Discrete scale invariance in turbulence?
| dc.creator | Sornette, D. | |
| dc.date | 1998-02-11 | |
| dc.date.accessioned | 2026-07-07T03:09:56Z | |
| dc.date.available | 2026-07-07T03:09:56Z | |
| dc.description | Based on theoretical argument and experimental evidence, we conjecture that structure functions of turbulent times series exhibit log-periodic modulations decorating their power law dependence. In order to provide ironclad experimental evidence, we stress the need for novel methods of averaging and propose a novel ``canonical'' averaging scheme for the analysis of structure factors of turbulent flows. The strategy is to determine the scale $r_c$ at which the dissipation rate is the largest in a given turn-over time series. This specific scale $r_c$ translates into a specific ``phase'' in the logarithm of the scale which, when used as the origin, allows one to phase up the different measurements of a structure factor $S_p(r) = A_p (\barεr)^{p/3}$ in different turn-over time realizations. We expect, as in Laplacian growth and in rupture, that the log-periodic oscillations will be reinforced by this canonical averaging. Demonstrating unambiguously the presence of log-periodicity and thus of discrete scale invariance (DSI) in turbulent time-series would provide an important step towards a direct demonstration of the Kolmogorov cascade or at least of its hierarchical imprint. | |
| dc.description | 3 pages, to appear in the Proceedings of the Seventh European Turbulence Conference (ETC-7), June 30-July 3 (1998) (Published by Kluwer, U. Frisch, editor) | |
| dc.identifier | https://arxiv.org/abs/cond-mat/9802121 | |
| dc.identifier | http://arxiv.org/abs/cond-mat/9802121 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/28086 | |
| dc.subject | Statistical Mechanics | |
| dc.title | Discrete scale invariance in turbulence? | |
| dc.type | text |