Environmental Engineering Reference
In-Depth Information
the spatial variation as a linear mixing process, salinity is used to estimate the freshwater of the estuary
over a pre-specified period:
SS
V
o
V
(8.6)
f
S
o
where
V
f
is the mean volume of freshwater in the embayment,
V
is the mean total volume of the
embayment,
S
o
and
S
are the sea water salinity and the salinity in the embayment, respectively. The flushing
time is then obtained by dividing the volume of fresh water (
V
f
) by the freshwater inflow (
Q
f
) to the estuary:
V
T
f
(8.7)
f
Q
f
This method provides a more realistic estimation of the flushing time, but can be used only when reliable
detailed salinity and flow measurements are available. Moreover, the method is prone to error when
salinity gradients along the coastal inlet are small (e.g., when most of the rainwater is routed to reservoirs,
resulting in negligible freshwater inflow into the sea).
For environmental management purposes, it is necessary to define both local and system-wide flushing
times to represent the effectiveness of the mass exchange with the surrounding water body and the open
sea, respectively. The local flushing time is useful for estimating the local impact of any foreign substance
or short-term effluent discharge from a small local region (e.g., a fish farm). However, for some water
quality parameters such as nutrient level, the outer bay has a non-zero concentration due to the return of
pollutants with the flood and ebb of tides. In this case, the system-wide flushing time needs to be considered
by looking at mass removal from a much larger water body which is connected to an adjoining “clean”
ocean. This definition takes into account the interactions between different parts of the water body which are
not assumed to be clean and represents the long-term flushing efficiency of the region of interest. For this
reason, it is often advantageous to model a semi-enclosed tidal region as a separate system within a larger
water body connected to the open sea (Fig. 8.24b). We denote the tracer mass in the inner segment of volume
V
1
as
M
1
and the rest of the system (segment 2) of volume
V
2
as
M
2
. Hence, the tracer concentrations are
C
1
(=
M
1
/
V
1
) and
C
2
(=
M
2
/
V
2
), respectively. Assuming the net tidal exchange flows between segments 1
and 2 are
Q
12
and
Q
21
and those between the system and the clean ocean are
Q
20
and
Q
02
, respectively,
the following two equations can be obtained by tracer mass conservation (Choi and Lee, 2004),
d
VC
11
QC
QC
(8.8)
12
1
21
2
d
t
d
VC
22
QC
QC QC
(8.9)
20
2
12
1
21
2
d
t
By applying different initial tracer distributions, both the local and system-wide flushing time can be
computed from the tracer experiments. For example, assuming that a conservative tracer mass is
instantaneously released into the fish farm (i.e., with the initial concentration of unity within the fish
farm and zero elsewhere), the tracer mass reduction process is computed by solving Eqs. (8.8) and (8.9):
M
J
e
kt
(1
J
)
e
k t
(8.10)
1
2
M
o
where, the three coefficients
Ȗ
,
k
1
and
k
2
are related to the segment volumes and tidal exchange flows.
Using the definition in Eq. (8.3), the local flushing time is given by:
J
1
J
T
(8.11)
f
k
k
1
2
Eq. (8.10) shows that the decrease in tracer mass follows a double-exponential curve described by
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