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Due to the nonlinear interaction between different flow patterns, forinstance, ocean current, meso-scale eddies, waves, etc, the movement of oceanis extremely complex, where a multiscale statistics is then relevant. In thiswork, a high time-resolution velocity with a time step 15 minutes obtained bythe Lagrangian drifter deployed in the Gulf of Mexico (GoM) from July 2012 toOctober 2012 is considered. The measured Lagrangian velocity correlationfunction shows a strong daily cycle due to the diurnal tidal cycle.  The estimated Fourier power spectrum $E(f)$ implies a dual-power-law behaviorwhich is separated by the daily cycle. The corresponding scaling exponents areclose 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 toidentify the possible multifractal property of the cascade process. The resultsshow an intermittent dynamics for the time scale larger than 1 day, while aless intermittent dynamics for the time scale smaller than 1 day. It isspeculated that the energy is partially injected via the diurnal tidal movementand then transferred to larger and small scales through a complex cascadeprocess, which needs more studies in the near future.

Lagrangian Statistics and Intermittency in Gulf of Mexico