Geoscience Reference
In-Depth Information
diminish,thelargedisparitybetweenmolecularthermalandhalinediffusivitieswill
effectdifferentialexchange,eveniftheflowremainssluggishlyturbulent.Theques-
tioncallsoutformoreresearch.
7.7 The Ice/Ocean Interface Submodel
An interface submodel is used to implement the ice/ocean interface characteristics
discussed in Chapter 6 as follows. The external forcing parameters
q
(kinematic
conductiveheatfluxintheice),
S
ice
(icesalinity),
w
p
(percolationvelocity),and
u
∗
0
are assumed specified as driving time series, or perhaps providedby a separate ice
model. Internal (to the model) variables are provided from the previous time step:
T
w
,
w
b
0
. If the last is zero or positive, the submodel assumes a
meltingorstationaryinterface,andusesspecifieddoublediffusiveexchangecoeffi-
cients. For example,
S
w
,
d
ml
,and
α
h
=
0
.
011
,
α
S
=
α
h
/
50 would be reasonable choices. It sets
theturbulentvelocityscale to
u
∗
0
.
If on the other hand, the previoustime step indicatesfreezing
w
b
0
<
(
0
)
,the
α
h
=
α
S
(say,0.0058),andmodifiestheturbulentscalevelocitytobe
submodelsets
3
. The submodel then solves for
S
0
as in (6.9), with
fluxesgivenby(6.4),usingin each case the appropriatevelocityscale (
u
∗
0
or
w
∗
0
).
Thesubmodelthencalculatesthenewvalueforbuoyancyflux
w
b
0
=(
u
3
∗
w
b
0
)
1
/
=(
−
c
ml
d
ml
w
∗
0
0
/
ρ
)(
β
S
w
S
0
−
β
T
w
T
0
)
g
(7.33)
where
β
S
and
β
T
arethehalinecontractionandthermalexpansionfactorsevaluated
at
T
0
andS
0
.
References
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McPhee, M. G.: A time-dependent model for turbulent transfer in a stratified oceanic boundary
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McPhee, M. G.: Small scale processes. In: Smith, W. (ed.) Polar Oceanography, pp. 287-334.
Academic Press, San Diego, CA(1990)
McPhee, M. G.: Scales of turbulence and parameterization of mixingin the ocean boundary layer.
J. Mar. Syst., 21, 55-65 (1999)
McPhee, M. G., Maykut, G. A., and Morison, J. H.: Dynamics and thermodynamics of the
ice/upper ocean system in the marginal ice zone of the Greenland Sea. J. Geophys. Res., 92,
7017-7031 (1987)
McPhee, M. G., Kwok, R., Robins, R., and Coon, M.: Upwelling of Arctic pycnocline as-
sociated with shear motion of sea ice. Geophys. Res. Lett., 32, L10616 (2005), doi:
10.1029/2004GL021819
Mellor, G. L. and Yamada, T.: Development of a turbulence closure model for geophysical fluid
problems. Rev. Geophys., 20, 851-875 (1982)
