  The EOLE Experiment is revisited to study turbulent processes in the lower
stratosphere circulation from a Lagrangian viewpoint and resolve a discrepancy
on the slope of the atmospheric energy spectrum between the work of Morel and
Larcheveque (1974) and recent studies using aircraft data. Relative dispersion
of balloon pairs is studied by calculating the Finite Scale Lyapunov Exponent,
an exit time-based technique which is particularly efficient in cases where
processes with different spatial scales are interfering. Our main result is to
reconciliate the EOLE dataset with recent studies supporting a k^{-5/3} energy
spectrum in the range 100-1000 km. Our results also show exponential separation
at smaller scale, with characteristic time of order 1 day, and agree with the
standard diffusion of about 10^7 m^2/s at large scales. A still open question
is the origin of a k^{-5/3} spectrum in the mesoscale range, between 100 and
1000 km.
