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Relative dispersion in the Gulf Stream and its recirculation

Rick Lumpkin (Rick.Lumpkin@noaa.gov) National Oceanic and Atmospheric Administration (NOAA) Atlantic Oceanographic and Meteorological Laboratory (AOML) Miami, Florida USA. Relative dispersion in the Gulf Stream and its recirculation. CLIMODE PI workshop, 6-7 August 2008. Ensemble average.

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Relative dispersion in the Gulf Stream and its recirculation

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  1. Rick Lumpkin (Rick.Lumpkin@noaa.gov) National Oceanic and Atmospheric Administration (NOAA) Atlantic Oceanographic and Meteorological Laboratory (AOML) Miami, Florida USA Relative dispersion in the Gulf Stream and its recirculation CLIMODE PI workshop, 6-7 August 2008

  2. Ensemble average Ut Dispersion: x’ x

  3. Richardson’s 4/3 law Richardson (1926): observed smoke spreading from a stack. Realized that diffusion must be scale-dependent (bigger at larger separation distances). Proposed Obukov (1941): Richardson’s law is a result of energy cascade from large to small scales (inertial subrange) in 3D turbulence. 2D turbulence: energy cascade to large scale, enstrophy cascade to small scale (Kraichnan, 1967). Richardson’s law followed in energy cascade range; exponential growth of particle separation in enstrophy cascade range (Lin, 1972). Energy cascade Energy E(k) Enstrophy cascade Energy input Wavenumber k

  4. Ut Finite Scale Lyapunov Exponents (FSLEs) Separation distance d. x Pick l such that growth of d is given by (Exponential growth if l is constant, but more generally l can vary with d.)

  5. FSLEs, continued. Over interval (dn, dn+1) in which l is approximately constant, For dn+1 = adn, this becomes: where Dtn is the mean time for the separation distance to grow from dn to adn. Unlike dispersion, which averages the data in time, this approach averages the data in separation distance.

  6. Dispersion regimes Relative Dispersion FSLE Dispersion D2(t) l(d) Regime exp(l0t) l0exponential t2d-1ballistic t3d-2/3Richardson td-2diffusive From Haza et al., 2007

  7. Relative dispersion observations in the ocean LaCasce and Bower, 2000: float pairs in the western North Atlantic. Dispersion follows Richardson’s law from the smallest resolvable distance (>deformation radius of 20km) to 60—100km. LaCasce and Ohlmann, 2003: drifter pairs in the Gulf of Mexico. Separation is exponential at scales smaller than deformation radius(~45km). Richardson law behavior at larger scales.

  8. Limitations of earlier data LaCasce and Bower (2000), LaCasce and Ohlmann (2003) were forced to rely on chance pairs. Floats: not enough chance pairs at distances smaller than 1st Baroclinic Rossby radius. Drifters: Dense array allowed resolution at smaller scales, but Argos positioning system provided only a few fixes per day on average, with gaps as long as a day common. Do chance pairs present an unbiased sample of the statistics of the turbulent field? This cannot be tested without intentional pairs: pairs launched close to each other at various points in the turbulent field. What is the effect of undersampling in time? Higher frequency data is needed. Argos multisatellite processing: introduced January 2005. Mean time between fixes decreased from 6 hours to 1 hour.

  9. CLIMODE observations Drifter observations during February—March 2007 cruise, R/V KnorrGoal: measure dispersion, eddy fluxes

  10. 60 drifters deployed: 16 trios, 6 pairs. Median spacing of satellite fixes: 1.2 hours

  11. 60 drifters deployed: 16 trios, 6 pairs. One drifter failed. Median spacing of satellite fixes: 1.2 hours

  12. Ro2 300-500km rms displacement: 1.5km 55 pairs with earliest fixes <700m dispersion Solid black: zonal. Dashed black: meridional. (5.8104 m2/s) t (2.9104 m2/s) t Grey dashed: D2=(3.5109m2s3 )t3 (Richardson’s Law) Noise level of Argos positioning

  13. Evidence of exponential behavior at short times? Ro2 Dashed black:. 95% confidence

  14. FSLEs Stars: methodology of LaCasce (first crossing approach). Circles: methodology of Haza, Özgökmen (fastest crossing approach). Methodologies converge at large scales. Slopes very different at intermediate scales. Neither approach indicates exponential behavior (constant l) from the smallest scales to the first baroclinic Rossby radius, ~30 km (Chelton et al., 1998).

