scholarly journals Maximum crosswind integrated ground level concentration in two stability classes

MAUSAM ◽  
2021 ◽  
Vol 64 (4) ◽  
pp. 655-662
Author(s):  
M.ABDEL WAHAB ◽  
KHALED SMESSA ◽  
M. EMBABY ◽  
SAWSAN EMELSAID
Keyword(s):  
Wind Speed ◽  
Laplace Transformation ◽  
Ground Level ◽  
Eddy Diffusivity ◽  
Concentration Data ◽  
Transformation Technique ◽  
Advection Diffusion Equation ◽  
Advection Diffusion ◽  
Ground Level Concentration ◽  
Vertical Height

bl 'kks/k i= esa fu"izHkkoh vkSj vfLFkj fLFkfr;ksa esa ØkWliou lekdfyr lkanz.k ysus ds fy, nks fn’kkvksa esa vfHkogu folj.k lehdj.k ¼ADE½ dks gy fd;k x;k gSA ykIykl :ikarj.k rduhd dk mi;ksx rFkk m/okZ/kj Å¡pkbZ ij vk/kkfjr iou xfr vkSj Hkaoj folj.k’khyrk dh leh{kk djrs gq, ;g gy fudkyk x;k gSA blds lkFk gh Hkw&Lrj  vkSj vf/kdre lkanz.kksa dk Hkh vkdyu fd;k x;k gSA geus bl ekWMy esa iwokZuqekfur vkSj izsf{kr lkanz.k vk¡dM+ksa ds e/; rqyuk djus ds fy, dksiugsxu ¼MsuekdZ½ ls fy, x, vkuqHkfod vk¡dM+ksa dk mi;ksx fd;k gSA  The advection diffusion equation (ADE) is solved in two directions to obtain the crosswind integrated concentration in neutral and unstable conditions. The solution is solved using Laplace transformation technique and considering the wind speed and eddy diffusivity depending on the vertical height. Also the ground level and maximum concentrations are estimated. We use in this model empirical data from Copenhagen (Denmark) to compare between predicted and observed concentration data.

scholarly journals Using dispersion modeling for ground level concentration

MAUSAM ◽  
2021 ◽  
Vol 62 (2) ◽  
pp. 239-244
Author(s):  
KHALEDS.M. ESSA ◽  
FAWZIA MUBARAK
Keyword(s):  
Exact Solution ◽  
Short Range ◽  
Meteorological Data ◽  
Ground Level ◽  
Eddy Diffusivity ◽  
Dispersion Modeling ◽  
Mixing Height ◽  
Advection Diffusion Equation ◽  
Advection Diffusion ◽  
Ground Level Concentration

A short range model calculating ground-level concentration from elevated sources is estimated, which realized a Fickian-type formula. Taking the source and mixing height are functions of the wind velocity and eddy diffusivity profiles. The model estimated with an exact solution of the advection diffusion equation is compared with experimental ground level concentrations using meteorological data collected near the ground.

scholarly journals Comparison between two analytical solutions of advection-diffusion equation using separation technique and Hankel transform

MAUSAM ◽  
2021 ◽  
Vol 72 (4) ◽  
pp. 905-914
Author(s):  
KHALED S. M. ESSA ◽  
H. M. TAHA
Keyword(s):  
Wind Speed ◽  
Diffusion Equation ◽  
Numerical Solutions ◽  
Separation Of Variables ◽  
Eddy Diffusivity ◽  
Hankel Transform ◽  
Advection Diffusion Equation ◽  
Advection Diffusion ◽  
Information Sets ◽  
Vertical Eddy Diffusivity

On this work, contrast between two analytical and numerical solutions of the advection-diffusion equation has been completed. We  use the method of separation of variables, Hankel transform and Adomian numerical method. Also, Fourier rework, and square complement methods has been used to clear up the combination. The existing version is validated with the information sets acquired at the Egyptian Atomic Energy Authority test of radioactive Iodine-135 (I135) at Inshas in unstable conditions. On this model the wind speed and vertical eddy diffusivity are taken as characteristic of vertical height in the techniques and crosswind eddy diffusivity as function in wind speed. These values of predicted and numerical concentrations are comparing with the observed data graphically and statistically.

An analytical model for dispersion of pollutants from a continuous source in the atmospheric boundary layer

2009 ◽  
Vol 466 (2114) ◽  
pp. 383-406 ◽  
Author(s):  
Pramod Kumar ◽  
Maithili Sharan
Keyword(s):  
Boundary Layer ◽  
Wind Speed ◽  
Atmospheric Boundary Layer ◽  
Analytical Model ◽  
Eddy Diffusivity ◽  
Horizontal Wind ◽  
Advection Diffusion Equation ◽  
Special Cases ◽  
Vertical Height ◽  
Continuous Source

For the dispersion of a pollutant released from a continuous source in the atmospheric boundary layer (ABL), a generalized analytical model describing the crosswind-integrated concentrations is presented. An analytical scheme is described to solve the resulting two-dimensional steady-state advection–diffusion equation for horizontal wind speed as a generalized function of vertical height above the ground and eddy diffusivity as a function of both downwind distance from the source and vertical height. Special cases of this model are deduced and an extensive analysis is carried out to compare the model with the known analytical models by taking the particular forms of wind speed and vertical eddy diffusivity. The proposed model is evaluated with the observations obtained from Copenhagen diffusion experiments in unstable conditions and Hanford and Prairie Grass experiments in stable conditions. In evaluation of the model, a recently proposed formulation for the wind speed in the entire ABL is used. It is concluded that the present model is performing well with the observations and can be used to predict the short-range dispersion from a continuous release. Further, it is shown that the accurate parameterizations of wind speed and eddy diffusivity provide a significant improvement in the agreement between computed and observed concentrations.

