Transactions on Ecology and the Environment vol 2, © 1993 WIT Press, www.witpress.com, ISSN 1743-3541
The
dispersion of treated effluent by tide
and wind in a stratified bay
A.M. Oakes, N.V.M. Odd, A.J. Copper, W. Roberts
HR Wallingford, Howbery Park, Wallingford, Oxfordshire
ABSTRACT
The paper describes how 3D modelling techniques were used to
simulate the interaction of tide and wind on circulations in St Andrews
Bay in Scotland, which has a weak but well defined halocline at mid
depth caused by the inflow from the River Tay.
INTRODUCTION
Fife Regional Council (FRC) intend to embark on a program of capital
works to provide a new sewage treatment plant south of the town of
St Andrews on the east coast of Scotland, Figure 1. In order to
demonstrate that the proposed sewage treatment and disposal options
meet Environmental Quality Objectives and Standards,
FRC
commissioned the preparation of marine hydrodynamic and bacterial
dispersion models of St Andrews Bay.
In vertically well mixed coastal waters, the standard method of
predicting the physical dispersal of treated effluents by tide and wind
from long sea outfalls and their impact on adjacent beaches, has been
the use of two-dimensional depth averaged flow models and quasi3D random walk pollutant dispersion models (Mead'). In the case of
semi-enclosed bays with weak or negligible tidal currents the interaction
of wind stress and the Coriolis force generates complex 3D residual
circulations governed by the geometry of the bay, with downwelling and
upwelling near the shoreline, which can not be simulated by the above
techniques. The situation is further complicated by the existence of a
thermocline or halocline which can trap effluent below the surface and
reduce the vertical exchange of momentum and solutes across the
pycnocline. In these cases it is important to use 3D modelling
techniques. St Andrews Bay outfall study is an example.
Transactions on Ecology and the Environment vol 2, © 1993 WIT Press, www.witpress.com, ISSN 1743-3541
184 Water Pollution
FLOW REGIME IN ST ANDREWS BAY
The tidal regime is dominated by the effects of the main flood and ebb
tides, which run from Arbroath to Fife Ness, the Firth of Tay, which
discharges at the northern end of the Bay and wind stress.
/I 2D far field mode
3D model area
Figure 1 Location plan
The Bay is relatively deep (-10m) and as a result the tidal
currents are generally low, despite the 5m spring tidal range. In
particular, the south western corner of the Bay has peak speeds rarely
greater than 0.2 m/s. The wind, which is predominantly from a south
westerly direction, interacts with the tide to produce complex 3D
circulation. The currents are further complicated by a mid depth
pycnocline, caused by the slightly brackish outflow of the Firth of Tay,
with a salinity change of around 0.6 ppt over a 3m depth of water.
FLOW MODELLING
The use of a fine gridded, fully 3D flow model is limited to relatively
small areas, due to the computing power required.
It is often
advantageous, therefore, to use a 2D far-field model to obtain accurate
boundary conditions for a more local 3D model.
2D far-field model
For the St Andrews study a uniform 200m gridded, 2D tidal flow model
was set up covering the whole of the Bay, including the River Tay.
Boundary conditions were extracted from a 2D model of the North Sea.
Transactions on Ecology and the Environment vol 2, © 1993 WIT Press, www.witpress.com, ISSN 1743-3541
Water Pollution
185
Calibration
The calibration of the 2D model was achieved by
comparison with Admiralty diamond velocity data for mean spring tide
conditions.
Further data was available in the form of DRCM
observations close to St Andrews, although the data was very variable
both in terms of speed and direction and no comparable wind records
were available. However, both model and observations showed an
almost continuous anticlockwise circulation throughout the tidal cycle
in the vicinity of the proposed outfall
3D model
The 200m gridded, three-dimensional model consists of 10 discrete
layers and uses mixing length theories (Odd and Rodger^) to define the
vertical exchange of turbulent momentum and solutes. In St Andrews
Bay, the layers were defined as equal divisions of the water column
at each model cell, giving good vertical resolution throughout the model
area and enabling the simple definition of a pycnocline at mid depth.
The pycnocline was defined as a 0.6 ppt salinity change across
0.3 - 0.7 of the depth. This salinity gradient has the effect of severely
damping the vertical turbulent exchange of momentum between the
upper and lower layers of the water column. This "delinking" is
particularly important when prevailing winds are applied to the surface,
thereby generating completely different current patterns in the surface
and bed layers.
Boundary conditions for the 3D model with various applied wind
stresses were obtained by first applying the wind conditions to the 2D
model. By extracting the tidal levels from the 2D model throughout the
tidal cycle a consistent set of boundary conditions for each wind
condition was generated.
Calibration The calibration of the 3D flow model was based on mean
spring tidal level and velocity profile data at the proposed outfall site.
Wind data was available for this period and was applied as a constant
wind stress to the flow model.
