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

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3.7. CONSERVATIVE PROPERTIES 15
3.7 Conservative Properties
The dynamics of a tracer S transported by an incompressible fluid of velocity field u, diffused
with the diffusion κ and subject to sources and sinks Q is govenred by the advection diffusion
equation:
∂ t S + u · ∇S − ∇ · (κ∇S) = Q. (3.6)
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A scalar is said to be conservative if Q = 0.
Besides their important influence on the density there is another reason why salinity and
potential temperature play such an important role in oceanography they are conservative.
Away from the boundaries these properties can only be changed by mixing with water masses
of different characteristics. Pleae note, that temperature is not conservative as it changes when
a water parcel is transported up or down in the ocean, when pressure changes. This is equivalent
to say, that there are no sources or sinks of salinity and potential temperature in the ocean
interior.
Other scalars like dissolved oxygene nutrients and biological concentrations are not conservative
as they have sinks and sources.
3.8 Water Masses in the Ocean
Water in the ocean mixes due to molecular diffusion and turbulent stirring (see section 10.2). In
large parts of the ocean, away from the boundaries, the mixing is small. Water parcels thus conserve
their conservative characteristics, salinity and potential temperature, when transported
over long distances and a mean large scale transport velocity of water masses and the velocity
field in the ocean can be determined by measuring potential temperature and salinity. Further
more, water mass characterisitics change only slowly in the deep ocean and show only
small variations over the years. These changes can be used as important indicators of climate
(long-time-large-space) variability.
3.9 Sea Ice and Ice Bergs
Fresh water freeszes at 0 o C and sea water with a salinity of 35psu freezes at −1.8 o C, at atmospheric
pressure. Fresh water has its maximal density at 4 o C, when lakes cool below this
temperature the cold water stays at the surface and freezing happens quickly near the surface
while 4 o C warm water is found in the deep lake. The ice formation of lakes mostly depends on
the atmospheric temperature and the wind speed. For water with a salinity over 24.7psu the
maximum density is at the freezing temperature. When the ocean is cooled the cold surface
water descents and is replaced by warmer water from depth until the freezing temperature is
reached. Sea water can only freeze when the cooling from the atmosphere is stronger than the
convective warming from the deep ocean. So, for the formation of sea ice, besides atmospheric
temperature and the wind speed, the water depth and the stratification of the ocean in temperature
and salinity are important parameters. No such convective warming is present for fresh
water lakes once the temperature is below 4 o C, and indeed you can go ice-skating on lakes in
northern Europe while the nearby sea is completely ice free. The vertical convection process is
studied in section 10.3.
Ice cover are crucial to the ocean dynamics as it: (i) has a strong influence on the reflection
of the incoming radiation, especially when they are covered by fresh snow (see section 4.1.1),