Midocean Geostrophic Turbulence

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Mid-ocean Geostrophic Turbulence
prototype two-dimensional turbulence
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Continuously stratified case
Energy transfer is to low
3
WKB form
Energy transfer is to low
Energy transfer is toward the equator and into
high vertical mode.
The energy in mode n shows an equatorial peak of
width W, determined by
i.e.
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Global characteristics of ocean variability
estimated from regional TOPEX/POSEIDON altimeter
measurements
D. Stammer, J. Phys. Oc. 1997
Eddy kinetic energy at the sea surface (cm/sec)2
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U. Send, C. Eden F. Schott Atlantic equatorial
deep jets J. Phys. Oc. 2002
Zonal flow (cm/sec) along the equator from six
cruises.
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Six-layer QG model
kinetic energy in modes 0 to 5 as a function of y
1982
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Six-layer QG model
mode
0
3
5
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Two-layer QG flow
3 quadratic invariants energy potential
enstrophy of each layer
This is not wrong, but it is incomplete. Not
all the information is being used.
To see what phenomena are being missed, consider
cases with a very high degree of asymmetry
between the layers.
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Two-layer flow with the lower layer at rest
Work of Jurgen Theiss (Rhines latitude)
Problem with this model the lower layer does not
remain at rest.
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Two-layer QG flow
top
bottom
2 sources of asymmetry
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Consistent equivalent barotropic dynamics
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Guidance from equilibrium stat-mech
(equipartition theory)
1976
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But beta doesnt actually vanish or does it?
2-layer QG with a zonal mean flow
Baroclinic instability requires opposite signs.
Therefore the threshold for instability is
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A view of the ocean
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The two cases of neutral stability
initial stream function
1000 sq km 512 x 512, rdef 40 km, depth
ratio10
tropical
extra-tropical
urms 10 km/day
upper layer
lower layer
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Stream function at 100 days
tropical
extra-tropical
Rhines scale 88 km
27 km
upper
7.20 k/d
4.02 k/d
lower
0.51 k/d
8.47 k/d
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Potential vorticity at 100 days
tropical
extratropical
upper
lower
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Second experiment lower layer initially at rest
Stream function at 150 days
tropical
extra-tropical
Rhines scale 77 km
25 km
upper
6.52 k/d
6.42 k/d
lower
0.49 k/d
1.18 k/d
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Potential vorticity at 150 days
tropical
extratropical
upper
lower