Relative Dispersion On The Inner Shelf: Evidence Of A Batchelor Regime

Oceanographic relative dispersion D-r(2) (based on drifter separations r) has been extensively studied, mostly finding either Richardson-Obukhov (D-r(2)similar to t(3)) or enstrophy cascade [D-r(2)similar to exp(t)] scaling. Relative perturbation dispersion D-r '(2) (based on perturbation separation r - r(0), where r(0) is the initial separation) has a Batchelor scaling (D-r '(2)similar to t(2)) for times less than the r(0)-dependent Batchelor time. Batchelor scaling has received little oceanographic attention. GPS-equipped surface drifters were repeatedly deployed on the Inner Shelf off of Pt. Sal, California, in water depths <= 40 m. From 12 releases of approximate to 18 drifters per release, perturbation and regular relative dispersion over approximate to 4 h are calculated for 250 <= r(0) <= 1500 m for each release and the entire experiment. The perturbation dispersion Dr ' 2 is consistent with Batchelor scaling for the first 1000-3000 s with larger r(0) yielding stronger dispersion and larger Batchelor times. At longer times, Dr ' 2 and scale-dependent diffusivities begin to suggest Richardson-Obukhov scaling. This applies to both experiment averaged and individual releases. For individual releases, nonlinear internal waves can modulate dispersion. Batchelor scaling is not evident in D-r(2) as the correlations between initial and later separations are significant at short time scaling as similar to t. Thus, previous studies investigating D-r(2)(t) are potentially aliased by initial separation effects not present in the perturbation dispersion D-r '(2)(t). As the underlying turbulent velocity wavenumber spectra is inferred from the dispersion power law time dependence, analysis of both D-r(2) and D '(2)(r) is critical.