Diffusion of dust particles from a point source above ground level and a line source at ground level

I. A. Eltayeb, M. H A Hassan

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

A pollutant of small particles is emitted both by a point source at a height h above ground level and by an infinite line source at ground level in an atmosphere in which a uni-directional wind speed, U, is prevailing. The pollutant is subjected to diffusion in all directions in the presence of advection and settling due to gravity. The equation governing the concentration of the pollutant is studied when the wind speed and the individual components of the diffusion tensor are proportional to the distance above ground Adopting a Cartesian system of coordinates in which the x-axis lies along the direction of the wind velocity, the z-axis is vertically upwards, and the y-axis completes the right-hand triad, the solution for the concentration is obtained in closed form. In the presence of the point source alone, the relative importance of the components of diffusion along the three axes is discussed. It is found that for any plane y = constant (= A), the concentration c(x, y, z) is focused along a curve of 'extensive pollution'. In the plane A = 0, the concentration decreases along the curve of extensive pollution with increasing distance from the source. For planes A ≠ 0, however, the curve of extensive pollution possesses a point of accumulation, which lies at a non-zero value of x. With increasing distance from the plane A = 0, the point of accumulation moves laterally away from the plane x = 0 and towards the ground. The presence of the point of accumulation is entirely due to the presence of lateral diffusion. When the infinite line source at ground level is also present, the solution can be obtained in closed form only for a 2-D concentration c(x, z) of dust. The relative importance of the two sources is illustrated by an example. It is found that the ground source flattens the line of extensive pollution and helps to enhance the transport of dust downwind. The solution for the line source acting alone is illustrated by an example relevant to soil erosion of agricultural land.

Original languageEnglish
Pages (from-to)426-438
Number of pages13
JournalGeophysical Journal International
Volume142
Issue number2
DOIs
Publication statusPublished - Aug 2000

Fingerprint

point sources
Particles (particulate matter)
point source
Dust
Pollution
dust
pollution
wind velocity
contaminants
pollutant
Advection
curves
soil erosion
Tensors
Erosion
Gravitation
settling
advection
Soils
agricultural land

Keywords

  • Dust concentration
  • Dust diffusion
  • Pollution
  • Wind erosion

ASJC Scopus subject areas

  • Geochemistry and Petrology
  • Geophysics

Cite this

Diffusion of dust particles from a point source above ground level and a line source at ground level. / Eltayeb, I. A.; Hassan, M. H A.

In: Geophysical Journal International, Vol. 142, No. 2, 08.2000, p. 426-438.

Research output: Contribution to journalArticle

@article{5494f3ef1db440cea8637e201e1e7a9a,
title = "Diffusion of dust particles from a point source above ground level and a line source at ground level",
abstract = "A pollutant of small particles is emitted both by a point source at a height h above ground level and by an infinite line source at ground level in an atmosphere in which a uni-directional wind speed, U, is prevailing. The pollutant is subjected to diffusion in all directions in the presence of advection and settling due to gravity. The equation governing the concentration of the pollutant is studied when the wind speed and the individual components of the diffusion tensor are proportional to the distance above ground Adopting a Cartesian system of coordinates in which the x-axis lies along the direction of the wind velocity, the z-axis is vertically upwards, and the y-axis completes the right-hand triad, the solution for the concentration is obtained in closed form. In the presence of the point source alone, the relative importance of the components of diffusion along the three axes is discussed. It is found that for any plane y = constant (= A), the concentration c(x, y, z) is focused along a curve of 'extensive pollution'. In the plane A = 0, the concentration decreases along the curve of extensive pollution with increasing distance from the source. For planes A ≠ 0, however, the curve of extensive pollution possesses a point of accumulation, which lies at a non-zero value of x. With increasing distance from the plane A = 0, the point of accumulation moves laterally away from the plane x = 0 and towards the ground. The presence of the point of accumulation is entirely due to the presence of lateral diffusion. When the infinite line source at ground level is also present, the solution can be obtained in closed form only for a 2-D concentration c(x, z) of dust. The relative importance of the two sources is illustrated by an example. It is found that the ground source flattens the line of extensive pollution and helps to enhance the transport of dust downwind. The solution for the line source acting alone is illustrated by an example relevant to soil erosion of agricultural land.",
keywords = "Dust concentration, Dust diffusion, Pollution, Wind erosion",
author = "Eltayeb, {I. A.} and Hassan, {M. H A}",
year = "2000",
month = "8",
doi = "10.1046/j.1365-246X.2000.00172.x",
language = "English",
volume = "142",
pages = "426--438",
journal = "Geophysical Journal International",
issn = "0956-540X",
publisher = "Wiley-Blackwell",
number = "2",

}

TY - JOUR

T1 - Diffusion of dust particles from a point source above ground level and a line source at ground level

AU - Eltayeb, I. A.

