1. Surface Mixed Layer Instabilities and Deep Flows
On Multi-Scale Dispersion Under the Influence of
Surface Mixed Layer Instabilities and Deep Flows
Tamay Özgökmen (U Miami)
Andrew Poje (CUNY), Paul Fischer (ANL), Hank Childs, Hari Krishnan (LLBL),
Christoph Garth (U Kaiserslautern), Angelique Haza and Edward Ryan (U Miami)
Ocean Sciences Meeting, Salt Lake City, February 21, 2012 1

2. Motivation: example of a multi-scale flow (“Wondereddy”):
t0: May 1, 2011
t0 + 1 day
t0 + 2 days
t days
(Some) observable submesoscale flows appear episodic; special circumstances are needed
for their generation and they lose in competition to mesoscale eddies.

3. More persistent in models - LCS in the Gulf Stream Region:
1/12 degree HYCOM
1/48 degree HYCOM
Haza, Özgökmen, Griffa, Piterbarg, 2012, Ocean Modelling, 42,
Which turbulent features control the transport?
Are the long-living, slow mesoscale features enough to compute transport?
(II) Or, rapidly-evolving, smaller submesoscale transport barriers are needed?

4. FSLE ~ 1/τ 2δ δ Metric: spatial scale dependent relative dispersion
Hypothesis-I : energetic and long-lasting mesoscale features in control
(non-local dispersion, Bennett, 1984)
current data-assimilating OGCMs adequate should give good predictions
Hypothesis-II : rapidly-evolving small scales dictate relative dispersion at submesoscales,
parameterizations for submesoscale processes would be needed in OGCMs

5. Representative results from recent studies:
Models:
Observations:
- All models have one characteristic eddy size; single plateau -> hypothesis-I
Some observations seem to be consistent with hypothesis-II, some with
hypothesis-I, but low pair numbers generate much uncertainty; inconclusive

6. In order to decide between hypothesis I and II, we need:
Either high-resolution models that are truly “multi scale”, i.e.,
capture the interaction of upper ocean submesoscale and
deeper mesoscale baroclinic instabilities
B) And/or simultaneous launch of O(100) drifters at submesoscale separations
* Attempt (A) now, and hopefully (B) in the near future…
Related scientific question of interest:
How MLI and deep flows interact? 6

7. Exp-I: shallow ML, no deep APE Exp-II: with deep APE
LES model setting:
Exp-I: shallow ML, no deep APE
Exp-II: with deep APE
* Domain: 25 km x 25 km x 0.75 km
* Shallow (25 m) weak ML front to get 10x scale separation between
MLI and deep eddies; no winds or other forcing
* Spectral element code Nek5000; 22x106 points (dx=17 m, dz=0.75 m),
2x105 time steps; 3 days on 256 CPUs of a Cray XE6m

8. Exp-I:

9. Exp-II:

10. (7 million particles advected in 3D, 2 days forward):
Finite Time Lyapunov Exponents
(7 million particles advected in 3D, 2 days forward):
Exp-I
Exp-II
Clearly different turbulent coherent structures in Exp-I vs Exp-II,
shallow submesoscale eddies vs deep mesoscale features…

11. Transformation in the 3D FTLE (from 7 million particles)
over two months of flow evolution:

12. Second moment (horizontal) of passive tracer:
Particle release 
An order of magnitude increase in frontal turbulent exchange
after the deep instability kicks in

13. Particle launches: (Lagrangian tools essential to minimize aliasing)
Exp-I
Exp-II
0 m
25 m ML base
0 m
25 m ML base
7803 particles over 5 km x 5 km area

14. Exp-I: submesoscale only Exp-II: multi scale
Main Result:
Exp-I: submesoscale only
Exp-II: multi scale
Surface
ML base
Hypothesis-I (single scale)
Towards Hypothesis-II
Two distinct FSLE plateau are obtained for surface FSLE in response to two processes of disparate scales: shallow MLI and deeper baroclinic instabilities

15. Practical sampling considerations for a field experiment:
- how many drifters?
- how long to leave them in water to capture both plateau?
(must be fast sampling, battery life issues…)

16. Summary:
a) LES is used to assess the transport properties of multi-scale oceanic
baroclinic instabilities.
b) We compare scale-dependent measures of Lagrangian relative dispersion
to explore whether transport in the submesocale separations is controlled
non-locally (hypothesis-I) or locally (hypothesis-II).
c) Visual inspection shows that MLI rapidly lose coherence in the presence
of larger-scale straining induced by the deep mesoscale motion.
d) During the period when both instabilities are present, FSLE shows two
distinct plateau associated with disparate instability scales.
e) Field experiments would require a combination of fast sampling,
accurate (10 min, 10 m) drifters and at least one-month long
trajectories to span the scale separation. 16