Geoscience Reference
In-Depth Information
where
2
tu
∗
0
Φ
θ
∆
∆
s
l
=
z
1
fromwhich
A
1
A
1
+
E
1
=
(7.16)
s
l
−
1
tQ
1
θ
−
θ
−
s
l
θ
2
∆
s
1
,
j
−
1
D
1
=
A
i
+
s
l
−
1
Formomentum,thedimensionlessvelocitychangefromthesurfacetothefirstgrid
pointis given by the law of the wall, provided
|
zz
1
|
is much less than the Obukhov
length,i.e.,
ln
1
κ
zz
1
z
0
u
Φ
=
(7.17)
where
z
0
isundersurfaceroughnesslength.Ifthegridisrelativelycoarseandsurface
buoyancyfluxissignificant,
u
maybeestimatedfromMonin-Obukhovtheorywith
somecorrectionforstressrotation(McPhee1990).
Fortheice/oceaninterfacewehavefoundthatthedimensionlesschangesintem-
perature and salinity near the boundary are much greater than for momentum (by
several orders of magnitude for salinity) complicated during melting by double-
diffusive effects (Chapter 6). Consequently the approach taken is to invoke a sub-
modelfortheheatandsaltexchangeattheinterface,whichprovidesfluxboundary
conditionsfortheheatandsaltconservationequations(Section7.7).
Φ
7.2.3 Dynamic Momentum Flux Condition
A special case exists for wind driven sea ice drift when internal ice stress gradi-
ents are small relative to other forces, but where the inertia of the solid ice coveris
important in the overall momentum balance. The following is an approach formu-
lated by G. Mellor (1984, personal communication). For ice draft (“equivalent ice
thickness”),
h
ice
, theicemomentumequationis
h
ice
∂
if
u
s
u
s
∂
t
+
+
τ
w
−
τ
a
=
0
(7.18)
where
a
is air stress at the ice upper surface divided by water density. To account
forshear betweenthe uppermostmeanquantitygridpointandthe interface,surface
velocityisexpressedas
τ
u
u
s
=
u
1
+
u
∗
0
Φ
u
is givenby(7.17).Thedifferenceformof(7.18)is
where
Φ
2
∆
t
τ
w
=
−
h
ice
(
u
1
,
j
+
1
−
u
1
,
j
−
1
)+
2
∆
t
τ
m
(7.19)
h
ice
Q
1
u
u
τ
m
=
τ
a
+
−
h
ice
if
Φ
