DESCAR Software: marine pollution · water pollution modeling

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Algorithms I

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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

e-mail: contact us

European network on pollution · European Union

Member of MAPO: European network on Marine Pollution. Project

funded by the European Commission through the

6th Framework Programme for Research and Development

marine pollution

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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.

Shropshire - outfall pipe -

Derbyshire - basin modeling -

Aberdeen - modeling management - design modeling - systems modeling -

Lancashire - stormwater modeling -

Oxfordshire - transport modeling -

Armagh - watershed modeling - plant modeling - project modeling -

Bangor - gis modeling - road modeling - urban modeling -

Birmingham - runoff modeling - wastewater modeling -

Bradford - river modeling - lake modeling - water resources modeling -

Bath - sewage outfall - pipe outfall - sewer outfall -

Belfast - flood modeling - groundwater modeling - hydrology modeling -

Brighton & Hove - environmental modeling - wastewater outfall - simulation modeling -

Bristol - drainage outfall - storm water outfall - outfall stormwater - outfall design -

Oxford - turbulent modeling - thermal modeling - particle modeling -

Peterborough - contamination modeling - water quality modeling - area modeling -

Cambridge - outfall channel - pond outfall - fluent modeling -

Nottingham - outfall protection - outfall structure - modeling theory -

Plymouth - construction modeling - water pollution modeling - water modeling -

Portsmouth - river outfall -stream modeling - analysis modeling -

Salford - ocean outfall - outfall system - sewer outfall -

Salisbury - wastewater outfall - marine outfall - sewage outfall -

Preston - outfall monitoring - surface modeling - sewer modeling -

Ripon - solution modeling - outfall construction - storm water modeling -

Essex - outfall canal - northern outfall -

St David's - storm water pollution prevention - water air and soil pollution - prevention of water pollution -

Stirling - effect of water pollution - stop water pollution - storm water pollution prevention plan -

Stoke-on-Trent - storm water pollution -pictures of water pollution - water pollution causes -

Sunderland - federal water pollution control act - types of water pollution -

Swansea - npdes outfall - ocean outfall design - septic tank outfall -

Truro - people opposed to outfall pollution - outfall locations - outfall map -

Wakefield - outfall line - concrete outfall - ms4 outfall -

Wells - coastal plain outfall - what is an outfall - south bay ocean outfall -

Westminster - left bank outfall drain - cso outfall - adequate outfall -

Cheshire - heat simulation -

Worcestershire - annual water quality report -

Northamptonshire - water supply water quality regulations -

Durham - simulation theory -

Cambridge - surface simulation - treatment simulation - numerical simulation -

Nottingham - solution simulation - number simulation - thesis simulation -

Plymouth - water quality standards - water quality uk - improve water quality -

Portsmouth - water quality objectives - poor water quality - salinity and water quality -

Oxford - water quality management - water quality assessment - water quality monitoring -

Peterborough - water quality testing - drinking water quality - water quality modeling -

Preston - water quality - irrigation water quality - water supply water quality regulations 2000 -

Ripon - water quality rating - coastal water quality - water quality study -

Sheffield - fluid simulation - outfall stormwater - diffusion simulation -

St Albans - outfall structure - simulation dynamics - water simulation -

Salford - importance of water quality - water quality trading - surface water quality -

Salisbury - water quality for agriculture - water quality pollution - water quality improvement -

St David's - wastewater simulation - simulation analysis - outfall design -

Stirling - outfall channel - construction simulation - simulation modelling -

Swansea - particle simulation - solid simulation - simulation engineering -

Truro - outfall water - flow simulation - mathematical simulation -

Stoke-on-Trent - drainage outfall - fluid mechanics simulation - drainage simulation -

Sunderland - simulation modeling - hydrodynamic simulation - turbulence simulation -

Copyright © 2005 Canarina Algoritmos Numéricos, Sociedad Limitada Unipersonal CIF-B38803110 registered for electronic commerce in sheet TF-35526, sheet 1 of the volume 2.671 of the General Section, First Registration, Registro de la Propiedad Número 2 y Marcantil of , Spain. All rights reserved.