Physical Processes - Coastal Lagoons: Ecosystem Processes and Modeling for Sustainable Use and Development - page 59

evaporation is important these values can be even higher. In all cases the constituents
of salt are nearly constant in all places of the world. It is, therefore, possible to
express the salt content through a concentration value called salinity. The salinity is
measured in grams per kilogram or psu (practical salinity unit).
It is, therefore, important to consider the salt content and its variation using a
conservation equation for salt. The salinity can be changed only through mass fluxes
such as evaporation and river input. These processes can be viewed as boundary
processes that will be discussed in Chapter 4. As with temperature, the only other
process that changes the salt content of a fluid volume is diffusion. The equation
for salinity is therefore

2

dS
dt

∂
∂

S
x

= v (3.17)

S 2

j

where S is the salinity of the fluid and v S is the molecular diffusivity for salt, a
parameter that again depends only on the properties of the fluid. Note that this
equation can be derived directly from Equation (3.8), with S the quantity to be
conserved and no external sources.

3.4.1.5 Equation of State

The equation of state is a thermodynamic equation that relates different quantities
in a fluid in equilibrium to each other. An example is the well-known equation of
state for an ideal gas

p = ρ T

, and the temperature T to one another. Here
R is the gas constant per unit mass that still depends on the specific property of the
gas. Its value for dry air is 287 J kg −1 K −1 .
In the case of a fluid the situation is complicated by the fact that the salinity S
is also influencing the equation of state. In this case the equation of state can be
formally written as

that relates the pressure p , the density ρ

ρ = fTSp (,,)

so that the density can be computed given a set of values for temperature, salinity,
and pressure. The equation itself is a complicated polynomial function of these
quantities that has been empirically deduced by different organizations (e.g.,
UNESCO). The formula is not given here in its general formulation. However, for
some applications the equation of state can be simplified to

ρρ α =− −+ −

0

( TT ) α ( SS ) (3.18)

T 0 S 0

where the dependence on pressure has been neglected and a simple linear dependence
on T and S has been used. Here ρ 0 is the reference density at the reference temperature