Transcript Account of the paper, “Stability of the (Western) Sargasso

Account of the paper, “Stability of the
(Western) Sargasso Sea Subtropical
Frontal Zone (SFZ),” by Halliwell, Peng,
and Olson (1994).
LT Keir D. Stahlhut, 13 SEP 2005
Cross Section with depth of the
Subtropical Frontal Zone (SFZ)
Sargasso Sea area
Basically three characteristically
different water types….
Depth of 26C Isotherm
Current SST
NOV 2004 AVHRR
SST 7-Day
composite (from
JHAPL) shows front
nicely…..
Analysis Strategy

Demonstrate the mean SFZ is (baroclinically) unstable

Characterize properties of the unstable eddies using 3layer model

Estimate growth rates and wavelengths

Consider absolute stability properties

Analyze evolution of turbulent (non-linear) eddy field
after some finite amplitude; compare these amplitudes to
satellite data
Stability analysis….
Equation to be solved (non-dimensional
PV equations for small perturbations)
Obtain the eigenvalue equation…..
Where these are the coefficients…..
Solution “Form”
Stability analysis continued….
•
Turns out that….
•
This analysis predicts instability regions,
dominated by wavelengths 150-200 km (agrees
with 3.9Rd rule)
•
Growth rate depends primarily on Shear
between top two layers (processes that effect
seasonal thermocline are very important)
•
Further “absolute stability” analysis by “Ripa’s
version” of “Arnol’d’s Theorems” also show
instability
Numerical Model set up….
•Three active layers
•Infinitely long, zonally oriented Beta plane
channel, bounded by solid walls to N/S
•Hydrostatic, quasi-geostrophic balance

“Case 1”--- Idealized
representation of the large
scale separating thermocline
structure of SFZ

“Case 2”---upper interface
intersects the surface near the
center of the frontal zone
Larger amplitudes of
sea surface elevation at
later time
•
“Case 1”--- Idealized
representation of the large
scale separating
thermocline structure of
SFZ
•
This figure shows
increased eddy variability
over time
•
“Most unstable”
wavelengths are ~ 150 200 km (agrees with 3.9Rd
rule)
•
After day 125, non-linear
energy transfer takes
place, eventually
becoming a true “cascade
regime” (think TimeSeries)
Characteristic Westward propagation
after day 200 is ~ 4km/day, but varies
with latitude
•
“Case 2”--- transition to higher
turbulence, higher sea
surface elevation amplitude
occurs more rapidly than for
Case 1
•
“Most unstable” wavelengths
are ~ 150 -200 km (agrees
with 3.9Rd rule)
•
Results are “comparable” to
satellite and XBT data for the
area
•
Thus, model results suggest
that baroclinic energy
conversion and atmospheric
forcing contribute roughly
equal (order of magnitude) to
the eddy variability within the
SFZ
Results/Conclusions:
•
Linear theory suggests the SFZ should be unstable to larger
disturbances, with “most unstable” wavelengths being ~150 to 200
km. This was also confirmed by “absolute stability” theory.
•
Numerical modeling confirmed predictions of linear theory in early
stages. After this, non-linear effects caused energy to transfer in
wavenumber space.
•
“Case 2” of this modeling, where upper interface intersected the
surface developed more rapidly, and the developed eddies were
confined to south of the surface front.
•
Processes that act to steepen the seasonal thermocline of the SFZ
are very important.
•
Mesoscale Oceanography is fun.