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

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 Strategy  Demonstrate the mean SFZ is (baroclinically) unstable  Characterize properties of the unstable eddies using 3- layer 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) Solution “Form” Obtain the eigenvalue equation….. Where these are the coefficients…..

Stability analysis continued…. Turns out that…. Turns out that…. This analysis predicts instability regions, dominated by wavelengths km (agrees with 3.9Rd rule) This analysis predicts instability regions, dominated by wavelengths km (agrees with 3.9Rd rule) Growth rate depends primarily on Shear between top two layers (processes that effect seasonal thermocline are very important) 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 Further “absolute stability” analysis by “Ripa’s version” of “Arnol’d’s Theorems” also show instability

Numerical Model set up….  “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 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 1”--- Idealized representation of the large scale separating thermocline structure of SFZ This figure shows increased eddy variability over time This figure shows increased eddy variability over time “Most unstable” wavelengths are ~ km (agrees with 3.9Rd rule) “Most unstable” wavelengths are ~ km (agrees with 3.9Rd rule) After day 125, non-linear energy transfer takes place, eventually becoming a true “cascade regime” (think Time- Series) After day 125, non-linear energy transfer takes place, eventually becoming a true “cascade regime” (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 turbulence, higher sea surface elevation amplitude occurs more rapidly than for Case 1 “Case 2”--- transition to higher turbulence, higher sea surface elevation amplitude occurs more rapidly than for Case 1 “Most unstable” wavelengths are ~ km (agrees with 3.9Rd rule) “Most unstable” wavelengths are ~ km (agrees with 3.9Rd rule) Results are “comparable” to satellite and XBT data for the area 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 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. 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. 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. “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. Processes that act to steepen the seasonal thermocline of the SFZ are very important. Mesoscale Oceanography is fun. Mesoscale Oceanography is fun.