Geoscience Reference
In-Depth Information
The hydrodynamic processes that occur in this zone are often neglected in river
engineering. Nevertheless there are cases where the groundwater velocity field
influences the open channel hydrodynamics (Herrera-Granados
2008b
), espe-
cially in shallow waters with flow velocities that close to the bottom tend to be
laminar.
In the majority of the European heavily modified rivers (according to the WFD
classification), several hydraulics structures were built for river regulation, flood
control, or for different socioeconomic purposes (Herrera-Granados
2008a
). The
water level, upstream these constructions, is higher than the water level down-
stream. Therefore, the difference between the downstream and tailwater levels
represents a hydraulic head that can provoke seepage under or beside the structure
(if the soil of the hyporheic zone is permeable enough). Hence, seepage cannot be
neglected for such conditions because it changes not only the velocity field, but also
the sediment transport rate and the bed forms (Herrera-Granados
2008b
). Down-
stream, in the vicinity of this kind of structures, the direction of the seepage is
practically upward. Hence, this chapter if focused on analyzing the influence of the
seepage in the free-surface flow at the laboratory scale where upward groundwater
flow was induced.
1.2 Theoretical Background about Turbulent
Incompressible Flows
The Navier-Stokes Equations (NSE) give an accurate description of a great variety
of fluid flows including turbulent flow with unordered seemingly chaotic fluid
dynamics. For incompressible turbulent flows, the momentum (
1
) and the continu-
ity (
2
) equations that describe the fluid's motion are:
2
u
i
@
@
u
i
@
u
j
@
@x
j
¼ u
@
u
i
1
r
p
@x
i
þ
@
t
þ
x
j
g
i
(1)
@
u
i
@x
i
¼
0
(2)
where
u
i
is the velocity component in the
i-
direction,
p
is the pressure,
r
is the
fluid's density,
is the kinematic viscosity, and
g
i
are the external body forces
acting on the system in the
i-
direction. A full analysis of all the turbulence
structures within the fluid is practically impossible in engineering and out of
the scope of this chapter. Thus, the Reynolds averaging form of the NSE or
RANS (Reynolds' Average Navier Stokes) equation (
3
) and its parameters are
briefly mentioned.
RANS is the basis of the most popular numerical approaches for analyzing
turbulent flows in engineering because not all the turbulent scales are resolved
u
