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the relatively mild thermal forcing typical of most of the data used to derive the
averagesinFig.6.5),thisisprobablyacceptable.However,it isoftenmoreextreme
situations that are interesting: e.g., survival of a large area of ice blown over water
that is relatively warm. The following example illustrates the impact of double-
diffusivestrength.Supposethaticewithmoderateoceanstress
015ms
−
1
(
u
∗
0
=
0
.
)
drifts over water with
1Kandthat
q
and
w
p
are negligible, more or less
typical of summer in the central Arctic. Now, if
R
∆
T
=
0
.
=
1 (no double diffusion) the
0058 yields the same basal heat flux, 34Wm
−
2
,asthe
solution for
α
h
=
α
S
=
0
.
bulk relation for
St
∗
=
0057 (the mean value for the SHEBA project). The inter-
facetemperatureandsalinityareonlyslightlydifferentfromthemixedlayervalues:
δ
0
.
T
=
0
.
098K.Ifinstead,doublediffusionisstrong,
R
=
70,thenthesolutionwhich
provides 34Wm
−
2
requires
α
h
=
70
α
S
=
0
.
0144. In this case
δ
T
=
0
.
040K. The
meltrateis slightlyovera centimeterperday.
Next consider a range in parameter space where measurements are scarce, but
which is likely to be encountered often when ice drifts into open water. We leave
u
∗
0
unalteredbut increase
T
twenty fold to 2K (water temperatureslightly above
0
◦
C), and consider the conditions at the interface for the two sets of
∆
α
h
and
α
S
0058,thecalculatedheatfluxis681Wm
−
2
,
so in this case the solution is almost exactly linear in
=
,
α
h
=
.
determinedabove.With
R
1
0
T
, hence nearlythe same as
thebulkrelation.Incontrast,thecalculatedheatfluxwhen
R
∆
=
α
h
=
.
0144
is 988Wm
−
2
, 45% greater. Approximate melt rates for the low and high double
diffusivestrengthsare22and32 centimetersper day,respectively.If onepicturesa
typical marginal ice zone where wind often pushes pack ice back and forth across
anoceantemperaturefront,thissimplethoughtexperimentdoesindeeddemonstrate
thatsurvivabilityofseaicemaybequitesensitivetothestrengthofdoublediffusion.
70and
0
6.6 Double Diffusion and False Bottoms
Evidencefor the importanceof doublediffusionduringmeltingcomesperhapsun-
expectedly from a curiosity of the summer ice pack: false bottoms. These occur
when concavities in the ice underside fill with fresh meltwater, which being in
contact with seawater well below 0
◦
C, forms a thin layer of ice at the fresh-
water/seawaterinterface.Thephenomenonwasdocumentednicelyduringthesum-
mer of 1975, when Arne Hanson maintained an array of depth gauges at the main
AIDJEX station Big Bear near the center of the Beaufort Gyre in the Canadian
Basin. Figure 6.7 (adapted from Notz et al. 2003) shows time series of bottom el-
evation (with respect to the upper surface) at seven of Hanson's thickness gauges,
threeinitially deployedin thickice (BB4-6)andfourothersdeployedin relatively
thinnerice(BB2,3,7,8).Thethickersitesallshowsteadyablationthroughthesum-
mer,butatthethinnersitesthereisasignificantincreaseindistancetotheicebottom
starting at aroundday 200(19 July), and in fact some of the thinner sites showed a
netincreaseinthicknessoverthesummer.Hansonattributedtheincreasedthickness
to formationof false bottoms. Notz et al. (2003) investigatedthe evolution of false
