DOI : 10.4197/Mar. 24-2.9
133
Computation and Classification of the Sediment Transport Model in El-Max Bay, Alexandria, Egypt
A.E. Rifaat* and N.A. El-Naggar
National Institute of Oceanography and Fisheries, Al-Anfushi 21556, Alexandria, EGYPT
Abstract. Hydrodynamic flow and sediment transport models in aquatic environments are essential in many studies such as sediment movements, accretion-erosion phenomena, and pollution dispersion. The pattern of sediment dispersion of El-Umoum Drain that discharges into El-Max Bay was not accurately studied. Therefore, the goal of this paper is to predict the sediment transport model in El-Max Bay and classify the flow type.
The equations of continuity and momentum were used to calculate the model parameters and the output was displayed using sophisticated computer programs. The computed sediment transport model of El- Umoum Drain flow into El-Max Bay showed that the flow type changes from wall jet following a southwestern path to shoreline attached jet moving northwestward then turns to be a free jet flowing northward. The model shows that the complete dispersion of the sediment flow is achieved in four hours and that its impact on El Dekhila Harbour is pronounced. As time passes, the accumulation of sediments near the harbour’s entrance might cause a siltation problem unless regular dredging is carried out.
Keywords: Hydrodynamic, flow, sediment, transport model, El-Max Bay, Alexandria, Egypt.
Introduction
Sediment transport models are frequently used tools to predict the movements of suspended particles in the water bodies. They are essential for studying the erosion-accretion phenomena, siltation of navigational channels and ports’ entrances, siltation of outlets of coastal lakes and estuaries….etc. Moreover, the dispersion of pollutants discharged into
the water bodies such as lakes and estuaries could be predicted using the transport models to assess their impacts on the aquatic environments temporally and spatially. The proximity of any computed sediment transport model from reality depends on the quality and adequacy of the input data and the integrity of the computational process.
In fact, positively buoyant surface jets and plumes are formed when a lighter water mass is being discharged continuously through a well- defined source, often an open channel, near or parallel to the free surface of a receiving water body. Such discharges are common both in natural geophysical situations, but also in hydraulic, environmental, and industrial applications, including various types of wastewater discharges into water courses or flows in treatment facilities. The buoyancy of these discharges is usually due to differences in temperature, salinity, or suspended solids. Depending on the geometric and dynamic characteristics of the receiving water that may be stagnant or flowing, a number of complex fluid mechanical processes will occur affecting the shape and extent of the resulting discharge plume and its degree of mixing. The major environmental engineering application concerns pollutant discharges from municipal or industrial sources, or from mining activities into lakes, rivers, estuaries, or coastal waters. This is oldest and, in the form of a simple surface channel at the shoreline, the least costly form of wastewater discharges. Recent water quality and mixing zone regulations in most industrialized countries prohibit or discourage the surface discharge mode, as it often impacts the ecologically sensitive shoreline which usually has low degrees of dilution (factor of 10 or less).
Much higher dilution rates can be achieved with offshore submerged discharges, in particular multiport diffusers (dilutions of order of 50 and 100), as required by modern water quality regulations, often in combination with advanced pre-discharge treatment processes.
Nevertheless, the surface discharge mode continues to be an option and reliable predictive planning methods are required, in particular for the relicensing of already existing discharges, for small sources, or for heavily polluted water courses.
Combined sewer overflows that can carry large intermittent pollutant or sediment loads into water bodies are another important application, as are waste heat discharges from once through thermal
power plants. In the latter case, temperature-related water quality regulations call for lower dilution rates of the order of 5 to 10 which can be readily achieved with a shoreline discharge, so that an offshore discharge is not necessary. As the cooling water flow rates can be very large, the resulting plumes can reach substantial dimensions.
Surface inflows also occur in other technical applications, e.g., the design of sewage or industrial treatment plants, where the high or low degree of mixing may be required depending on process needs, so that the dynamics of the buoyant inflow need to be matched with the geometry of the treatment tank (Jones et al., 2007).
