Pollutant distribution from a coastal

            outfall is studied accounting for tidal currents. The problem is solved using k-eps

            model. The constants in the logarithmic law for vertical velocity profile in the bbl

            (bottom boundary layer) are obtained by processing experimental data from a current

            profiler. The near-field distribution of pollutant concentration at different distances

            from the diffusor are obtained for different times, in terms of ambient flow velocity

            and outfall discharge characteristics

LUO, Shengping

LYUBIMOVA, Tatyana

ROUX, Bernard

SHUMILOVA, Natalya

English

I-Revues

19ème Congrès Français de Mécanique                                                                                       Marseille, 24-28 août 2009 
  1
Modeling of the near-field distribution of pollutants from a 
coastal outfall subject to tidal currents 
T.P. LYUBIMOVAa, N. SHUMILOVAa, S.P. LUOb, B. ROUXb 
a. Institute of Continuous Media Mechanics UB RAS, 1, Koroleva Str., 614013, Perm, Russia 
b. Laboratoire Mécanique, Modélisation et Procédés Propres/UMR 6181 CNRS, 38, rue Frederic Joliot 
Curie, 13451 Marseille Cedex 20 
 
 
Résumé: 
On étudie la distribution des polluants émis par un émissaire marin soumis à de forts courants de marée. Le 
problème est résolu en utilisant un modèle k-ε . Les constantes utilisées dans la loi logarithmique pour le 
profil vertical de la vistesse dans la couche limite de fond (BBL) sont obtenues à partir de données 
expérimentales données par un profiler acoustique. La distribution spatiale et temporelle de la concentration 
des polluants dans le champ proche du diffuseur est obtenue en fonction de la vitesse du courant ambient et 
des caractéristiques de l’effluent industriel. On montre que même lorsque la densité de l’effluent est 
notablement plus faible que la densité du milieu récepteur, le panache de l’effluent est susceptible 
d’impacter le fond marin, créant ainsi un risque de pollution des sédiments de fond remobilisables. 
Abstract : 
Pollutant distribution from a coastal outfall is studied accounting for strong tidal currents. The problem is 
solved using k-ε  model. The constants in the logarithmic law for vertical velocity profile in the BBL (bottom 
boundary layer) are obtained by processing experimental data from a current profiler. The near-field 
distribution of pollutant concentration at different distances from the diffuser are obtained for different times, 
in terms of ambient flow velocity and outfall discharge characteristics. It is shown that even in the case 
where the effluent density is substantially lower than the ambient sea density the plume can impact the sea 
bottom, creating a risk of pollution of removable bottom sediments. 
Keywords :  near-field distribution of pollutants, environmental risk analysis, tidal currents, 
bottom boundary layer 
1 Introduction 
Traditionally, the sea has been considered as the ultimate sink of most pollution, due to its huge volume and 
assimilating capacities, and the coastal waters, because of their intermediate position between deep seas and 
human activities, has been acting as a buffer zone. During the past years, the interest in environmental issues 
in general, and in the conservation of the water quality in coastal regions, in particular, has steadily increased. 
Here, we consider the nearfield dilution of an industrial effluent discharged by a large and deep water outfall. 
A typical, large discharge diffuser (for a flow of 5m3/s) may be a kilometer in length and located in 60m 
water depth at a distance of 5-10kms offshore. There might be several hundred discharge jets (typical 
diameter (4-10cm) spaced along the diffuser [1]. The present paper is aimed to understand the environmental 
risk of the discharged effluent to pollute the seafloor sediments, even in the case of a buoyant effluent (i.e., 
less dense than the receiving marine water). Indeed, these bottom sediments could accumulate the pollution 
during several months, and suddenly migrate in response to storm-driven currents for example. In addition, 
the movable bottom sediments can accumulate, due to alternate semi-diurnal tidal currents, below the 
diffuser and obstruct the interval between the pipe and the sea bottom. 
Our study is mainly devoted to the distribution of pollutants in the bottom boundary layer (BBL) which may 
be defined as the layer adjacent to the seafloor in which the flow is affected by processes occurring at the 
boundary and in which strong gradients of physical, chemical, and biological properties may occur [2]. In 
thickness it extends to a height of a few metres above the seafloor. Numerous studies have been devoted to 
the BBL and sediment dynamics on the shoreface; e.g., see [3-7]. 
19ème Congrès Français de Mécanique                                                                                       Marseille, 24-28 août 2009 
  2
So the present work concerns the BBL dynamics in the nearfield of a multiport ocean outfall with submerged 
buoyant jets discharging in the vicinity of the water bottom into a flowing ambient subject to a strong semi-
diurnal tidal effect (with a current speed up to 0.6m/s). It concerns the risk of pollution of sea bottom 
sediments by an industrial effluent emitted by an outfall, even in the case of buoyant effluent (i.e., effluent 
density < ambient sea density). So, special attention is devoted to the problem of interaction between the 
effluent plume and the sea bottom. The aim is to determine the conditions for a bottom attachment (Coanda 
attachment), in terms of ambient flow characteristics and discharge characteristics.  
 
