5244 
JOURNAL OF PHYSICAL OCEANOGRAPHY 
— 
| — 
- — Cyclonic 
— Non-cyclonic 
VOLUME 50 
1.5 
a. 
1 
L 
3.5 
) 
” 
Ar} 
PN 
x) 
Ü 
E 200 + 
= 
Z. 400 - 
© 
ä 
500 
0 
Distance (km) 
FIG. 9. Composite Froude number G as a function of across-strait distance, for the cyclonic 
cases (red) and anticyclonic cases (blue). The individual values for the 22 occupations are 
open circles, and the mean values at each location are the filled circles. The critical value of 
G = 1 is indicated by the dashed line. (bottom) The bathymetry. 
80 
60 
40 
-20 
20 
40 
60 
80 
5. Dynamics in the trough 
where Fr, = v./V/g’D. is the Froude number in the nth layer. 
The quantity v„ is the vertically averaged advective speed in 
‚ayer n, and D, is the layer thickness. A two-layer flow that is 
:aterally uniform is considered supercritical when G > 1 and 
suberitical when G < 1. For flows with strong lateral variations 
n layer thickness and velocity, a local value of G > 1 indicates 
“hat the flow is locally supercritical, but does not necessarily 
.ndicate that the flow as a whole is supercritical. In this case, 
‚ocally generated disturbances will propagate downstream 
whereas disturbances that exist over the whole channel width 
may still propagate upstream (Pratt and Helfrich 2005). Thus, a 
low may be supercritical at certain locations but also suberit- 
cal as a whole. We choose the 27.8kgm* isopycnal as the 
nterface between the two layers, since this is the top of the 
dense overflow water and also corresponds to the maximum in 
stratification (see also von Appen et al. 2017). (Using a slightly 
denser or lighter isopycnal did not change the results.) 
For each occupation we calculated G at the grid points 
across the section corresponding to the southward flow. 
Figure 9 shows the results, where we have distinguished be- 
‚ween the cyclonic cases (red) and noncyclonic cases (blue). 
The individual realizations are plotted as open circles, and the 
neans for the two cases at each cross-stream location are the 
solid circles. One sees that, for the cyclonic state, the mean G 
sxceeds 1 on the western flank of the trough where the merged 
NIJ-separated EGC is strongest (Fig. 6a). In all, 11 out of the 
15 cyclonic realizations had G > 1 in this part of the strait. By 
contrast, the mean G for the noncyclonic state is less than 
L everywhere, although 4 out of the 7 realizations had a value of 
G > 1 somewhere in the domain. As noted above, models and 
observations indicate that the overflow plume descending from 
a. Hydraulic criticality 
Previous observations have shown that the density structure 
of the overflow water in Denmark Strait is consistent with that 
of hydraulic flow over a sill (e.g., Spall and Price 1998; 
Nikolopoulos et al. 2003). Using observations and a numerical 
model, Käse et al. (2003) diagnosed the hydraulic conditions in 
Denmark Strait using the local Froude number Fr = v/g'D, 
where v is the flow speed, D is the vertical length scale, 
g’ = gAp/p is the reduced gravity, g is the gravitational ac- 
celeration, and Ap is the density difference across the in- 
;erface. Käse et al. (2003) considered different parts of the 
domain and found that the flow upstream of the sill is sub- 
critical (Fr < 1), but, as the flow descends into the Irminger 
Basin and accelerates, it becomes supercritical (Fr > 1). The 
;ransition location is roughly 100 km downstream of the sill. As 
shown by Pratt (1986), bottom friction can shift the transition 
point (critical section) from the sill to a location downstream. 
Such a downstream shift is evident in observations (Price and 
Baringer 1994), and in other models (Spall and Price 1998). 
We investigated the Froude number using our 22 sections. In 
:he scenario where the dense water flows beneath a motionless 
or slowly moving upper layer, the Froude number is the ex- 
pression given above. In our case, especially for the cyclonic 
state, there is strong flow throughout the water column. As 
such, it is more appropriate to use the composite Froude 
ıumber G for two active layers (Armi 1986: Kösters 2004: 
Pratt 2008): 
a 
= Fr* 
- Fr 
{1) 
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