CANARINA:
DESCAR:
INPUT DATA:
ALGORITHMS:
POLLUTANTS:
Algorithms I · software · marine pollution
Mathematical algorithms:
The application uses two different mathematical models: Buoyant jet model or Stratified model. The Buoyant model is ideal for pollutant discharges located in the proximities of the coast and in rivers, (using little depth). This model is based on a time-independent Gaussian equation which simulates the pollutant dispersion in the water. The Stratified model takes into account the formation of the picnocline in the sea. This model is ideal for outfall discharges in the sea (using a lot of depth). The program calculates the pollutant concentration in each point of the water considering each one of the pollutant sources and the conditions of the water.
1. Buoyant jet model
A type of mathematical model that has been developed for sumerged round buoyant jets is the length-scale model. Discharges flows can be divided into different regimes each dominated by particular flow properties. Within each regime, the flow may be approximated with simple mathematical relations describing the simplified problem. A model that uses asymptotic solutions is refered to as length-scale model because of length scales to delineate the extent of the regimes for which the mathematical expressions are valid. The pollutant concentration, in a certain instant, and at a distance x (meters) in the X-Axis and at a distance y(meters) in the Y-Axis will be given by:
c =cc exp[-(r/b)2] (1)
where c is the pollutant concentration, r is the distance from the point (that we are calculating) to the center of the line that forms the polluting plume, cc is the pollutant concentration in the center of the plume line and b is the plume half-width. We attempt to link the momentum dominated and buoyanvy dominated regimes into one relationship by using proposed relations for the transition where:
z/Lb =24/3[(1/2)(x/Lb)2+(Lm/Lb)(x/Lb)]1/3 (2)
b/Lb =cb[(1/2)(x/Lb)2+(Lm/Lb)(x/Lb)]1/3 (3)
S=cs(uo/ua)[(1/2)(Lb/Lm)(x/Lm)2+(x/Lm)]1/3 (4)
Lb=plume-to-crossflow length scale
Lm=jet-to-crossflow length scale
x=horizontal downstream coordinate in global coordinate system
y=horizontal coordinate in coordinate system perpendicular to ambient crossflow
z=vertical coordinate
ua=ambient velocity
uo=discharge velocity
S=dilution along the plume centerline C/C0 being C the centerline pollutant concentration and the C0 initial pollutant concentration at the discharge.
cb=constant of proportionality that can be modified by the user (can be determined experimentally)
cs=constant of proportionality that can be modified by the user (can be determined experimentally)
cxy=constant of proportionality that can be modified by the user (can be determined experimentally)
We obtain solutions for a vertical buoyant jet in a crossflow. And buoyant jets discharged horizontally perpendiculat to crossflow.
z/Lb =cxy(x/Lm)1/3 (5)
This model performs satisfactorily for simple flows with no shoreline interaction or attachment. Strong crosscurrents or limited depths causing attachment with the downstrean bank or strong initial buoyancy render this model invalid. In addition, they are incapable of simulating any far-field processes that occur after a certain distance.
software · marine pollution
DESCAR software: water discharge system mixing zone model waste water discharge standards wastewater treatment chemical contamination of water wastewater simulation water analysis sewage treatment effluent effluent and environment sewage discharge modeling environment management and protection environmental impact evaluation environmental science · engineering environmental audit reports marine pollution monitoring sewage treatment discharge marine pollution pollution and water environmental sewage water pollution control oil environmental impact GIS · environment