2 Presentation of the problem 
2.1 Geometry and problem parameters 
We consider a circular ocean multiport oufall with vertical discharge placed near the seafloor 
perpendicularly to the main direction of the ambient current as shown in Fig.1. The diffuser involves 
hundred discharge jets (with circular opening of diameter d=5cm) spaced every 5m along the pipe. 
 
FIG. 1 – Schematic description of the multiport ocean outfall (the current direction being parallel to the mean shoreline 
and perpendicular to the diffuser; the discharge jets from circular ports are vertical) 
 
We consider two main configurations, when the interval under the diffuser (which is surelevated from the 
seafloor of 0.5m) is empty or filled by removable bottom sediments. The first case corresponds to the 
“nominal” configuration (Fig.2), the second one would simulate the risk of sediment accumulation under the 
diffuser due to alternate semi-diurnal tidal currents (the pipe behaving as a barrier). 
 
FIG. 2 – Schematic representation of the problem and coordinates: (a) view perpendicular to the diffuser;  
(b)  transversal view (along the diffuser) 
 
 
We undertake the numerical simulation of the pollution of coastal waters from a point source (Fig.2) which 
corresponds to one port (circular opening with a diameter of d) of the ocean outfall diffuser. The diffuser 
pipe has a circular section of diameter D at the height L from the sea bottom. We consider a buoyant  effluent 
which is discharged vertically at an average velocity w . The velocity of the ambient current is denoted V
r
.  
19ème Congrès Français de Mécanique                                                                                       Marseille, 24-28 août 2009 
  3
Environmental characteristics: density of sea water 31024 /a kg mρ ≈ , ambient temperature 24
o
aT C= , 
Current speed (perpendicular to the diffuser) 0.1 0.6 /V m s= ÷ , ambient water dynamic viscosity 
49.55 10a Pa sμ
−= ⋅ ⋅ . Effluent characteristics: density at diffuser 31004 /e kg mρ ≈ , effluent temperature 
40oeT C= , mean discharge speed , 1.35 /w m s= , dynamic viscosity, 
49.55 10e Pa sμ
−= ⋅ ⋅ . 
2.2 Modeling of the 3D BBL dynamics 
To get a realistic near-field distribution of pollutants a 3-D approach is needed. In addition, as the multiport 
diffuser is placed near the seafloor (i.e., in the sea bottom boundary layer), it is important to analyze the 
effect of the ambient BBL dynamics. For that purpose, we consider two types of vertical profile for the 
ambient current )(yV : (a) constant in y (i.e., without BBL effect), and (b) a logarithmic profile of ambient 
velocity; the constants are extracted from experimental data obtained from ADCP data (Acoustic Doppler 
Current Profiler) .  
We consider the pollutant transport in the three-dimensional stationary nonisothermal turbulent flow of 
viscous incompressible fluid. Numerical modeling is conducted with the help of commercial software 
package Fluent 6.3.26, by using the following options: k ε−  model for turbulent flows, species transport 
model for admixture distribution.  
The boundary conditions are: on the seafloor and on the pipe surface  0, , / 0av T T c n= = ∂ ∂ =
r
; at the 
entrance of computational domain 0( 0) 0, 0, , ,x y z az v v v V T T c c= = = = = = ; at the pipe exit (port) 
0, , 0, ,x y z e ev v w v T T c c= = = = = ; on the remaining boundaries  / 0, / 0, / 0,x y zv n v n v n∂ ∂ = ∂ ∂ = ∂ ∂ =  
/ 0, / 0T n c n∂ ∂ = ∂ ∂ =  
3. Nominal configuration (surelevated pipe); stationary case 
First, let us examine the nominal configuration (surelevated pipe; fig.2), in the stationary case (the speed of 
the ambient flow being time-independent), and study the admixture distribution in the two following cases: 
(1) the ambient current is assumed to be constant along the vertical coordinate y  ; (b) it depends on y  
according to a logarithmic law (BBL formulation):  
( ) ln( )V y a b y= +  (1) 
where a  and b are constants obtained from experimental data.  
 
