  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.
