Geoscience Reference
In-Depth Information
To offseta changein salinity so thatdensity remainsunchangedwouldrequirethat
δ
T
/
δ
S
=
−
β
S
/
β
T
. For the conditions of Fig. 2.9a
(
S
=
34psu
)
, this ratio is about
4
◦
C. Thus for water close to freezing,
density variation is almost exclusively a function of salinity, and temperature may
oftenbetreatedasa passivescalar contaminant.
In situ
density depends on pressure, but in terms of the impact of vertical den-
sity gradient on dynamics, generally the pressure dependence is neglected by con-
sidering
potential density
, i.e.,
86
◦
C and about 8 for
T
33 for
T
=
−
1
.
=
1000. The
reason for this is clear: a well mixed layer with uniform
T
and
S
, will have a pres-
sureinducedverticaldensitygradient,butthereisnegligiblework(besidesfriction)
involvedinmovingaparcelfromonelevel(pressure)toanother.Yetthereareidio-
syncrasiesassociated with nonlinearitiesin the equationof state that makethis less
straightforwardthan itmightat firstappear.Consider,forexample,the dependence
of the expansion and contraction factors on pressure (Fig. 2.9b). Here the ratios of
β
T
and
ρ
(
T
,
S
,
p
=
0
)
or
σ
0
=
ρ
(
T
,
S
,
p
=
0
)
−
β
S
totheirvaluesatsurfacepressureare plottedasfunctionsofpressure.
β
S
has very little pressure dependence, but the magnitude of
β
T
increases with pres-
sure. Plots are shown for two differenttemperaturesto emphasize that the pressure
dependence of
T
is much greater for cold water, resulting from the fact that cold
waterismorecompressiblethanwarm.
An example drawn from near Maud Rise in the Weddell Sea (Fig. 2.10) nicely
illustrates certain consequences of nonlinearities inherent in the equation of state.
β
σ
0
65.12
8
S, 003.63
8
E
ANZFLUX YOYO #75, 1994
0
0
0
c
a
b
-
20
-
20
-
20
-
40
-
40
-
40
-
60
-
60
-
60
-
80
-
80
-
80
-
100
-
100
-
100
-
120
-
120
-
120
-
140
-
140
-
140
-
160
-
160
-
160
-
180
-
180
-
180
-
200
-
200
-
200
-
2
-
1
0
34.5 34.6
Practical Salinity Scale
27.78 27.8
kg m
-
3
8
C
Fig. 2.10
YOYOStation75fromANZLUX1994,ontheeasternedgeofMaudRiseintheWeddell
Sea.
a
Temperature;
b
salinity;
c
.
0
(potentialdensity—1,000). Dashedlinesareanidealizedtwo-
layer system based on the measurements
σ
