Relative Dispersion on the Inner Shelf: Evidence of a Batchelor Regime

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  • 1 Scripps Institution of Oceanography, La Jolla, California, USA
  • 2 Naval Post Graduate School, Monterey, California, USA
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Abstract

Oceanographic relative dispersion Dr2 (based on drifter separations r) has been extensively studied mostly finding either Richardson-Obukhov (Dr2 ~ t3) or enstrophy cascade (Dr2 ~ exp(t)) scaling. Relative perturbation dispersion (Dr2, based on perturbation separation rr0 where r0 is the initial separation) has a Batchelor scaling (Dr2 ~ t2) for times less than the r0-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, CA in water depths ≤ 40 m. From 12 releases of ≈ 18 drifters per release, perturbuation and regular relative dispersion over ≈ 4 h are calculated for 250 ≤ r0 ≤ 1500 m for each release and the entire experiment. The perturbation dispersion Dr2 is consistent with Batchelor scaling for the first 1000-3000 s with larger r0 yielding stronger dispersion and larger Batchelor times. At longer times, Dr2 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 Dr2 as the correlations between initial and later separations are significant at short time scaling as ~ t Thus, previous studies investigating Dr2(t) are potentially aliased by initial separation effects not present in the perturbation dispersion Dr2(t). As the underlying turbulent velocity wavenumber spectra is inferred from the dispersion power law time dependence, analysis of both Dr2 and Dr2 is critical.

Corresponding author address: Matthew S Spydell, Scripps Institution of Oceanography, UCSD, 9500 Gilman Dr., La Jolla, CA 92093-0209, mspydell@ucsd.edu

Abstract

Oceanographic relative dispersion Dr2 (based on drifter separations r) has been extensively studied mostly finding either Richardson-Obukhov (Dr2 ~ t3) or enstrophy cascade (Dr2 ~ exp(t)) scaling. Relative perturbation dispersion (Dr2, based on perturbation separation rr0 where r0 is the initial separation) has a Batchelor scaling (Dr2 ~ t2) for times less than the r0-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, CA in water depths ≤ 40 m. From 12 releases of ≈ 18 drifters per release, perturbuation and regular relative dispersion over ≈ 4 h are calculated for 250 ≤ r0 ≤ 1500 m for each release and the entire experiment. The perturbation dispersion Dr2 is consistent with Batchelor scaling for the first 1000-3000 s with larger r0 yielding stronger dispersion and larger Batchelor times. At longer times, Dr2 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 Dr2 as the correlations between initial and later separations are significant at short time scaling as ~ t Thus, previous studies investigating Dr2(t) are potentially aliased by initial separation effects not present in the perturbation dispersion Dr2(t). As the underlying turbulent velocity wavenumber spectra is inferred from the dispersion power law time dependence, analysis of both Dr2 and Dr2 is critical.

Corresponding author address: Matthew S Spydell, Scripps Institution of Oceanography, UCSD, 9500 Gilman Dr., La Jolla, CA 92093-0209, mspydell@ucsd.edu
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