Physical Processes - Coastal Lagoons: Ecosystem Processes and Modeling for Sustainable Use and Development - page 47

FIGURE 3.4 Representation of a generic transparent surface, an elementary area on that

surface, the respective exterior normal, and the fluid velocity.

3.2.4 E A E V

LEMENTARY REA AND LEMENTARY OLUME

The transport across a finite surface is obtained as the integration of the transport

across elementary areas where properties can be assumed to be uniform. Mathemati-
cally, elementary areas are infinitesimal, but physically they are just small enough
to allow the assumption that properties assume constant values on their surfaces,
allowing for the substitution of the integrals by summations. Fluxes across an
elementary surface are obtained by multiplying fluxes per unit of area with the area
of the elementary surface. This is a basic assumption of modeling.
An elementary volume is a volume limited by elementary areas, inside which
properties can be considered as having uniform values. The total amount of a
property contained inside an elementary volume is given by the product of its specific
value with its elementary volume.

A

3.2.5 N F C S

ET LUX ACROSS A LOSED URFACE

Let us consider a closed surface as represented in Figure 3.4. In the figure an
elementary area

, which can vary from point to
point, are represented. In regions where normal and velocity have opposite senses
the internal product is negative, meaning that property

∆ A , local normal n, and velocity u

is being advected (trans-
ported) into the interior of the volume limited by the surface. Where the internal
product is positive, the property is being transported outward. Thus, the integral of
the flux (advective or diffusive) over a closed surface gives the difference between
the amount of property being transported outward and inward.

B

3.3 TRANSPORT AND EVOLUTION

An evolution equation describes the transformations suffered by a property as time
progresses. The properties of a fluid limited by solid surface can be modified only
by production (sources) or destruction (sinks) processes. If the boundary of the