Physical Processes - Coastal Lagoons: Ecosystem Processes and Modeling for Sustainable Use and Development - page 70

a free slip condition. However, it must be clear that in doing so the only process
that can remove energy from the system is the bottom friction (to be discussed
below). For coastal lagoons and estuaries this hypothesis is adequate, but when
dealing with deep-water bodies it may not hold true.

3.4.4.3 Conditions on Open Boundaries

Open boundaries do not actually exist in nature. Nevertheless, all those boundaries
of the artificially created water body that are not made out of material boundaries
(e.g., the boundary is in the water body itself) are called open boundaries. In this
case the conditions for material boundaries cannot be applied because there is
actually a strong flux of all the variables through the open inlets.
Mathematically speaking, fluxes have to be described through the open bound-
aries. In the case of mass flow the water level or the current velocities as well as
river discharges must be provided. For the other variables heat and salt fluxes have
to be prescribed.
An alternative, as described previously, is to fix temperature and salinity values.
This corresponds to a boundary condition of the first type. In this case, it must be
pointed out that the value of the property can be described only in conditions of
inflow, when the information is transported into the domain. In the case of outflow,
no information is necessary as the value at the boundary is adjusting dynamically
to the value that is advected out of the water body.
The Venice Lagoon is an example. The lagoon communicates with the Adriatic
Sea through three inlets through which it exchanges water. On these boundaries
either the mass flux into the lagoon (velocities) or the tide (water level) must be
prescribed. Moreover, properties of the water such as temperature or salinity must
be imposed if the water is entering the lagoon.
The same parameters and variables also must be specified on the inner boundary
where the lagoon waters combine with the mainland. Here rivers enter the basin,
bringing different water masses into the lagoon. In this case it is more convenient
to impose fluxes instead of water levels because they are very often better known.

3.4.4.4 Conditions on the Sea Surface and the Sea Bottom

In lagoons and estuaries the water surface and the bottom of the water body are the
largest surfaces in contact with the water. This is true because, for a typical basin,
the horizontal dimensions are always much larger than the vertical ones. Therefore,
the fluxes across these two interfaces will be very important for dynamics of the
fluid and particular attention must be devoted to these boundaries.
At the sea surface, fluxes of various kinds can be observed. There is momentum
input due to the mechanical action of the wind across the air-sea interface. It is this
force that drives large parts of the oceanic circulation, and it is also important on a
local scale. The wind stress acting across the surface can be parameterized by the
bulk formula

s ww s ww

τ = c ρ | uu | τ = c ρ | uu |

1 Da i 1 2 Da i 2