1998/02/11 by D. Sornette, Sornette, D. · 2 citations
Economics, Econometrics and Finance · Engineering · Environmental Science · Physics and Astronomy · #Climate variability and models #Complex Systems and Time Series Analysis #FOS: Physical sciences #Fluid Dynamics and Turbulent Flows #Statistical Mechanics (cond-mat.stat-mech) #cond-mat.stat-mech
paper · pdf · doi:10.48550/arxiv.cond-mat/9802121
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)
arxiv created 1998/02/11 · openalex publication_date 1998/02/11 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 rc at which the dissipation rate is the largest in a given turn-over time series. This specific scale rc 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 Sp(r) = Ap (εr)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.