AU - Hassan, M. H A

PY - 2000/8

Y1 - 2000/8

N2 - A pollutant of small particles is emitted both by a point source at a height h above ground level and by an infinite line source at ground level in an atmosphere in which a uni-directional wind speed, U, is prevailing. The pollutant is subjected to diffusion in all directions in the presence of advection and settling due to gravity. The equation governing the concentration of the pollutant is studied when the wind speed and the individual components of the diffusion tensor are proportional to the distance above ground Adopting a Cartesian system of coordinates in which the x-axis lies along the direction of the wind velocity, the z-axis is vertically upwards, and the y-axis completes the right-hand triad, the solution for the concentration is obtained in closed form. In the presence of the point source alone, the relative importance of the components of diffusion along the three axes is discussed. It is found that for any plane y = constant (= A), the concentration c(x, y, z) is focused along a curve of 'extensive pollution'. In the plane A = 0, the concentration decreases along the curve of extensive pollution with increasing distance from the source. For planes A ≠ 0, however, the curve of extensive pollution possesses a point of accumulation, which lies at a non-zero value of x. With increasing distance from the plane A = 0, the point of accumulation moves laterally away from the plane x = 0 and towards the ground. The presence of the point of accumulation is entirely due to the presence of lateral diffusion. When the infinite line source at ground level is also present, the solution can be obtained in closed form only for a 2-D concentration c(x, z) of dust. The relative importance of the two sources is illustrated by an example. It is found that the ground source flattens the line of extensive pollution and helps to enhance the transport of dust downwind. The solution for the line source acting alone is illustrated by an example relevant to soil erosion of agricultural land.

AB - A pollutant of small particles is emitted both by a point source at a height h above ground level and by an infinite line source at ground level in an atmosphere in which a uni-directional wind speed, U, is prevailing. The pollutant is subjected to diffusion in all directions in the presence of advection and settling due to gravity. The equation governing the concentration of the pollutant is studied when the wind speed and the individual components of the diffusion tensor are proportional to the distance above ground Adopting a Cartesian system of coordinates in which the x-axis lies along the direction of the wind velocity, the z-axis is vertically upwards, and the y-axis completes the right-hand triad, the solution for the concentration is obtained in closed form. In the presence of the point source alone, the relative importance of the components of diffusion along the three axes is discussed. It is found that for any plane y = constant (= A), the concentration c(x, y, z) is focused along a curve of 'extensive pollution'. In the plane A = 0, the concentration decreases along the curve of extensive pollution with increasing distance from the source. For planes A ≠ 0, however, the curve of extensive pollution possesses a point of accumulation, which lies at a non-zero value of x. With increasing distance from the plane A = 0, the point of accumulation moves laterally away from the plane x = 0 and towards the ground. The presence of the point of accumulation is entirely due to the presence of lateral diffusion. When the infinite line source at ground level is also present, the solution can be obtained in closed form only for a 2-D concentration c(x, z) of dust. The relative importance of the two sources is illustrated by an example. It is found that the ground source flattens the line of extensive pollution and helps to enhance the transport of dust downwind. The solution for the line source acting alone is illustrated by an example relevant to soil erosion of agricultural land.

KW - Dust concentration

KW - Dust diffusion

KW - Pollution

KW - Wind erosion

UR - http://www.scopus.com/inward/record.url?scp=0033944740&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0033944740&partnerID=8YFLogxK

U2 - 10.1046/j.1365-246X.2000.00172.x

DO - 10.1046/j.1365-246X.2000.00172.x

M3 - Article

VL - 142

SP - 426

EP - 438

JO - Geophysical Journal International

JF - Geophysical Journal International

SN - 0956-540X

IS - 2

ER -