Environmental Engineering Reference
In-Depth Information
Landfill
Advective transport
Groundwater Flow
Surface Water
Wet and dry
deposition
Outgasing
Wi
nd
Seepage
Sedimentation
River
flow
Groundwater
flow
Fig. 11.1 Pollutant environmental pathways with relevant advective transport
fluid flow occurs within the pore space of a solid material, as in aquifers, aquatic
sediments or the soil, the latter with seepage and air flow in the unsaturated or
vadose zone.
11.1 The Navier-Stokes Equations for Free Fluids
Considering all the different phenomena of flow fields, it may seem to be amazing
that one mathematical approach is well accepted as a fundamental description. It is
valid for all types of free flow, either laminar or turbulent, in bounded or unbounded
domains. The equations are a basis for many situations, although simplifications or
extensions are necessary. The generally accepted
Navier
1
-Stokes
2
equations
can be
noted as follows:
r
@
@t
2
v
v
þ r
ð
v
r
Þ
v
r
f
þrp þ r
¼
0
(11.1)
with fluid density
, velocity vector v, volume force f and pressure
p
.
p
and v are the
dependent variables. For a one-dimensional description the system (
11.1
) reduces
r
1
Louis Marie Henri Navier (1785-1836), French mathematician and physicist.
2
George Gabriel Stokes (1819-1903), Irish mathematician and physicist.