An important factor was the choice of the single vertical density
(salinity) profile that was representative of conditions in the bay. In
this case, the model was not used to simulate an evolving density
field.
It was also necessary to decide whether to base the damping
function on the local or peak gradient Richardson Number. In the
latter case, the heavy damping effect of the salinity gradient on vertical
turbulent exchange in the pycnocline region also controls the level of
turbulence in the whole of the upper and lower layers. This often
happens in estuaries if the pycnocline is in the lower 0.7 of the depth.
However, in St Andrews Bay, model calibration tests showed that the
Transactions on Ecology and the Environment vol 2, © 1993 WIT Press, www.witpress.com, ISSN 1743-3541
186 Water Pollution
pycnocline appears merely to form a zone of locally reduced turbulence
separating the surface and bed layers.
A detailed simulation of the observed velocity data was hindered
by a great deal of variability in the observations, caused in part by the
difficulty in obtaining accurate readings of very low current velocities.
Local variability of the wind speed and direction also has an effect on
the surface current velocities, which the 3D flow model is unable to
reproduce, being only able to simulate the general flow pattern in the
Bay from an averaged wind. Figure 2 shows comparisons between
the observed and modelled velocities at surface, mid depth and bed.
Mid depth
-20
2 4 6 8 1 0 - 2 0 2 4 6 8 10 -2
Hours after High Water (Dundee)
Hours after High Water (Dundee)
0 2 46
8 10
Hours after High Water (Dundee)
Model Speed
Model Direction
Observed Speed
Observed Direct,o
Figure 2 Comparison of observed and modelled velocities
Overall, reasonable agreement was achieved between model and
observations, with the lower layers showing better agreement than the
surface layers, which were affected by the local wind drift. Table 1
gives the calibration statistics for the observed and modelled velocities.
Table 1
Depth
Surface
0.3D
0.5D
0.7D
Bed
Spring tide velocity calibration statistics
Correlation
coefficient
0.5
0.6
0.7
0.8
0.7
Model current speed Clockwise deviation
as a % of observed of model current
current speed
from observed
88
73
61
76
79
-3
-14
-13
-37
-4
RCM near bed velocity data was also available over a period of
a month at two sites, together with daily wind information. A low pass
filter was applied to the RCM data to investigate the magnitude and
direction of the residual currents. Comparison with residual, bed layer
Transactions on Ecology and the Environment vol 2, © 1993 WIT Press, www.witpress.com, ISSN 1743-3541
Water Pollution
187
currents from the 3D model with appropriate wind stress indicated a
good degree of agreement both in speeds and directions. A good
representation of the 3D residual circulation in the Bay is essential in
order to be able to predict the dispersal of discharged effluent.
The 3D model simulated a complex pattern of residual currents
with upwelling and downwelling resulting from the interaction of the
anticlockwise tidal residual circulation, the surface wind stress and
coriolis forces, which has an over-riding influence on the pattern of
dispersal of effluents in the Bay, as shown in Figure 3. This can not
be simulated in a 2D model.
Figure 3
Residual current pattern in bed and surface layers
RANDOM WALK POLLUTANT DISPERSION MODEL
Random walk dispersion models simulate the movement of pollutant
plumes discharged from sea outfalls or storm water overflow, using a
random walk representation of turbulent dispersion in both the
horizontal and vertical planes.
The 3D random walk model used for the St Andrews study was
driven by the 3D tidal flow model, including 3D residual currents driven
by winds crossing the whole Bay and used the same representation of
the layers and the density gradient. The local Richardson number was
used to evaluate the solute mixing length, assuming a critical flux
Richardson Number of 0.15 (Odd and Rodger^). A finer grid resolution
of 50m was used.
Calibration In order to calibrate the random walk model a dye release
in the surface layer was simulated and compared with field
observations. Figure 4 shows a comparison between the modelled
and observed surface dye plume, 10 hours after the start of the dye
Transactions on Ecology and the Environment vol 2, © 1993 WIT Press, www.witpress.com, ISSN 1743-3541
188
Water Pollution
release (HW+13.5hrs). The prevailing wind during the period of the
dye release was simulated by applying a constant wind stress to the
3D flow model used to drive the random walk model. It was also
decided to apply the actual time varying superposed wind drift to the
surface layer of the random walk model, in order to simulate the local,
short term surface drift fluctuations which the 3D flow model is unable
to reproduce. These short term fluctuations tended to increase the
local rate of dispersion of dye in the surface layer. The wind drift
factor, which expresses the surface, wind-driven current as a
percentage of wind speed, was considered a calibration parameter and
a value of 1.5% was found to give the best results. This was
additional to the wind driven currents simulated by the 3D flow model.
Figure 4 Comparison of observed and predicted surface dye plume
An objective statistical comparison between each observation and
the model results within a 100m search radius of that observation is
given in Table 2. It should be noted that the observations were nonsimultaneous and were batched into hourly groups for ease of
comparison with the model results. A search radius of 100m was not
considered unreasonable since the 3D flow model, which drives the
random walk model, had a grid size of 200m.