Buoyant plumes from natural river discharges are of great oceanographic and limnological interest due to the unique biogeochemical processes they support (Amon and Benner, 1998) and their large regions of influence. Studies of small-scale plumes, such as those which flow as pulses from tidal estuaries or lagoons (e.g., the Leschenault Estuary, Australia; Luketina and Imberger, 1987; 1989, have provided excellent geophysical laboratories for plume studies. In contrast, large-scale plumes, such as those from the Amazon and Columbia rivers (Hickey et al., 1998), can attain dimensions of hundreds of kilometers. On these scales, the Earth’s rotation alters the plume structure and controls its dynamics; the importance of the Coriolis force is a function by the Kelvin number, the ratio of the width of the plume to the baroclinic Rossby radius (Garvine, 1995). Intense mixing at horizontal fronts and convergence zones that form at plume boundaries support high biogeochemical activity and are dynamically important to the plume evolution (Orton and Jay 2005). These regions also gather surface debris, displace fluid vertically, and release large amplitude internal waves that propagate through the ocean interior (Washburn et al., 2003 and Nash and Moum, 2005).
In river systems, the lateral inflow of a tributary branch, containing water of a different temperature or turbidity into a main river, also represents a surface discharge situation. The resulting thermal bar can offer thermal refugia for migrating fish or have a blocking effect on fish and other species and thus is an important application for ecological management (Torgersen et al., 1999). Whereas a buoyant surface
discharge into an adjacent water body represents a seemingly simple problem configuration, a number of complex flow phenomena can arise in actuality. These can be grouped into near field and far field processes.
In the near field jet mixing modified by buoyant damping and collapse motions and by interaction with confining boundaries and with any ambient cross flow takes place. In the far field the plume is advected by the ambient current, but will undergo further mixing and lateral spreading through buoyant frontal motions and through passive diffusion. In general, complete information over the whole spatial extent, covering all these processes, is required. For example, water quality regulations can be applicable in the near field or the far field (Doneker and Jirka, 1991).
Predictive modeling approaches for buoyant surface jets are, of course, rooted in the fluid mechanics of free turbulent jet motions. The key historical advancements for submerged jet analysis, including the developments of the entrainment concept, of the integral modeling technique, and of the length scale analysis for the display of overall similarity aspects, have been summarized by Jirka (2004). All that work is pertinent, even though in modified form, to the surface jet configuration as well.
El-Umoum Drain is the main channel transporting the surplus wastewater together with significant quantities of suspended sediments from Lake Maryut to El-Max Bay west of Alexandria city. Lake Maryut is the main sink of agricultural drainage water of El Beheirah Governorate, the municipal wastewater of Alexandria city and its suburbs, and also the wastewater from the industrial zone west of Alexandria city. The motion behaviour of the suspended load discharged from El-Umoum Drain into El-Max Bay was not well studied. Mohamed et al. (2007), based on wind and current data collected in 1996-1997, mentioned that the water surface flow from El-Umoum Drain moves to the east and northeast directions towards Alexandria Western Harbour.
This means that the suspended load is transported to the entrance of the Western Harbour, where they are deposited and accumulated with time causing a siltation problem. On the other hand, satellite images of different dates showed that the surface plume from El-Umoum Drains follow a south-western direction towards El-Delkheila Harbour rather than the north-eastern direction as mentioned by Mohamed et al. (2007).
The purpose of this paper is to provide a more realistic predictive sediment transport model for the buoyant surface effluent discharged from El-Umoum Drain into El-Max Bay with variable geometry, momentum and buoyancy.
