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INPUT DATA:

Data I

Data II

Data III

Import

Commands

Graphs I

Graphs II

ALGORITHMS:

Algorithms I

Algorithms II

Algorithms III

Algorithms IV

Algorithms V

Algorithms VI

POLLUTANTS:

Pollutants I

Pollutants II

The sea I

The sea II

Pycnocline

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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 =c_c 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, c_c 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/L_b =2^4/3[(1/2)(x/L_b)²+(L_m/L_b)(x/L_b)]^1/3  (2)

b/L_b =c_b[(1/2)(x/L_b)²+(L_m/L_b)(x/L_b)]^1/3    (3)

S=c_s(u_o/u_a)[(1/2)(L_b/L_m)(x/L_m)²+(x/L_m)]^1/3 (4)

L_b=plume-to-crossflow length scale

L_m=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

u_a=ambient velocity

u_o=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.

c_b=constant of proportionality that can be modified by the user (can be determined experimentally)

c_s=constant of proportionality that can be modified by the user (can be determined experimentally)

c_xy=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/L_b =c_xy(x/L_m)^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.

ALGORITHMS: Algorithms I -  Algorithms II - Algorithms III - Algorithms IV - Algorithms V - Algorithms VI

Canarina Algoritmos Numéricos, S.L.

Environmental software solutions

Software para contaminación del medio ambiente  

Canary Islands, Spain

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marine pollution

CANARINA: Home - Air pollution · DISPER - Noise pollution · CUSTIC - Water pollution · DESCAR - Contact us

DESCAR: DESCAR: water pollution - Data I - Algorithms I - Pollutants I

SOLUTIONS: DESCAR: water pollution - Advantages - Price

INPUT DATA: Data I - Data II - Data III - Import - Commands - Graphs I - Graphs II

ALGORITHMS: Algorithms I -  Algorithms II - Algorithms III - Algorithms IV - Algorithms V - Algorithms VI

POLLUTANTS: Pollutants I - Pollutants II - The sea I - The sea II - Pycnocline

DESCAR software solutions: This application has been used in great number of environmental reports, courses and water pollution studies in the last years. We currently have users in more than 10 countries.