13.2 Transport and Mixing in Estuaries
401
in which c and u are the cross-sectional averaged concentration and stream velocities, respectively, and x is the longitudinal spatial dimension. In a laterally
uniform flow, only vertical shear contributes to the shear dispersion. Thus,
using Taylor's (1953) approach (see Sect. 8.3.3), we can express the dispersion
coefficient, K x , as follows: (Elder, 1959):
1 jO
jZ jZ2
Kx = --- u'(z)
U'(Zl) dZ 1 dZ2 dz,
hKz -h
-h -h
(13.25)
in which h is the water depth, u' is the deviation of the velocity, u( z), from the
mean velocity, and K Z is the turbulent diffusion coefficient.
In vegetated estuaries additional dispersion mechanisms arise due to the
physical obstruction associated with plant stems and wakes behind the stems.
These mechanisms are known as mechanical dispersion and they are common in
porous media or in flow through random media, for example, flow in mangrove
forests (Massel et al., 1998).
In general, the resulting dispersion coefficient, K x , depends on the biological
morphology and density of the vegetation in the estuary. Nepf et al. (1997a),
studied the influence of vegetation on longitudinal diffusion in a laboratory
flume, for various flow velocities and population densities. Spartina attermifiora, the dominant marsh grass in much of Eastern North America, was
modelled with 0.6 cm diameter hard-wood dowels. Rhodamine was injected
continuously upstream of the dowel array. For the no-dowel cases with velocities 2.9, 5.5 and 7.4 cm/s, respectively, the observed dispersion coefficient, K x ,
was found to be 7.5, 7.3 and 8.4 cm 2 /s. However, for 5.5% dowel density, the
coefficient, K x , drops to about l.2 cm 2 /s. The influence of the mechanical
dispersion appears to be small in comparison with the shear dispersion.
Detailed laboratory velocity measurements of N epf et al. (1997b) showed
that the production of turbulence within a stand of emergent vegetation is
dominanated by the stem wakes rather than by the bottom boundary shear.
Using this observation, they formulated a random walk model which can be
used to determine the contribution of stem wakes to the turbulent diffusivity
within a plant canopy.
The influence of mangrove swamps on the longitudinal dispersion in mangrovefringed tidal creeks was examined by Ridd et al. (1990). The effect of turbulent
diffusion was found to be negligible compared with the dispersion due to the
trapping effect of the mangroves. The longitudinal dispersion coefficient was
proportional to the square of the water velocity. Therefore, at the creek head,
the mixing rates are very small. The resulting residence time of contaminants
becomes longer for water close to the head of the creek.
13.2.4 Influence of Mixing on Primary Production
Definition of Primary Production. Productivity of biomass is the basic
biological quantity measured in the aquatic environment. In this chapter, as
401
in which c and u are the cross-sectional averaged concentration and stream velocities, respectively, and x is the longitudinal spatial dimension. In a laterally
uniform flow, only vertical shear contributes to the shear dispersion. Thus,
using Taylor's (1953) approach (see Sect. 8.3.3), we can express the dispersion
coefficient, K x , as follows: (Elder, 1959):
1 jO
jZ jZ2
Kx = --- u'(z)
U'(Zl) dZ 1 dZ2 dz,
hKz -h
-h -h
(13.25)
in which h is the water depth, u' is the deviation of the velocity, u( z), from the
mean velocity, and K Z is the turbulent diffusion coefficient.
In vegetated estuaries additional dispersion mechanisms arise due to the
physical obstruction associated with plant stems and wakes behind the stems.
These mechanisms are known as mechanical dispersion and they are common in
porous media or in flow through random media, for example, flow in mangrove
forests (Massel et al., 1998).
In general, the resulting dispersion coefficient, K x , depends on the biological
morphology and density of the vegetation in the estuary. Nepf et al. (1997a),
studied the influence of vegetation on longitudinal diffusion in a laboratory
flume, for various flow velocities and population densities. Spartina attermifiora, the dominant marsh grass in much of Eastern North America, was
modelled with 0.6 cm diameter hard-wood dowels. Rhodamine was injected
continuously upstream of the dowel array. For the no-dowel cases with velocities 2.9, 5.5 and 7.4 cm/s, respectively, the observed dispersion coefficient, K x ,
was found to be 7.5, 7.3 and 8.4 cm 2 /s. However, for 5.5% dowel density, the
coefficient, K x , drops to about l.2 cm 2 /s. The influence of the mechanical
dispersion appears to be small in comparison with the shear dispersion.
Detailed laboratory velocity measurements of N epf et al. (1997b) showed
that the production of turbulence within a stand of emergent vegetation is
dominanated by the stem wakes rather than by the bottom boundary shear.
Using this observation, they formulated a random walk model which can be
used to determine the contribution of stem wakes to the turbulent diffusivity
within a plant canopy.
The influence of mangrove swamps on the longitudinal dispersion in mangrovefringed tidal creeks was examined by Ridd et al. (1990). The effect of turbulent
diffusion was found to be negligible compared with the dispersion due to the
trapping effect of the mangroves. The longitudinal dispersion coefficient was
proportional to the square of the water velocity. Therefore, at the creek head,
the mixing rates are very small. The resulting residence time of contaminants
becomes longer for water close to the head of the creek.
13.2.4 Influence of Mixing on Primary Production
Definition of Primary Production. Productivity of biomass is the basic
biological quantity measured in the aquatic environment. In this chapter, as