  15. Early behavior (<1.5km) 1—2 m/s 5—20 s 25 m2/s

  16. Long time behavior (>300km) Diffusive behavior, governed by a two-particle diffusivity of K=3—6 104 m2/s at separation scales greater than 300—500 km. This is consistent with a single-particle effective diffusivity of keff=1.5—3104 m2/s.

  17. Mean interpolated onto CLIMODE drifter positions: 1.6104 m2/s (std.dev. 7103) Mean semimajor axis: 5.8 104 m2/s. Single-particle diffusivities Davis (1991): Zhurbas and Oh (2003): Use minor principle component for robust scalar lateral diffusivity in presence of mean shear. Left: single-particle diffusivity from 1500 unique drifters in the Gulf Stream and recirculation region, 1989—present. Pair dispersion: keff=1.5—3104 m2/s. Comparison suggests that mean shear amplifies zonal pair spreading, but not meridional spreading, to lowest order.

  18. Intermediate behavior 1.5 km—300 km: Then diffusion Lagrangian structure function vs. separation distance for 55 CLIMODE drifter pairs. Inertial range behavior is seen for separations from 1.5-300km.

  19. Why no enstrophy cascade in Gulf Stream recirculation? (Why so different from Gulf of Mexico drifters of LaCasce and Ohlmann, 2003?) • Hypothesis 1: there isn’t an observable enstrophy cascade in CLIMODE region at these scales (with respect to dispersion). • Significant energy input at a scale of 1-2 km (2—4x mixed layer depth) to the first baroclinic Rossby radius. Mixed layer submesoscale turbulence. This is overwhelming an enstrophy cascade from larger scales. • Richardson’s Law scaling may not be due to energy cascade. E.g., Bowden, 1965: 4/3 law behavior can be caused by small-scale mixing superimposed on large-scale shear. • Test of hypothesis 1a: in a more quiet part of the ocean, away from the energetic Gulf Stream region, drifters will behave more like LaCasce and Ohlmann’s Gulf of Mexico drifters and demonstrate enstrophy cascade-like behavior at scales smaller than 1st BC.

  20. Eastern subtropical Atlantic drifters Drifters deployed as part of a 2005—2006 comparison study of drifters from different manufacturers. All drifters deployed within a few meters of each other. 18 drifter pairs had initial separation distances less than 700m (accuracy of Argos positioning).

  21. Eastern subtropical Atlantic drifters

  22. Why no enstrophy cascade in Gulf Stream recirculation? (Why so different from Gulf of Mexico drifters of LaCasce and Ohlmann, 2003?) • Hypothesis 2: chance pairs (like in LaCasce and Ohlmann) present a biased sampling of the statistics of the turbulent field. • Where energetic submesoscale features exist, they may prevent chance encounters. Convergent regions may be characterized by a steeper wavenumber spectral slope. • Test of hypothesis 2: repeat study for chance pairs in the Gulf Stream region.

  23. Gulf Stream chance pairs 29 chance pairs in the region 25—45°N, 40—80°W, 2005—2007, that came within 10 km of each other (bullets). Trajectories before (light grey) and after (dark grey) closest approach are also shown. Only 9 pairs came within 700m of each other.

  24. Gulf Stream chance pairs

  25. Why so different from Gulf of Mexico drifters of LaCasce and Ohlmann, 2003? • Hypothesis 3: Increased temporal resolution of these data, due to multisatellite processing introduced since LaCasce and Ohlmann (2003). • Some transitions from d to ad are extremely fast, even for relatively large d. These would be missed at daily resolution, and lead to smaller FSLEs. • Test of hypothesis 3: repeat study for CLIMODE drifters subsampled to daily resolution. LaCasce (2008, in press): original Gulf of Mexico data, daily resolution (open white stars). Interpolated to higher resolution (stars, triangles): plateau of constant l shifts to very small scales.

  26. CLIMDE drifter FSLEs, daily resolution

  27. Conclusions • As part of CLIMODE, an array of 60 drifters were deployed in February and March 2007 to resolve relative dispersion, mixing and stirring in the Gulf Stream and its recirculation. • Drifters collected velocity and SST measurements at ~hourly resolution. • Relative dispersion consistent with Richardson’s Law behavior at separation of 1.5—300 km. At larger separation, pairs exhibit diffusive spreading with effective eddy diffusivities of 1—3 x 104 m2/s. • No evidence of enstrophy cascade at sub-deformation scales. • Most likely reason: significant energy input at submesoscale, via frontal and mixed layer instabilities. • This appears to be a ubiquitous characteristic of the ocean, even away from the Gulf Stream front, as suggested by eastern subtropical Atlantic drifters. • Earlier results consistent with QG turbulence expectations at sub-mesoscale were affected by temporal resolution of those data.

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