2746 
JOURNAL OF PHYSICAL OCEANOGRAPHY 
VOLUME 50 
y 
(a) Total PV (m! 
gar 08 
{b) Planetary stretching PV {m} ss) x 
Se EZ - a 
D+ 
00 
00 
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200 
E30 | 
s 
® 
8 40 
500 
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700 - 
1120 
3 300 + 
3 
\ 400 
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July, 2007 | 
5 
in 
„July, 2007 | 
40 0 40 
Distance (km) 
80 120 
80 40 0 40 80 120 
Distance (km) 
IQ 
„120 
„80 
(c) R_ (Vertiml relative PV / Planetarv stretching PV)Y 
(d) R, (Horizontal relative PV / Planetary stretching PVY 
a 
00 
1) +— 
100 
wo 
*, 300 
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E 300 
s 
3 400 
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J5 
July, 2007 
800 
July, 2007 
40 0 40 80 120 40 0 40 80 
Distance (km) Distance (km) 
FIG. 11. Vertical sections of the components of the Ertel potential vorticity (colors) for the July 2007 Lätrabjarg 
occupation, overlain by potential density (kg m7*, contours). (a) Total potential vorticity (X107!*m7!s7). 
‘b) Planetary stretching PV (x107'* m”! s7'). (c) The ratio of vertical relative PV to planetary stretching PV (R,). 
‘d) The ratio of horizontal relative PV to planetary stretching PV (R;). The highlighted isopycnal of 27.8 kg m * is 
che upper boundary of the overflow water. The inverted triangles indicate the station locations. 
00 
1920 
700 
120 
0] 
nonlinear, and may be barotropically unstable (Pickart et al. 
2005). Furthermore, the lateral gradient of the total PV 
changes sign with depth in the trough (Fig. 11a), which is a 
necessary condition for baroclinic instability. This is in line 
with the model results of Spall et al. (2019), who identified 
:hat both the merged NIJ-separated EGC and NIIC are 
varoclinically unstable. This instability acts to weaken the 
aydrographic front that is maintained by the convergence of 
:he large-scale mean flow. 
Note also in Fig. 11 that, due to the steeply sloped iso- 
pycnals of the hydrographic front (and corresponding strong 
velocity shear via thermal wind), the shear Rossby number 
is less than —1, i.e., the same order as the Rossby number. 
This results in regions of negative total PV; in particular, 
note the correspondence between the strong horizontal rela- 
ive PV in Fig. 11d and negative IT in Fig. 11a. The condition of 
1egative total PV can lead to symmetric instability (Haine and 
Marshall 1998; D’Asaro et al. 2011), a fast-growing instability 
that generally occurs on the order of a few hours (Brearley 
et al. 2012). At finite amplitude this results in intense, rapid 
diapycnal mixing (Haine and Marshall 1998). We now explore 
[urther the signature of symmetric instability in our data. 
ce. Symmetric instability 
Based on the July 2007 occupation, we seek to elucidate the 
relationship between the horizontal relative PV, or more spe- 
cifically R,, and the occurrence of negative PV. Using all the 
grid points of the 22 realizations, we regressed R, against II 
(Fig. 12). This shows that when R, < —1, 73% of the time this 
corresponds to negative PV (if the threshold is strengthened 
to —1.5, the percentage of negative PV is 93%). For the re- 
maining 27% of the data points, the strong positive vertical 
celative PV on the eastern side of the merged NIJ-separated 
EGC overcomes the horizontal relative PV, such that the total 
PV remains positive. This is seen in Fig. 12, where the value of 
R. for each data point is indicated using color. The points in 
]uestion generally have 0.5 < R, < 1.5. Alternatively, the color 
n Fig. 12 reveals that when negative PV does not correspond to 
R; < —1 this is due to large negative R, on the western side of 
:he merged NIJ-separated EGC (dark blue symbols in Fig. 12). 
We thus conclude that, outside of extreme instances of large 
vertical relative PV (of either sign), it is generally the case that 
when the shear Rossby number is less than —1, the total PV 
Ss negative—which will result in symmetric instability. This 
:hreshold is consistent with the classification of symmetric in- 
stability in Thomas et al. (2013), who also considered the 
contribution of the vertical relative PV. 
Part of our rationale for casting the symmetric instability 
zondition in terms of R, is that this ratio does not depend on 
(he velocity of the flow, but only on the density structure [see 
Eq. (5)]. As such, we can extend the application of the proxy 
co the complete set of historical hydrographic Lätrabjarg 
zections (we exclude 9 short sections that did not cross the 
‚rough). We find that R;, < —1 in 60 of the 112 sections, Le., 
over 50% of the time (for the more restrictive criterion of 
R, < —1.5 it is 42%). This suggests that symmetric instability 
accurs quite frequently in Denmark Strait. Interestingly, the 
aresence of symmetric instability does not seem to be tied to 
‚he cyclonic or noncyclonic velocity states, or to the presence of 
poluses versus pulses. 
Zroncht to van hy RUNDFSAMT FÜR SFPFFSCHIFTAHP" 
|Inaunthenticatern |! Dawnlaadend 01/12/72 AR- 
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