Account of the paper, “Stability of the Account of the paper, “Stability of the (Western) Sargasso Sea Subtropical (Western) Sargasso Sea Subtropical

Frontal Zone (SFZ),” by Halliwell, Peng, Frontal Zone (SFZ),” by Halliwell, Peng, and Olson (1994).and Olson (1994).

LT Keir D. Stahlhut, 13 SEP 2005LT Keir D. Stahlhut, 13 SEP 2005

Sargasso Sea area

Cross Section with depth of the Subtropical Frontal Zone (SFZ)

Basically three characteristically different water types….

Current SST

Depth of 26C Isotherm

NOV 2004 AVHRR SST 7-Day composite (from JHAPL) shows front nicely…..

Analysis StrategyAnalysis Strategy Demonstrate the mean SFZ is (baroclinically) unstableDemonstrate the mean SFZ is (baroclinically) unstable

Characterize properties of the unstable eddies using 3-Characterize properties of the unstable eddies using 3-layer modellayer model

Estimate growth rates and wavelengthsEstimate growth rates and wavelengths

Consider absolute stability propertiesConsider absolute stability properties

Analyze evolution of turbulent (non-linear) eddy field Analyze evolution of turbulent (non-linear) eddy field after some finite amplitude; compare these amplitudes to after some finite amplitude; compare these amplitudes to satellite datasatellite data

Stability analysis….Stability analysis….Equation to be solved (non-dimensional PV equations for small perturbations)

Solution “Form”

Obtain the eigenvalue equation…..

Where these are the coefficients…..

Stability analysis continued….Stability analysis continued….• Turns out that….Turns out that….

• This analysis predicts instability regions, This analysis predicts instability regions, dominated by wavelengths 150-200 km (agrees dominated by wavelengths 150-200 km (agrees with 3.9Rd rule)with 3.9Rd rule)

• Growth rate depends primarily on Shear Growth rate depends primarily on Shear between top two layers (processes that effect between top two layers (processes that effect seasonal thermocline are very important)seasonal thermocline are very important)

• Further “absolute stability” analysis by “Ripa’s Further “absolute stability” analysis by “Ripa’s version” of “Arnol’d’s Theorems” also show version” of “Arnol’d’s Theorems” also show instabilityinstability

Numerical Model set up….Numerical Model set up….

““Case 1”--- Idealized Case 1”--- Idealized representation of the large representation of the large scale separating thermocline scale separating thermocline structure of SFZstructure of SFZ

““Case 2”---upper interface Case 2”---upper interface intersects the surface near the intersects the surface near the center of the frontal zonecenter of the frontal zone

•Three active layers

•Infinitely long, zonally oriented Beta plane channel, bounded by solid walls to N/S

•Hydrostatic, quasi-geostrophic balance

• ““Case 1”--- Idealized Case 1”--- Idealized representation of the large representation of the large scale separating scale separating thermocline structure of thermocline structure of SFZSFZ

• This figure shows This figure shows increased eddy variability increased eddy variability over timeover time

• ““Most unstable” Most unstable” wavelengths are ~ 150 -wavelengths are ~ 150 -200 km (agrees with 3.9Rd 200 km (agrees with 3.9Rd rule)rule)

• After day 125, non-linear After day 125, non-linear energy transfer takes energy transfer takes place, eventually becoming place, eventually becoming a true “cascade regime” a true “cascade regime” (think Time-Series)(think Time-Series)

Larger amplitudes of sea surface elevation at later time

Characteristic Westward propagation after day 200 is ~ 4km/day, but varies with latitude

• ““Case 2”--- transition to higher Case 2”--- transition to higher turbulence, higher sea turbulence, higher sea surface elevation amplitude surface elevation amplitude occurs occurs more rapidlymore rapidly than for than for Case 1Case 1

• ““Most unstable” wavelengths Most unstable” wavelengths are ~ 150 -200 km (agrees are ~ 150 -200 km (agrees with 3.9Rd rule)with 3.9Rd rule)

• Results are “comparable” to Results are “comparable” to satellite and XBT data for the satellite and XBT data for the areaarea

• Thus, model results suggest Thus, model results suggest that baroclinic energy that baroclinic energy conversion and atmospheric conversion and atmospheric forcing contribute roughly forcing contribute roughly equal (order of magnitude) to equal (order of magnitude) to the eddy variability within the the eddy variability within the SFZSFZ

Results/Conclusions:Results/Conclusions:• Linear theory suggests the SFZ should be unstable to larger Linear theory suggests the SFZ should be unstable to larger

disturbances, with “most unstable” wavelengths being ~150 to 200 disturbances, with “most unstable” wavelengths being ~150 to 200 km. This was also confirmed by “absolute stability” theory.km. This was also confirmed by “absolute stability” theory.

• Numerical modeling confirmed predictions of linear theory in early Numerical modeling confirmed predictions of linear theory in early stages. After this, non-linear effects caused energy to transfer in stages. After this, non-linear effects caused energy to transfer in wavenumber space. wavenumber space.

• ““Case 2” of this modeling, where upper interface intersected the Case 2” of this modeling, where upper interface intersected the surface developed more rapidly, and the developed eddies were surface developed more rapidly, and the developed eddies were confined to south of the surface front. confined to south of the surface front.

• Processes that act to steepen the seasonal thermocline of the SFZ Processes that act to steepen the seasonal thermocline of the SFZ are very important. are very important.

• Mesoscale Oceanography is fun.Mesoscale Oceanography is fun.