mathematical models, Scaling laws (Statistical physics) |
| Journal or Publication Title: | Physical Review E (Statistical, Nonlinear, and Soft Matter Physics) |
| Publisher: | American Physical Society |
| ISSN: | 1539-3755 |
| Date: | March 2010 |
| Volume: | Vol.81 |
| Number: | No.3 |
| Number of Pages: | 6 |
| Page Range: | Article no. 036303 |
| Identification Number: | 10.1103/PhysRevE.81.036303 |
| Status: | Peer Reviewed |
| Publication Status: | Published |
| Access rights to Published version: | Restricted or Subscription Access |
| Related URLs: | |
| References: | [1] V. Zakharov, V. Lvov, and G. Falkovich, Kolmogorov Spectra of Turbulence (Springer-Verlag, Berlin, 1992). [2] C. Connaughton, A. Newell, and S. Nazarenko, Physica D 184, 86 (2003). [3] A. Newell, S. Nazarenko, and L. Biven, Physica D 152- 153, 520 (2001). [4] C. Connaughton, Physica D 238, 2282 (2009), arxiv: cond-mat/0905.1589. [5] C. Connaughton and Y. Pomeau, Comptes Rendus Physique 5, 91 (2004). [6] R. Lacaze, P. Lallemand, Y. Pomeau, and S. Rica, Phys- ica D 152, 779 (2001). [7] G. Falkovich and A. Shafarenko, J. Nonlinear Sci. 1, 452 (1991). [8] S. Galtier, S. Nazarenko, A. Newell, and A. Pouquet, J. Plasma Phys. 63, 447 (2000). [9] C. Connaughton and S. Nazarenko, Phys. Rev. Lett. 92, 044501 (2004). [10] C. Connaughton, A. Newell, and Y. Pomeau, Physica D 184, 64 (2003). [11] C. Connaughton and P. Krapivsky (2009), arXiv : 0909.5399v1 [cond-mat.stat-mech] [12] G. Barenblatt, Scaling, self-similarity, and intermediate asymptotics (CUP, Cambridge, 1996). [13] F. Leyvraz, Phys. Reports 383, 95 (2003). [14] C. Connaughton, R. Rajesh, and O. Zaboronski, Phys. Rev. E 69, 061114 (2004), cond-mat/0310063. [15] S. Cueille and C. Sire, Phys. Rev. E 55, 5465 (1997). [16] M. Lee, J. Phys. A: Math. Gen. 34, 10219 (2001). [17] S. Bhattacharjee and F. Seno, J. Phys. A–Math. Gen. 34, 6375 (2001). |
| URI: | http://wrap.warwick.ac.uk/id/eprint/6140 |
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