The relationships between Eulerian and Lagrangian (or drifter) diffusivities and spectra are explored in detail using the Lagrangian correlation predictor due to Corrsin (1959). The analysis, applicable to homogeneous, isotropic velocity fields shows that an important dimensionless parameter in the Euler-Lagrange transformations is the ratio α of Eulerian integral TE to advective Ta time scales. It is found that the diffusivity may be approximated to within 10% by the function qν2TE (q2 + α2)−1/2 where ν2 is the mean-square velocity component and q ≃ 0.63. This result is found to be insensitive to the shape of the Eulerian spectra. It is also shown that a (wavenumber)−3 energy spectrum may be identified in Lagrangian frequency space by a corresponding (frequency)−3 spectrum. The relationships between drifter and fixed current meter spectra and time-scales are also explored. It is suggested that for regions of strong mean flow, U > ν, that the diffusivity might well be approximated by q √3 νUTu where Tu is the mooring velocity time scale.
Middletown, John F.. 1985. "Drifter spectra and diffusivities." Journal of Marine Research 43, (1). https://elischolar.library.yale.edu/journal_of_marine_research/1763