scholarly journals Derivation of the Gaussian plume model in three dimensions

MAUSAM ◽  
2021 ◽  
Vol 65 (1) ◽  
pp. 83-92
Author(s):  
M.M. ABDELWAHAB ◽  
KHALED S.M.ESSA ◽  
H.M. ELSMAN ◽  
A.SH. SOLIMAN ◽  
S.M. ELGMMAL ◽  
...  
Keyword(s):  
Power Law ◽  
Eddy Diffusivity ◽  
Three Dimensions ◽  
Gaussian Plume Model ◽  
Concentration Data ◽  
Plume Model ◽  
Advection Diffusion Equation ◽  
Statistical Measures ◽  
Advection Diffusion ◽  
Gaussian Plume

Gaussian plume model is a common model to study advection diffusion equation which is solved in three dimensions by using Laplace transformation considering constant eddy diffusivity and wind speed power law. Different schemes such as Irwin, Power Law, Briggs and Standard methods are used to obtain crosswind integrated concentration. Statistical measures are used in this paper to know which is the best scheme which agrees with the observed concentration data obtained from Copenhagen, Denmark. The results of model are compared with observed data.

scholarly journals INFLUENCE OF SETTLING VELOCITY OF PARTICULATE MATTER ON GROUND LEVEL CONCENTRATIONS

2016 ◽  
Vol 38 ◽  
pp. 560 ◽  
Author(s):  
Tiziano Tirabassi ◽  
Davidson Martin Moreira
Keyword(s):  
Particulate Matter ◽  
Analytical Solution ◽  
Diffusion Equation ◽  
Concentration Distribution ◽  
Settling Velocity ◽  
Atmospheric Stability ◽  
Ground Level ◽  
Advection Diffusion Equation ◽  
Advection Diffusion ◽  
Ground Level Concentration

The settling velocity and deposition of particulate matter on the earth's surface has been introduced in an analytical solution of advection-diffusion equation. The influence of particle diameters in ground level concentration distribution was investigated in function of different atmospheric stability condiyions 

scholarly journals Different solutions of the diffusion equation and its applications

2021 ◽  
Vol 10 (1) ◽  
Author(s):  
Khaled S. M. Essa ◽  
Soad M. Etman ◽  
Maha S. El-Otaify ◽  
M. Embaby ◽  
Ahmed M. Mosallem ◽  
...  
Keyword(s):  
Diffusion Equation ◽  
Ground Surface ◽  
Ground Level ◽  
Urban Atmosphere ◽  
Vertical Diffusion ◽  
Simple Diffusion ◽  
Advection Diffusion Equation ◽  
Ground Level Concentration ◽  
Simple Diffusion Model ◽  
Vertical Height

AbstractIn this  report, we solved the advection–diffusion equation under pollutants deposition on the ground surface, taking wind speed and vertical diffusion depend on the vertical height. Also, we estimated a simple diffusion model from point source in an urban atmosphere and the conservative material with downwind was evaluated. Then, we calculated the extreme ground-level concentration as a function of stack height and plume rise in two cases. Comparison between the proposed models and the emission from the Egyptian Atomic Research Reactor at Inshas had been done. Lastly, we discussed the results in this report.

A Discussion on recent research in air pollution - Variability and upper bounds for maximum ground level concentrations

1969 ◽  
Vol 265 (1161) ◽  
pp. 209-220 ◽  
Keyword(s):  
Wind Speed ◽  
Upper Bound ◽  
Power Laws ◽  
Ground Level ◽  
Eddy Diffusivity ◽  
Conservation Equation ◽  
Ground Level Concentration ◽  
Mean Wind Speed ◽  
Source Level ◽  
Definition Of

The properties of the various factors which arise in the conventional formula for maximum hourly mean ground level concentration (max. g.l.c.) after fixing mean wind speed and source strength are studied with a view to assessing variability and comparing with results from the Tilbury field trial. The analysis indicates some ambiguity in defining vertical spread for dispersion from tall stacks and suggests that the formula might be more profitably rearranged. A natural rearrangement is pointed out and this leads to a simple upper bound for max. g.l.c. in an unbounded atmosphere which is only 20 % larger than the familiar result for a uniform atmosphere. This result is obtained using the diffusion equation with simple power laws for wind speed and eddy diffusivity. The general conservation equation is then considered and this leads to a specific definition of mean wind speed below source level and the indication of a general upper bound some 50 % larger than the uniform atmosphere value provided certain reasonable conditions are met. The practical implications of these results are discussed and the extra effects introduced by stable layers are pointed out.

scholarly journals A simple formula for the evaluation of value and position of ground level concentration from a point source

2018 ◽  
Vol 40 ◽  
pp. 69
Author(s):  
Tiziano Tirabassi ◽  
Daniela Buske
Keyword(s):  
Analytical Solution ◽  
Diffusion Equation ◽  
Point Source ◽  
Simple Formula ◽  
Ground Level ◽  
Approximate Expression ◽  
Simple Expression ◽  
Advection Diffusion Equation ◽  
Advection Diffusion ◽  
Ground Level Concentration

After setting realistic scenarios of the wind and diffusivity parameterizations the Ground Level Concentration is worked out by an analytical solution of the advection-diffusion equation, then an explicit approximate expression is provided for it allowing a simple expression for the position and value of the maximum.

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