NOVEMBER 2020 
LIN ET AL. 
Denmark Strait reaches hydraulic criticality approximately 
100km downstream of the sill. One is tempted to conclude 
‘rom our measurements that localized hydraulic criticality also 
occurs intermittently at the sill itself, in the cyclonic configu- 
zation when the merged NIJ-separated EGC is intensified 
on the western flank of the trough. However, the presence of 
such a confined region where G > 1 does not necessarily imply 
‘hat strait-wide hydraulic control is occurring (Pratt and Helfrich 
2005). Further work is required to shed light on this. 
d-+— 
100 -' 
! 
200 - 
5, 300 + 
n 
400 
3 
500 
300 
‚July, 2007 
(a) Richardson Number 
RIES — 
a 
3245 
"00 
b. Mixing and potential vorticity 
Although it remains unclear if the Denmark Strait sill can 
act as a location of strait-wide hydraulic control akin to what 
‘1appens farther south, the strong flow at the Lätrabjarg line, in 
conjunction with the weak stratification, result in another im- 
portant aspect of supercritical flow—that of mixing. This can 
be assessed by considering the gradient Richardson number, 
defined as the ratio of the buoyancy frequency to the square of 
vertical shear in velocity. 
zu 
‚80 
40 
0 
Distance (km) 
An 
AN 
120 
d 
100 - 
200 + 
300 / 
£ 
e 
&; 400 
500 
300 
nl Absolute * 
"strophic velocity (m s 1 
A 
zz 
d Ö. 
Ri= 308 (*) 
Pn9Z \OZ 
(2) 
July, 2007 
’00 
40 0 40 
Distance (km) 
FIG. 10. Vertical sections of (a) the log of the gradient Richardson 
aumber [log(R7), colors] and (b) absolute geostrophic velocity (m s”, 
zolors) overlain by potential density (kg m 7*, contours) for the 
Lätrabjarg occupation in July 2007. The highlighted isopycnal 
f 27.8kgm* is the upper boundary of the overflow water. The 
inverted triangles indicate the station locations. 
80 
where p is the local density, p, is the background density 
‘section-wide average), and u is the along-strait velocity. When 
Riis less than the critical value of 0.25 the flow can be subject to 
Kelvin-Helmholtz instability, which leads to vertical mixing 
(in many studies the critical value is taken to be in the range 
3.2-1.0; e.g., Galperin et al. 2007). To compute Ri we use a Az 
of 10m, although the results are not sensitive to this choice 
(we get comparable results for Az ranging from 5 to 20m). In 
Fig. 10 we show the vertical section of Ri (plotted using a 
logarithmic scale) for the July 2007 occupation, which is one 
of the sections where G > 1 within the trough. This reveals a 
region of Ri < 0.25 [Le., log(Ri) < —1.4, the red patch in 
Fig. 10a] along the steeply sloped density front separating the 
cold overflow water from the warm Irminger Water. In this 
case both the weak stratification and strong velocity shear 
contribute to the small value of Ri. It is expected that strong 
vertical mixing would be occurring in this region. 
To further investigate the nature and extent of mixing at the 
Lätrabjarg line, we consider the potential vorticity dynamics 
of the flow using our 22 occupations. We did this by evaluating 
the Ertel potential vorticity (e.g., Spall and Pedlosky 2008; Lin 
et al. 2018). 
109u 
R =- 2 
9 Foy 
For the horizontal relative PV. the ratio is 
R 
g& dp 
f?pyOv 
(5) 
where a is the isopycnal slope; to derive this, we used the 
‘hermal wind relation, du/dz = (g/fpo)(9p/9y). 
Using a representative length scale L and velocity scale U, 
:he first ratio [Eq. (4)] can be expressed as R, = U/fL, which 
is the Rossby number. Taking AU as the change in velocity over 
:he depth scale, the second ratio [Eq. (5)] can be expressed as 
R, = AU/fL, which has the form of a Rossby number associated 
with the depth variation in velocity; we refer to this as the shear 
Rossby number [it is also the negative of the inverse balanced 
Richardson number discussed in Thomas et al. (2013)]. Note 
hat when the flow is barotropic R, will be small, even though 
R, could be large. When the flow is strongly baroclinic R, could 
3e large. 
Returning to the July 2007 occupation, we computed the 
:otal Ertel PV and its three components, where the latter two 
:;erms have been normalized to show R, and R, (Fig. 11). One 
sees that over most of the section the total PV is qualitatively 
similar to the stretching term, particularly in the upper layer. 
However, in the trough the other two terms are significant. 
The large Rossby number (up to 1.5) changes sign across the 
merged NIJ-separated EGC., indicating that this flow is highly 
Ö 1 9u 9 1 9u 0 
n= Le, 1 9udp_ 1 du dp @® 
Po99zZ PoaOvOZ pyOzZOy 
where the y direction is cross-strait, positive toward Iceland. 
Che Ertel potential vorticity (PV) has three components: 1) the 
»lanetary stretching PV term, dictated by the vertical stratifi- 
cation and Earth’s rotation; 2) the vertical relative PV term, 
due to the combination of the lateral gradient of the horizontal 
velocity and vertical stratification; and 3) the horizontal rela- 
ive PV term, due to the vertical gradient of horizontal velocity 
and lateral gradient of density. It is instructive to normalize the 
second and third terms by the planetary stretching term. For 
the vertical relative PV, this gives 
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