Etudes et évaluation de processus océaniques par des hiérarchies ...

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3.3. θ-S DIAGRAMS 11
3.3 θ-S Diagrams
If one mixes the mass m 1 (measured in kg) of sea water of salinity S 1 with the mass m 2 of sea
water of salinity S 2 one obtains the mass m 1 + m 2 of sea water of salinity
S 3 = m 1S 1 + m 2 S 2
m 1 + m 2
. (3.2)
This follows from the definition of the salinity and the mass conservation.
If one mixes the mass m 1 of sea water of temperature θ 1 with the mass m 2 kg of sea water
of temperature θ 2 one obtains the mass m 1 + m 2 of sea water of temperature (see fig. 3.3)
θ 3 = m 1θ 1 + m 2 θ 2
m 1 + m 2
. (3.3)
tel-00545911, version 1 - 13 Dec 2010
The above is only strictly true if the heat capacity does not vary with temperature and salinity,
which is approximatrely true if we restrict ourselves to oceanic values (errors are typically
smaller than 1%), and when the (negligible) heat of mixing is neglected.
The analysis of water masses are performed with the help of θ-S diagrams as shown in fig. 3.3
θ ( o C)
✻
θ 1 –
θ 3 –
θ 2 –
S 1
S 3
S 2
✲
S (psu)
θ ( o C)
✻
θ 1 –
θ 3 –
θ 4 –
θ 2 –
S 1
S 2
S 4
✲
S 3
S (psu)
Figure 3.1: θ-S–diagram. Left: mixing of two water masses, the mixture of two water masses
lies on a line between water masses. Right: mixing of three water masses, the mixture of 3
water masses lies within the triangle formed by the three water masses. The exact location can
be obtained by eqs. 3.2 and 3.3.
3.4 Pressure
Pressure is measured in Pascal (1 Pa = 1 N m −2 ). When pressure is considered, oceanographers
usually mean hydrostatic pressure:
p(x,y,z) = p atmos + g
∫ 0
z
ρ(z ′ )dz ′ , (3.4)