To analyze the role of BBL formulation, we will compare the results of numerical simulation with constant 
ambient velocity to the results obtained with a logarithmic profile (eq. 1) normalized according to the 
following rule: at the height 1.2 m. from the seafloor (which corresponds to the height of the discharge exit) 
the value of both velocity profiles coincides (i.e., 2 1(1.2) ln(1.2)V a b V= + = ).  
Tab. 1. Correspondence between constant and logarithmic speed of ambient current  
1V const= , m/s 2 ( ) ln( )V y a b y= + , m/s 
0.05 
2 ( ) 0.048 0.014 ln( )V y y= +  
0.15 
2 ( ) 0.144 0.033 ln( )V y y= +  
0.25 
2 ( ) 0.241 0.014 ln( )V y y= +  
0.35 
2 ( ) 0.340 0.062 ln( )V y y= +  
 
3.1. Numerical results 
The effect of BBL formulation is analyzed for two values of current speed: V = 0.15 m/s  and V = 0.25 m/s. 
Figs. 3 and 4 show the patterns of the propagation of admixture for the two types of vertical profile of the 
ambient velocity: (a) constant in y, (b) logarithmic in y. 
19ème Congrès Français de Mécanique                                                                                       Marseille, 24-28 août 2009 
  4
(a) 
 
(b) 
 
 Longitudinal pollutant distribution transversal pollutant distribution 
 Fig. 3. Typical patterns of the 3D admixture plume:  
(a) constant velocity of the ambient flow :  V = 0.15 m/s 
(b) logarithmic BBL profile ( ) 0.144 0.033ln( ), /V y y m s= +  
 
 
(a) 
  
(b) 
  
 Longitudinal pollutant distribution transversal pollutant 
distribution 
  
Fig. 4. Typical patterns of the 3D admixture plume:  
(a) constant velocity of the ambient flow: V = 0.25 m/s 
(b) logarithmic BBL profile  ( ) 0.241 0.014ln( ), /V y y m s= +   
 
In both cases our results recover the classical horse-shoe structure of a turbulent round jet deviated by a 
transverse flow (see for ex., Sherif & Pletcher, 1998).  
 
In fig.4, for a higher speed of ambient current (V = 0.25 m/s), there is an evidence of bottom attachment. For 
the logarithmic profile formulation, the bottom attachment occurs at a slightly larger distance from the 
diffuser.  
4. Configuration with deposit under the pipe (blockage) 
The configuration examined above is idealized. In the real life, the bottom sediments can be accumulated 
under the pipe due to the alternate semi-diurnal tidal current, as the pipe constitutes a barrier to the bottom 
sediment transport. In this case let us introduce a new configuration with a rigid wall under the pipe (Fig. 5).  
19ème Congrès Français de Mécanique                                                                                       Marseille, 24-28 août 2009 
  5
 
Fig. 5. Configuration with the deposit under the pipe 
 
Let us analyze the effect of BBL in the configuration with blockage in the case of high enough velocity of 
the ambient current (V = 0.25 m/s) considered here above.  We present the pollutant distributions at different 
distances above the seafloor obtained numerically with and without taking into account BBL (Figs.6 and 7).  
 
(a) 
(b) 
 
(c) 
 
(d) 
 
(e) 
 
 
 Fig.6. Longitudinal pollutant distribution for 
an ambient flow with constant velocity V = 
0.25 m/s.: a) – vertical cross-section, b-e) – 
top view at different distances above the 
seafloor: (b) 0.5m; (c) 1.2m; (d) 2.5m; (e) 
3m. 
Fig.7. Longitudinal pollutant distribution for 
logarithmic profile ( ) 0.241 0.014ln ( )V y y= +  
m/s: 
 a) – vertical cross-section, b-e) – top view 
at different distances above the seafloor: (b) 
0.5m; (c) 1.2m; (d) 2.5m; (e) 3m. 
 