Area of Study
El-Max Bay situated along the Egyptian Mediterranean Sea coasts and extends for about 5 km between El-Dekheila Harbour west and the entrance of Alexandria Western Harbour east (Fig. 1). The bathymetry follows the normal pattern increasing seaward having a depth of 1.8 m just off El-Umoum Drain outlet to 14 m offshore with a mean depth of 8 m. Its surface area is about 15 km2 (measured from Google Earth Pro 2013) and its volume is about 0.6 km3. It receives significant amounts (varies from 143x106 to 208x106 m3 /month) of drainage water from El- Umoum drain loaded with mixed municipal-industrial-agricultural wastes from Lake Maryut via El-Max pumping station which lies about one kilometer upstream from the outlet (El-Naggar, 2013 and Mohamed and Fahmy, 2005). Moreover, several industrial plants discharge their effluents directly into the bay; these are: Misr Petroleum Company, Cement factory and tanneries, Alexandria Petroleum Company, Misr Chemicals Industries Company and Alexandria Iron and Steel Factory.
Moreover, more than 75% of the Egyptian external trade and shipping activities are handled through Alexandria Western and El-Dekheila harbours (Rifaat and Khalil, 2011). The surface water temperature varies from a minimum of 14.5°C in January to a maximum of 31.0°C in July.
Seawater salinity varies regionally within a wide range, from Mediterranean shelf water in the north to brackish water near El-Umoum Drain outlet. The minimum surface salinity (3.5) occurs during January off El-Umoum Drain outlet and the maximum (39.3) occurs in July at about 1.7 km off El-Umoum Drain outlet. Four types of water could be identified; mixed land drainage with a salinity of < 10; mixed water with salinity 10 to 30; diluted sea water with salinities range from 30 to 38.5;
and Mediterranean seawater of salinity > 38.5. The horizontal extension of each water type is highly variable and depends upon the pattern of circulation and the rate of outflow (Emara et al., 1984; 1992; Dorgham et al., 1987; Said et al., 1991; Nessim, 1994; Fahmy et al., 1995; and Labib, 1997).
Fig.1. An image showing the study area (source: Google Earth Pro 2013).
Model Computations
The sediment transport model computation is carried out using the equations of continuity and momentum (Jirka, 2007). The equation of continuity is given by:
d/dx(uH) + d/dy (vH) + dn/dt = Q where,
H= h+n h is mean water depth, m
n is change in water level, m
H is total water depth, m
u is velocity component in x-direction, m/sec v is velocity component in y-direction, m/sec t is time, sec
Q is injected water, m3/sec.
As the continuity equation includes three unknown variables u, v, and h, two more equations are involved. These are given by the momentum equations in two directions.
The momentum equations in the x and y directions are given by:
du/dt + u du/dx + v du/dy = –g dn/dx + fv – g/HC2 (u2+v2)1\2 u + k/H Wx |W| – Q/H (u-uo)
and
dv/dt + u dv/dx + v dv/dy = –g dn/dy + fu – g/HC2 (u2+v2)1\2 v + k/H Wy |W| - Q/H (v-vo)
The Coriolis parameter f, is defined as:
f = 2 w sin z
where z is the latitude and w is the Earth's rate of rotation equal to 7.2722×10-5sec-1.
The wind shear stress parameter, k, is defined as:
k = raCD/r where,
g Acceleration of gravity, m/sec2 w The Earth's rate of rotation, sec-1 z Latitude, deg
C Chézy bottom friction coefficient, m1/2/sec ra Density of air, kg/m3
CDWind drag coefficient r Fluid density, kg/m3
Wx Wind velocity in x-direction, m/sec Wy Wind velocity in y-direction, m/sec
|W| Wind speed, m/sec
uo Velocity of injected water in x-direction, m/sec vo Velocity of injected water in y-direction, m/sec
The momentum equations together with the equation of continuity complete the specification of the shallow water sediment transport problem.
The program Aquasea 7.2 developed by Vatnaskil Consulting Engineers is used to calculate the sediment flow and transport model.
