157
6
Analytical Models for the
Dispersion of Pollutants
in Low Wind Conditions
Pramod Kumar and Maithili Sharan
6.1 Introduction .................................................................................................. 157
6.2 General Mathematical Formulation .............................................................. 158
6.3 Analytical Models ........................................................................................ 159
6.3.1 Gaussian Plume Model ..................................................................... 159
6.3.2 Gaussian Puff Model ........................................................................ 161
6.3.3 Non-Gaussian Models ...................................................................... 163
6.3.4 Limitations of Gaussian Models in Low Wind Conditions .............. 164
6.4 Analytical Models in Low Wind Conditions ................................................ 165
6.4.1 Constant K-Models ........................................................................... 165
6.4.1.1 Unsteady-State Models ...................................................... 165
6.4.1.2 Steady-State Models .......................................................... 166
6.4.2 Variable K-Models ............................................................................ 167
6.4.2.1 Integrated Puff Model with Dispersion Parameters
as the Linear Functions of Time ........................................ 168
6.4.2.2 Model with Eddy Diffusivities as Linear Functions
of Downwind Distance ...................................................... 168
6.4.3 Models for Steady Source of Short Duration ................................... 170
6.4.4 Models in Finite Layer ...................................................................... 171
6.4.4.1 Constant K-Models............................................................. 172
6.4.4.2 Variable K-Models ............................................................. 173
6.4.5 Models Based on Crosswind Integrated Concentrations .................. 174
6.5 Summary ...................................................................................................... 175
References .............................................................................................................. 175
6.1 INTRODUCTION
Mathematical models are indispensable tools to understand the ad hoc problems fashioned by the adverse effect of the developments in the atmosphere due to the rapid
expansion of industrialization, urbanization, and air pollution episodes with the accidental toxic gases, radioactive release, and the growing risk of climate change associated with long-term undesirable effects of urban air. These models are employed to
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