Physical Processes - Coastal Lagoons: Ecosystem Processes and Modeling for Sustainable Use and Development - page 71

ρ a is the density of air, is the components of the wind vector, and is
the modulus of the wind speed. The parameter c D is called the drag coefficient and
it has an empirical value between 1.5

where u i w | u i w |

10 −3 . Several formulations exist
where the drag coefficient is parameterized through the wind velocity.
Other fluxes at and through the sea surface concern the mass, salt, and heat flux.
Mass and salt fluxes are due to precipitation and evaporation that is occurring at the
water interface. Rain contributes to the mass flux, also diluting the surface waters,
whereas evaporation represents a loss of water and consequentially an increase in
salinity. Solar radiation heats the upper part of the oceans through absorption of
short waves, while outgoing long wave radiation and evaporation contribute to a
heat loss of water. Sensible heat flux (due to conduction of heat) also plays a role
in the heat budget of the oceans.
The bottom of the water body represents a material boundary to the fluid. It is,
therefore, clear that the above-mentioned no-flux condition is valid also for this
lower boundary. In this case, the role of sediment as a reservoir for nutrients, true
water, and other variables has been completely neglected. If these processes have
to be included in the description of the dynamics then a different approach has to
be taken. However, the no-flux condition is normally a good approximation.
On the other side a very important momentum flux is taking place across the
bottom boundary that normally cannot be ignored. The bottom exerts a drag (friction)
on the water column that slows down the fluid layers in contact with the bed. This
is the same principle as the wind action through the surface that accelerates the
upper fluid layers.
The bottom friction stress can be expressed in a similar way as the wind stress.
A bulk formula of the form

⋅ 10 −3 and 3.2 ⋅

b b

τ = c ρ | uu | τ = c ρ | uu |

1 B 0 i 1 2 B 0 i 2

ρ 0 the density of the water, u i the components of the current velocity
in the vicinity of the bottom, and

can be used with

the modulus of the current velocity. The
parameter c B is called the bottom friction coefficient and has an empirical value of
about 2.5

| u i |

10 −3 , similar to the wind drag coefficient. Other forms of bottom friction
parameterizations are also possible but will not be discussed further here.

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3.5 BOUNDARY PROCESSES

In the above paragraphs, generic evolution equations have been given for a generic
property and for properties directly involved on water movement. Evolution
equations involve the computation of the transport of properties between neigh-
boring points and the computation of the rate of accumulation of those properties.
The transport of properties requires computation of fluxes, including computation
along the boundary. In the same way, the simulation of the time evolution requires
the knowledge of initial conditions. Boundary conditions are usually not well
known and their specification has to be based on a good knowledge of boundary
processes.