The input parameters were, the bathymetry of the study area (1.8m – 14m), the direction of the injected plume (315°), period of sinusoidal forcing (12 hours), the most common wind direction (258°), the monthly average wind speed (3.4 m/sec), the discharge average flow rate (80 m3/sec), the cross-section area of the outlet (24m2), the Chézy coeffiecient (23 m1/2/sec), the sediment settling velocity (2.1 x 10-4 m/sec) and the convective term at latitude 30° (El-Naggar, 2013;
unpublished data). The spatial boundary condition is defined by the extent at which normal seawater salinity is prevailed. The output of the Aquasea application is presented using the computer application Surfer 11 from Goldensoftware Company.
Results and Discussions
Mohamed et al. (2007) based on the data of 1996-1997 computed a model for the surface discharge from El-Umoum Drain and their model showed that the discharged water from El-Umoum drain would be dispersed in the open sea and carried into the Western Harbour (north- eastern and eastern trends). They mentioned that the effects of the Coriolis force, the advective terms and the tides were ignored in their model calculations. Moreover, Mohamed et al. (2007) did not include the geometry of the injecting channel in their calculations. Contrarily, satellite images of different dates (Fig. 2) showed that the water plume that is loaded with significant amount of solids (that is why it could be viewed in the satellite images) from El-Umoum Drain is moving south- westward parallel to the shore. To verify the real behaviour of the inflow, the sediment transport model is re-computed herein taken into consideration the ignored variables.
Fig.2. Satellite images showing El-Umoum Drain plume patterns at different dates (source:
Google Earth Pro 2013).
The sediment transport model for the discharge from El-Umoum drain is presented in Fig. (3). The plume follows the long-shore transport trend in a more or less south-western direction in the first 2 hours of continuous discharge (Fig. 3a). The wind induced current that blows from the 258° direction forced El-Umoum Drain water to follow the south-western path. As the water continues to discharge from the outlet the jet path turns to the western and north-western directions, gradually, overcoming the SE and E surface currents and this could be noticed from the 3 hours discharge model (Fig. 3b). After 4 hours of continuous discharge the jet path is towards north and the complete mixing of fresh water from El-Umoum Drain and seawater of El-Max Bay is achieved (Fig. 3c). At this instance the suspended load of the injected water might be finally deposited on the bottom. The surface flow could be classified into four types (Jones et al., 2007):
1- Free jets (Fig. 4a) are characterized by a gradual bending so that the flow does not interact with the near shoreline. The cross flow has two effects on a free jet. The first is to entrain ambient momentum into the jet causing a gradual bending of the jet, and the second is to advect the plume downstream, eliminating an unsteady buoyant spreading regime in favor of lateral spreading that increases with increasing downstream distance.
2- Shoreline-attached jets (Fig. 4b) are characterized by dynamic attachment of the flow to the downstream shoreline, creating a zone of re-circulating effluent. This phenomenon may be caused by two effects.
First, a strong cross current can bend the jet over far enough to cause it to dynamically attach to the bank. Alternatively, a discharge that occupies the full depth of the receiving water can effectively “block off” the ambient current causing the flow to be pushed against the downstream shoreline. The zone of re-circulating effluent along the downstream bank is caused by the wake effects in the lee of the jet.
3- Wall jets (Fig. 4c) can be considered as weakly deflected jets which are discharged in a coflow (or nearly so) along the bank. The bank then acts as a reflective boundary along which a mirror image of the discharge can be assumed. The initial mixing within the near field is jet- like. However, at the transition to the far field, this jet mixing becomes secondary, and the far-field processes of buoyant spreading and/or passive diffusion become dominant.
4- Upstream intruding plumes (Fig. 4d) occur when a strongly buoyant effluent is discharged into a slowly moving environment. They are characterized by a front in which the buoyant upstream intrusion is balanced by a drag force at the head of the plume. The near field is limited primarily to the area of the plume upstream of the discharge. At a short distance down- stream from the discharge, the plume exhibits the far-field processes of buoyant spreading and, eventually, passive diffusion.
