Geoscience Reference
In-Depth Information
µ
*
vs melt rate for u
*
0
= 7 mm s
-
1
25
20
15
10
5
0
0
5
10
15
20
25
Melt rate (cm da
-
1
)
Fig. 4.7
The ratio of planetary scale to Obukhov length
(
µ
∗
)
for a range of basal melt rates and
fixed interface stress typical of average values for Arctic sea ice
m
2
s
-
2
2 x10
-
5
5x10
-
5
-
0
τ
x
,
µ
*
= 0
-
10
τ
x
µ
*
= 5
µ
*
= 25
τ
y
-
20
-
30
-
40 m
Fig. 4.8
Profiles ofkinematic stress components for three values of the stabilityparameter,
µ
∗
similar,buteventhough
u
∗
0
/
f
remainsfixed,themagnitudeofdimensional
z
varies
as
η
∗
, which is 1, 0.60, and 0.32, respectively,for the given range of
µ
∗
. Note that
µ
∗
,equivalentroughlytoabout25cmda
−
1
meltrate,thestress is
confined to the upper 15m or so of the water column, which would therefore limit
the depth to which mixing of the meltwater would reach. A new pycnocline would
rapidly form at about that level. Even with a relatively modest melt rate of about
5cmda
−
1
,thedepthofmixingwouldbesignificantlyreduced.
Velocityinthesurfacelayerisobtainedinthesamewayasbeforebyintegrating
dimensionlessshearfromthevelocityatthetopoftheouterlayer
forthemaximum
V
s
u
∗
0
=
U
0
/
η
∗
(4.30)