In the case of logarithmic profile, i.e. when we take into account BBL a spot of pollutant near the bottom is 
also of low enough concentration (as in the previous case) but differing from the previous case it occupies 
much smaller area. As one can see, pollutant is distributed to larger distances in horizontal direction and 
maximal values of pollutant concentration are observed at larger distances from the bottom which can be 
attributed to the formation of vortex just after  the blockage  (in the case of constant velocity such vortex also 
exists but it has lower intensity and occupies smaller area).  This vortex shifts the pollutant plume upward. 
19ème Congrès Français de Mécanique                                                                                       Marseille, 24-28 août 2009 
  6
 
5. Tidal effect 
Preliminary study concerning the tidal effect has been also carried out, in the frame of the BBL formulation. 
In this case the ambient velocity was imposed in the form: 
   ( , ) 0.45sin(0.202 0.042 / 300) 0.065ln( ) sin(0.202 0.042 / 300)V y t t y t= − − − − . 
Both configurations, with and without blockage, have been analyzed. The results concerning the temporal 
evolution of pollutant concentration at the distance of 1.2 m above the seafloor are shown in Fig. 8 and 9, in 
both cases (without and with blockage, respectively).  
0 40000 80000 120000 160000
0
1e-007
2e-007
3e-007
4e-007
  0 40000 80000 120000 160000
0
2e-007
4e-007
6e-007
8e-007
1e-006
 
Fig.8. Temporal evolution of pollutant concentration in the case without blockage at the distance 1.2 meters 
from the bottom: a) in 10, 50 and 90 meters to the left of discharge port (green, orange and violet lines 
respectively);  b) in 10, 50 and 90 meters to the right of discharge port (black, red and blue lines respectively)  
   
0 20000 40000 60000 80000 100000
0
1e-006
2e-006
3e-006
  0 20000 40000 60000 80000 100000
0
1e-006
2e-006
3e-006
 
Fig.9. Temporal evolution of pollutant concentration in the case with blockage at the distance 1.2 m above 
the seafloor: a) in 10, 50 and 90 meters to the left of discharge port (green, orange and violet lines 
respectively);  b) in 10, 50 and 90 meters to the right of discharge port (black, red and blue lines respectively)   
 
19ème Congrès Français de Mécanique                                                                                       Marseille, 24-28 août 2009 
  7
6. Conclusion 
In the case of buoyant effluent 31004 /e kg mρ ≈ ) discharged vertically in sea water (
31024 /a kg mρ ≈ ), 
we can predict a bottom attachment as soon as the current velocity is of the order of V = 0.25 m/s. This 
attachment effect is increased in the case of blockage under the diffuser. The role of the BBL formulation has 
been discussed. Preliminary results for tidal effect are presented. 
References 
[1] Managing wastewater in coastal urban areas. National Research Council Report  (1993) , 477 p. 
[2] Bowden K.F.. Physical problems of the benthic boundary layer. Geophysical Surveys 3 (1978) 255-296. 
[3] Holmedal L.E., Myrhaug D. Rue H.. The sea bed boundary layer under random waves plus current. 
Continental Shelf Research 23 (2003) pp. 717-750. 
[4] Kleinhans M.G. Sediment dynamics on the shoreface and upper continental shelf, a review, 2002. 
[5] Our seabed frontier. National Research Council Report  (1989) , 121 p. 
[6] Styles R., Glenn S.M.. Modeling stratified wave and current bottom boundary layer on the continental 
shelf. J. Geophysical Research, 105 (2000) pp. 24,119 –24,139. 
[7] Kim S-C., Friedrichs C.T., Maa J.P.-Y., Wright L.D. Estimating bottom stress in tidal boundary layer 
from acoustic Doppler velocimeter data. J. Hydraulic Engineering,  (june 2000) pp. 399-406.  


Modelling of the enar-field distribution of pollutants from a coastal

            outfall subject to tidal currents

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Modelling of the enar-field distribution of pollutants from a coastal outfall subject to tidal currents

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