Physics – Condensed Matter – Statistical Mechanics
Scientific paper
1998-02-11
Physics
Condensed Matter
Statistical Mechanics
3 pages, to appear in the Proceedings of the Seventh European Turbulence Conference (ETC-7), June 30-July 3 (1998) (Published
Scientific paper
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 $S_p(r) = A_p (\bar\epsilon r)^{p/3}$ 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.
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