  Due to the nonlinear interaction between different flow patterns, for
instance, ocean current, meso-scale eddies, waves, etc, the movement of ocean
is extremely complex, where a multiscale statistics is then relevant. In this
work, a high time-resolution velocity with a time step 15 minutes obtained by
the Lagrangian drifter deployed in the Gulf of Mexico (GoM) from July 2012 to
October 2012 is considered. The measured Lagrangian velocity correlation
function shows a strong daily cycle due to the diurnal tidal cycle.
  The estimated Fourier power spectrum $E(f)$ implies a dual-power-law behavior
which is separated by the daily cycle. The corresponding scaling exponents are
close to $-1.75$ and $-2.75$ respectively for the time scale larger (resp.
$0.1\le f\le 0.4\,{day^{-1}}$) and smaller (resp. $2\le f\le 8\,{day^{-1}}$)
than 1 day. A Hilbert-based approach is then applied to this data set to
identify the possible multifractal property of the cascade process. The results
show an intermittent dynamics for the time scale larger than 1 day, while a
less intermittent dynamics for the time scale smaller than 1 day. It is
speculated that the energy is partially injected via the diurnal tidal movement
and then transferred to larger and small scales through a complex cascade
process, which needs more studies in the near future.