Table 2
Spring tide plume calibration statistics
Hours after high water
9.5
11.5
12.5
13.5
14.5
mean
% of observations within a
factor of 2 of model results
73
48
95
92
83
71
Transactions on Ecology and the Environment vol 2, © 1993 WIT Press, www.witpress.com, ISSN 1743-3541
Water Pollution
189
Similarly accurate results for the dispersal of dye in the surface
layer were obtained by driving a quasi-3D random walk model with
the 2D depth averaged tidal flow model. In this case the flow model
has no applied wind and the observed winds are directly applied to the
random walk model assuming a logarithmic decrease in wind influence
with depth and a return current near the bed. A higher wind drift
factor of about 3% was found to give the best results, to compensate
for the lack of a wind driven circulation in the flow model.
THE DISPERSAL OF A TRAPPED PLUME
The proposed new outfall in St Andrews Bay is to release treated
effluent from a diffuser on the sea bed. The predicted impact of the
effluent on the beaches of St Andrews would depend on whether the
plume was trapped below the mid depth pycnocline, since the surface
and bed residual circulations differed so greatly.
In order to estimate the initial rise height of the effluent plume,
the EPA plume model ULINE (Schuldt et aP) was used. The model
utilises the diffuser design, pollutant output flow and density, together
with the ambient cross-flow velocity and density structure to determine
the trapping level. This trapping level can then be used as the effluent
input level in the random walk model.
In the case of St Andrews, the effluent will be trapped at the
base of the pycnocline. The random walk model predicted that in this
case, the effluent would mix downwards throughout the lower layers,
but very little upwards dispersion would take place because of the
damping of vertical turbulent exchange by the pycnocline. Without the
pycnocline, the random walk model would mix the effluent throughout
the water column, resulting in pollutant in the surface layers travelling
in the opposite direction to the pollutant in the lower layers.
The trapping of effluent below the pycnocline causes worst case
contamination of beaches to occur with offshore winds, when the near
bed current carries the pollutant onshore. In this case the use of a
quasi-3D random walk model, driven by 2D depth averaged flow
results, would give totally misleading predictions. This is mainly due
to the wind drift profile in the quasi-3D random walk model, where an
unrealistic return current in the opposite direction to the wind is
assumed. In fact, the wind driven current in the bed layer may be in
any direction, depending on the geometry of the bay. In St Andrews
Bay, the tide averaged residual current speed at the proposed outfall
site from the depth averaged, 2D model is 0.2 m/s in a southerly
direction, whereas that for the bed layer of the 3D model is 0.02 m/s
in a north westerly direction. The 2D flow model results would be
seriously misleading in predicting the environmental effects of an
effluent plume trapped in the lower layers.
Transactions on Ecology and the Environment vol 2, © 1993 WIT Press, www.witpress.com, ISSN 1743-3541
190 Water Pollution
CONCLUSIONS
1. In St Andrews Bay, the accuracy of the 3D flow model was
improved by obtaining consistent boundary conditions from a calibrated
far-field 2D model with appropriate wind stress.
2. Representation of the damping of vertical turbulent exchange of
momentum across a pycnocline is essential in reproducing the 3D
pattern of residual circulation in the Bay,
3. Wind effects play a significant part in the dispersal of effluent
plumes due to their impact on residual circulation in the Bay.
4. Short term variations in the local wind cause a secondary drift and
lateral dispersal of a surface plume over that caused by 3D far field
wind driven current circulations.
5. Effluent plumes discharged near the sea bed may be trapped by
a pycnocline resulting in very different patterns of movement to that
of a surface plume. An accurate representation of the effect of the
pycnocline in the random walk model is essential to give valid
predictions of beach contamination.
6. 2D flow models and quasi-3D random walk models are inadequate
in modelling effluent plumes trapped below the surface by a
pycnocline.
ACKNOWLEDGEMENTS
The authors would like to thank Fife Regional Council and
Environmental Management Ltd for giving permission to show results
from a study of St Andrews Bay.
REFERENCES
1. Mead, C.T. Random walk simulations of the dispersal of sewage
effluent and dredged spoil, Proceedings of the 10th Australasian
Conference on Coastal and Ocean Engineering, pp477-480, 1991.
2. Odd, N.V.M and Rodger, J.G. Vertical Mixing in Stratified Tidal
Flows, Journal of the Hydraulics Division, ASCE, Vol 104, No HY3,
Paper 13599, 1978.
3. Schuldt, M.D., Davis, L.R., Frick, W.E., Muellenhoff, W.P., Soldate,
A.M. and Baumgartner, D.J. Initial Mixing Characteristics of Municipal
Ocean Discharge - Volume 1: Procedures and applications,
Environmental Protection Agency, EPA/SW/MT-86/012a, 1985.