Accordingly, during the first 2 hours of discharge, El-Umoum Drain jet could be considered as a wall jet. After 3 hours the discharge behaves as a shoreline-attached jet. By the end of 4 hours of continuous discharge the effluent behaves like a free jet and the mixing of the drain water and the seawater is completed.
Fig. 3. Sediment transport model of El-Umoum Drain discharge into El-Max Bay: (a) after 2 hours from discharge; (b) after 3 hours from discharge; (c) after 4 hours from discharge. The arrows define the directions of the transport.
Fig. 4. The buoyant surface discharges for four major flow categories: free jets, shoreline- attached jets, wall jets, and upstream intruding plumes (adapted from Nash and Jirka, 1995). (a) Buoyancy dominated free jet, (b) Shoreline attached jet, (c) Wall jet and (d) Upstream intruding plume.
Conclusions
The computed sediment transport model of El-Umoum Drain flow into El-Max Bay showed that it takes 4 hours to reach the maximum mixing with seawater at the boundary conditions. During the first two hours it behaves as a wall jet flow having a south-western direction parallel to the seashore towards the entrance of El Dekheila Harbour. As time passes it turns to behave as a shoreline attached jet having a more or less western to north-western directions. By the end of four hours the jet is of free type flowing northward. Its impact on El Dekhila Harbour is
pronounced and with time the accumulation of sediments near the harbour’s entrance might cause a siltation problem unless regular dredging is carried out.
The computation of the sediment transport model of the surface jets should involve all the hydrodynamic and channel geometry variables to obtain a more realistic model. Ignoring some variables may lead to incorrect prediction of the flow behaviour such as the case in El-Max Bay presented in this paper. The model was computed without considering the basin and channel geometrical parameters, the Coriolis force and the tide effects have yielded a pseudo north-eastern flow model, whereas recalculation of the flow using the ignored parameters yielded a near realistic flow model simulation.
References
Amon, R.M.W. and Benner, R. (1998) Seasonal patterns of bacterial abundance and production in the Mississippi River plume and their importance for the fate of enhanced primary production. FEMS Microbiol. Ecol., 35(3): 289-300.
Doneker, R.L. and Jirka, G.H. (1991) Expert systems for mixing zone analysis and design of pollutant discharges. J. Water Resour. Plann. Manage., 117(6): 679-697.
Dorgham, M.M. and Osman, M.M. (1987) Environmental Conditions in Abu-Qir Bay, East of Alexandria. II-Plankton Distribution, Downstream from Land-Based Effluents.
Chemosphere, 16 (2/3): 559-564.
El-Naggar, N.A. (2013) Studies on some disposed toxic organic contaminants into Mex-Bay and its adjacent areas, Alexandria-Egypt. Ph.D. Thesis, Faculty of Science. Al-Azhar Univ., Egypt (Unpublished).
Emara, H.I., Iskandar, M.F. and Assad, F.N. (1984) Chemistry of the Water West of Alexandria, Bull. N.I.O.F, A.R.E., 10: 35-49.
Emara, H.I., Shridah, M.A., Moustafa, T.H. and El-Deek, M.S. (1992) Effect of Sewage and Industrial Wastes on the Chemical Characteristic of the Eastern Harbour and El-Mex Bay waters of Alexandria, Egypt. Marine Coastal Eutrophication, Proc. Int. Conference Bologna, Italy, 21-24 March, Elsevier, pp: 773-784.
Fahmy, M.A., Tayel, F.T. and Shridah, M.A. (1995) Effect of Pollution on the Water Quality of El-Mex Bay and El-Dekhaila Harbour of Alexandria, First Int. Conference on Present and Future Technology of Navigation and Marine Science of Mediterranean and Red Sea, 29- 31 Oct. 1995.
Garvine, R.W. (1995) A dynamical system for classifying buoyant coastal discharges.” Cont.
Shelf Res., 15(13): 1585-1596.
