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Transcript of Relative dispersion in the Gulf Stream and its recirculation Rick Lumpkin ([email protected])...
![Page 1: Relative dispersion in the Gulf Stream and its recirculation Rick Lumpkin (Rick.Lumpkin@noaa.gov) National Oceanic and Atmospheric Administration (NOAA)](https://reader033.fdocuments.net/reader033/viewer/2022052603/56649d045503460f949d7e92/html5/thumbnails/1.jpg)
Relative dispersion in the Gulf Stream and its recirculation
Relative dispersion in the Gulf Stream and its recirculation
Rick LumpkinRick Lumpkin([email protected])([email protected])
National Oceanic and Atmospheric Administration (NOAA)Atlantic Oceanographic and Meteorological Laboratory (AOML)
Miami, Florida USA
CLIMODE PI workshop, 6-7 August 2008
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.)('2 tx
Ensemble average
x
U t
x’
Dispersion:
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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.
.3/4rmsx
En
erg
y in
pu
t
Wavenumber k
En
erg
y E
(k)
Energy cascade
Enstrophy cascade
3k
3/5k2D 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).
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Finite Scale Lyapunov Exponents (FSLEs)
x
U t
Separation distance
Pick such that growth of is given by ).exp(0 t
(Exponential growth if is constant, but more generally can vary with .)
![Page 5: Relative dispersion in the Gulf Stream and its recirculation Rick Lumpkin (Rick.Lumpkin@noaa.gov) National Oceanic and Atmospheric Administration (NOAA)](https://reader033.fdocuments.net/reader033/viewer/2022052603/56649d045503460f949d7e92/html5/thumbnails/5.jpg)
FSLEs, continued.
Over interval (n, n+1) in which is approximately constant,
)./ln()( 11 nnnn tt
For n+1 = n, this becomes:
nn t
ln
)(
where tn is the mean time for the separation distance to grow from n to n.
Unlike dispersion, which averages the data in time, this approach averages the data in separation distance.
![Page 6: Relative dispersion in the Gulf Stream and its recirculation Rick Lumpkin (Rick.Lumpkin@noaa.gov) National Oceanic and Atmospheric Administration (NOAA)](https://reader033.fdocuments.net/reader033/viewer/2022052603/56649d045503460f949d7e92/html5/thumbnails/6.jpg)
Dispersion regimes
D2(t) Regime
exp(0t) 0 exponential
t2 ballistic
t3 Richardson
t diffusive
Relative Dispersion FSLE Dispersion
From Haza et al., 2007
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Relative dispersion observations in the oceanLaCasce 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.
)(
)ln()(
t
![Page 8: Relative dispersion in the Gulf Stream and its recirculation Rick Lumpkin (Rick.Lumpkin@noaa.gov) National Oceanic and Atmospheric Administration (NOAA)](https://reader033.fdocuments.net/reader033/viewer/2022052603/56649d045503460f949d7e92/html5/thumbnails/8.jpg)
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.
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Drifter observations during February—March 2007 cruise, R/V Knorr
Goal: measure dispersion, eddy fluxes
CLIMODE observations
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60 drifters deployed: 16 trios, 6 pairs.
Median spacing of satellite fixes: 1.2 hours
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60 drifters deployed: 16 trios, 6 pairs. One drifter failed.
Median spacing of satellite fixes: 1.2 hours
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dispersion
rms displacement: 1.5km
300-500km
55 pairs with earliest fixes <700m
Solid black: zonal. Dashed black: meridional.
Grey dashed: D2=(3.5109 m2 s3 )t3
(Richardson’s Law)
Noise level of Argos positioning
Ro2
(5.8104 m2 /s)
(2.9104 m2 /s)
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Evidence of exponential behavior at short times?
Dashed black:.
95% confidence
Ro2
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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.
nn t
ln
)(
Neither approach indicates exponential behavior (constant ) from the smallest scales to the first baroclinic Rossby radius, ~30 km (Chelton et al., 1998).
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Early behavior (<1.5km)
.2urmseff Tu
~rmsu 1—2 m/s
~uT 5—20 s
eff 25 m2/s
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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 eff=1.5—3 104 m2/s.
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Single-particle diffusivities
Davis (1991):
Zhurbas and Oh (2003): Use minor principle component for robust scalar lateral diffusivity in presence of mean shear.
.),|(),|(),( 00'
00' tttdttvt kjjk xxx
Left: single-particle diffusivity from 1500 unique drifters in the Gulf Stream and recirculation region, 1989—present.
Pair dispersion: eff=1.5—3 104 m2/s. Comparison suggests that mean shear amplifies zonal pair spreading, but not meridional spreading, to lowest order.
Mean interpolated onto CLIMODE drifter positions:
1.6104 m2/s (std.dev. 7103)
Mean semimajor axis:
5.8 104 m2/s.
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1.5 km—300 km:
Then diffusion .2
3'
d
d
2
1 3/43/12rmsxax
t
,' 2/32 axxrms .1043
29
s
ma
Lagrangian structure function vs. separation distance for 55 CLIMODE drifter pairs. Inertial range behavior is seen for separations from 1.5-300km.
2
21 )(d
d
xx
t
Intermediate behavior
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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.
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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).
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Eastern subtropical Atlantic drifters
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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.
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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.
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Gulf Stream chance pairs
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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 to are extremely fast, even for relatively large . 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 shifts to very small scales.
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CLIMDE drifter FSLEs, daily resolution
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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.