Geoscience Reference
In-Depth Information
V
s
δ
U
V
E
z
0
= 36 mm
β
= 23.7
a
0.1 m s
-
1
V
s
V
E
δ
U
β
= 16.5
z
0
= 1 mm
b
Fig. 4.5
Impact of different undersurface roughness lengths on surface velocity for the same sur-
face stress and Ekmanlayer velocity.Vectors labeled V
E
are velocityatthetopoftheEkman layer
as described in the text (Adapted from Fig. 4.1)
01ms
−
1
whentheentireIOBLwasconsidered,butthatthenearsurfacevelocityprofilewas
distortedbylocalundericetopography.However,sincetheicemovedasaunitover
theentire areaobservablefromtheicestation,thetotalshearacrosstheIOBLdoes
reflectan integrationovera muchlargerregionthan the relatively smootharea sur-
rounding the instrument mast. It is thus reasonable to assume that the difference
between the vector labeled
u
E
and
u
ice
(
Fig. 4.1. We estimated (McPhee and Smith 1976) that
u
∗
0
was close to 0
.
U
in Fig. 4.5a) is representative of shear
across the regional surface layer, from which it is straightforward to calculate
z
0
assumingthatthe surfacelayer extendsto thepointwhere
δ
f
.Forthe
conditionsshown,
z
0
is about 0.04m, which is fairly typical of multiyear pack ice.
InthefirstyeariceoftheWeddellSea,
z
0
iscloserto1mm(McPheeetal.1999),so
all else being equal,
κ
|
z
|
=
u
∗
0
Λ
∗
/
U
is larger as shown in Fig. 4.5b. The ice moves about 40%
fasterforthesamestress, with asignificantreductionin turningangle.
If
u
∗
0
varies instead of
z
0
, then clearly
u
E
and
δ
U
will change. However, in
the similarity sense, the nondimensional Ekman velocity remains the same. What
changes is the scaled value for the surface roughness
δ
u
∗
0
, so that the
impact of increased stress is to decrease the scaled surface roughness, and in-
creasethenondimensionalsurfacelayershear.Inotherwords,forfixedundersurface
roughness, the impact of increased stress is to lower the effective drag coefficient
magnitudeandtodecreasetheangleofturningbetweensurfacestressandvelocity.
Relating boundary stress to surface (ice) velocity is analogous to relating wind
stress at the surface to the geostrophic wind aloft. For the atmosphere, a method
ξ
0
=
fz
0
/
