Geoscience Reference
In-Depth Information
For cold seawater, representative values for molecular diffusivities are
ν T =
10 10 m 2 s 1 (Notzetal.2003).Fromthelabora-
toryresultsofOwensandThomson(1963)andYaglomandKader(1974), n ranges
from2/3to0.8,implying35
10 7 m 2 s 1 and
1
.
39
×
ν S =
6
.
8
×
R
70.
6.5 Double Diffusion—Melting
When sea ice melts there is strong evidence both by analogy with the laboratory
studies and from the formation and vertical migration of “false bottoms” during
the summer season (Notz et al. 2003, discussed below) that double diffusion is
important. In principle, measurements during rapid melting of turbulent fluxes of
momentum, heat, and salt near the interface, along with far-field temperature and
salinity,wouldsufficetodetermine
α S , providedtheinterfaceisatfreezing.
Inpracticeitisdifficulttoachieveunequivocalvalues,because
α h and
(
)
precisemeasure-
ment of salinity flux is difficult, and ( ii ) rapid melting of sea ice, particularly pack
ice in the marginalicezone, oftenoccursin markedlyheterogeneousenvironments
withrapidtemporalchangesandlargehorizontalgradients.
The nonlinearcharacterof (6.9)precludesa one-to-onerelationbetween
i
α h and
St ;however,for acommonlyobservedrangeofforcingparameters,say 5
u 0
15mms 1 and 0
5K (and ignoring heat conduction or percolation in
the ice column), the equation may be solved for an envelope of values for
.
05
T w
0
.
α h over
the range of R identified above that produce the same basal heat flux as the bulk
formula (6.10) with St =
, α h is
more than twice as large as St : when ice melts, interface salinity will be less than
S w ,so
0
.
0057 (Fig. 6.6). Over most of the range of R
T .
It is germane to ask whether the distinction between
δ
T
<
T and
α h /
St =
T
/ δ
α h and St is important. If
the bulk coefficient is relatively constant as indicated by Fig. 6.5, is that not suf-
ficient to gauge the basal heat flux? In most situations (i.e., conditions similar to
Fig. 6.6 Envelope of values of
α h that produce the same basal heat flux as the bulk formula
w T 0 =
15mm s 1
St u 0
T for ranges 5
u 0
,
0
.
05
T
0
.
5Kwhen St =
0
.
0057
 
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