### 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 language | English |
---|---|

Pages (from-to) | 426-438 |

Number of pages | 13 |

Journal | Geophysical Journal International |

Volume | 142 |

Issue number | 2 |

DOIs | |

Publication status | Published - Aug 2000 |

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### Keywords

- Dust concentration
- Dust diffusion
- Pollution
- Wind erosion

### ASJC Scopus subject areas

- Geochemistry and Petrology
- Geophysics

### Cite this

*Geophysical Journal International*,

*142*(2), 426-438. https://doi.org/10.1046/j.1365-246X.2000.00172.x

**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.

Research output: Contribution to journal › Article

*Geophysical Journal International*, vol. 142, no. 2, pp. 426-438. https://doi.org/10.1046/j.1365-246X.2000.00172.x

}

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 -