Aggregation-Fragmentation Processes and Wave Kinetics
| Autor: | Connaughton, C., Krapivsky, P. L. |
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| Rok vydání: | 2009 |
| Předmět: | |
| Zdroj: | Phys. Rev. E 81, 035303(R), 2010 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1103/PhysRevE.81.035303 |
| Popis: | There is a formal correspondence between the isotropic 3-wave kinetic equation and the rate equations for a non-linear fragmentation--aggregation process. We exploit this correspondence to study analytically the time evolution of the wave frequency power spectrum. Specifically, we analyzed a 3-wave turbulence in which the wave interaction kernel is a constant. We consider both forced and decaying turbulence. In the forced case, the scaling function diverges as $x^{-3/2}$ as expected from Kolmogorov-Zakharov theory. In the decaying case, the scaling function exhibits non-trivial, and hitherto unexpected, divergence with both algebraic and logarithmic spectral exponents which we calculate. This divergence leads to non-trivial decay laws for the total wave action and the number of primary waves. All theoretical predictions are verified with high quality numerical simulations of the 3-wave kinetic equation. Comment: 4 pages, 5 figures |
| Databáze: | arXiv |
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