Geoscience Reference
In-Depth Information
Salt Balance at the Ice / Ocean Interface
Advection int
o
control volume
w
0
=
+
w
p
S
ice
S
0
Advection out of control volume
w
'
S
'
0
=
Turbulent salinity flux
α
S
u
*0
S
w
S
0
(
-
)
Fig. 6.3
As inFig. 6.2except salt balance at theice/ocean interface
Sincethereisnocounterpartintheinterfacesaltbalancetolatentheatexchange,
a similar control volume approach (Fig. 6.3) yields a balance between turbulent
salinity flux and the advection of relatively fresh meltwater entering the control
volume at the top (for positive
w
) and water with interface salinity
(
S
0
)
leaving at
thebottom:
w
S
0
+
w
(
S
ice
−
S
0
)=
0
(6.3)
Inthiscase
w
w
p
representsthetotalinterfaceverticalvelocity,thusallowsa
salinityfluxassociatedwithpercolation,evenintheabsenceofmeltingorfreezing.
=
w
0
+
6.2 Turbulent Exchange Coefficients
It is customary in considering parameterization of turbulent exchanges to express
the flux of some quantity at the boundaryas the productof a scale velocity and the
change in the quantity from the boundaryto some reference level. For example, in
the surface layer discussed in Chapter 5, momentum flux may be parameterized in
termsofanexchangecoefficient
α
m
as
u
∗
0
2
τ
0
=
=
α
m
u
∗
0
∆
U
where
U
is thefluidspeedmeasuredatsomedistance
d
fromthe boundary(since
surfacevelocityis zero).Thus
∆
1
κ
−
1
u
∗
0
∆
log
d
z
0
=
√
c
D
α
m
=
U
=
where
c
D
isaconventionalquadraticdragcoefficientreferencedto
d
.Formultiyear
pack ice a representative value of
z
0
is 0.05m, and if we choose
d
in the surface
layer,say2m,
α
m
=
0
.
11.