Jirka, G.H. (2004) Integral model for turbulent buoyant jets in un- bounded stratified flows. 1:
The single round jet. Environmental Fluid Mechanics, 4: 1-56.
Jirka, G.H. (2007) Buoyant Surface Discharges into Water Bodies. II: Jet Integral Model. J.
Hydraul. Engineer., 133(9): 1010-1020.
Jones, G.R., Nash, J.D., Doneker, R.L. and Jirka, G.H. (2007) Buoyant Surface Discharges into Water Bodies. I: Flow Classification and Prediction Methodology, J. Hydraul.
Engineer., 133(9): 1021-1036.
Hickey, B.L., Pietrafesa, D.J. and Boicourt, W. (1998) The Columbia River plume study:
Subtidal variability in the velocity and salinity fields. J. Geophys. Res., 103(10): 339-368.
Labib, W. (1997) Eutrophication in Mex Bay (Alexandria, Egypt), Environmental Studies and Statistical Approach, Bull. N.I.O.F, A.R.E., 23: 49-68.
Luketina, D. and Imberger, J. (1987) Characteristics of a surface buoy-ant jet. J. Geophys. Res., 92(C5): 5435-5447.
Luketina, D. and Imberger, J. (1989) Turbulence and entrainment in a buoyant surface plume. J.
Geophys. Res., 94(C9): 12619-12636.
Mohamed E.E., El-Sayed M.E., Saad, N.N. and Abou Tahoun, H.A. (2007) Application of a Mathematical Model for Estimating the Pattern of Pollution Dispersion at the Coast of Alexandria, JKAU: Mar. Sci., 18: 149-167.
Nash, J.D. and Jirka, G.H. (1995) Buoyant discharges in reversing ambient currents:
Experimental investigation and prediction. Technical Rep., DeFrees Hydraulics Laboratory, Cornell Univ., Ithaca, N.Y. (also published by Maryland Dept. of Natural Resources, Tech.
Rep. No. CBWP-MANTA-TR-97-2, 1997).
Nash, J.D. and Moum, J.N. (2005) River plumes as a source of large-amplitude internal waves in the coastal ocean. Nature (London), 437: 400-403.
Nessim, R.B. (1994) Environmental Characteristics of Mex Bay, First Arab Conference on Marine Environment Protection, 5-7 Feb., Sheraton, Alexandria, pp: 221-243.
Orton, P.M. and Jay, D.A. (2005) Observations at the tidal plume front of a high-volume river outflow. Geophys. Res. Lett., 32: L11605.
Rifaat A.E. and Khalil, M. Kh. (2011) The Impact of the Unplanned Structural Adjustment of Breakwaters on the Marine Environment of Port of Alexandria, Egypt: A Lesson Learnt for Future Concern. J. KAU: Mar. Sci., 23(2): 165-178.
Torgersen, C.E., Price, D.M., Li, H.W. and McIntosh, B.A. (1999) Multiscale thermal refugia and stream habitat associations of Chi- nook salmon in Northeastern Oregon. Ecol. Appl., 9(1): 301-319.
Washburn, L., McClure, K.A., Jones, B.H. and Bay, S.M. (2003) Spatial scales and evolution of stormwater plumes in Santa Monica Bay. Mar. Environ. Res., 56(1/2): 103-125.
!
.
!
!
"
# .
$% & '( ) &
* + , , ' !( - $% /0 1 1
'2 ,3 4 "# ! ,
5 6 7 *7 , *
! '(
7 8 '( $%
.
! &%9 % '2 7 $ & % :% ;# & <
.
= 2)>
& / !
6 8 4 & '( , ,> 2
wall jet
?%
@
@ A6
&# "!B !: *:
A6 &% /0 ;
shoreline attached jet
?
< ; *:
% &#
free jet
? ; *:
. C ,
*7
- $% /0 & '( ; ,>
<
! & #D ,> E>
(
@B % F ;% F60 & 7
F :G %
@ F ;% 26 .
