Dispersion of Aerosols in Atmospheric Airflows

The discussion in Section 3.2.2 provides a basis for the assumption that, for particles in the optimal size range for weaponized aerosols, advection is the dominant transport mechanism. Since airflows in the planetary boundary layer exhibit significant turbulence under most conditions, this will cause aerosol releases to disperse into a cloud (more rigorously denoted as a plume or puff, depending on the nature of the source) that expands as the distance traveled downwind from the source increases. 

To understand atmospheric dispersion, therefore, it is necessary to understand the nature of turbulent flows and the structure of the atmosphere near the Earth s surface. Turbulent flows exhibit apparently random fluctuations in local velocity and pressure (Mathieu and Scott 2000). These fluctuations appear over a wide range of length and time scales. Reynolds (1895) drew an analogy between the behavior of the velocity in a turbulent flow and the velocity of the individual molecules in a gas, leading to the definition of the instantaneous velocity at a point as having a mean and a fluctuating component  

The use of bold denotes that all quantities are vectors. The velocity V on the left-hand side is the instantaneous velocity, which is comprised of the sum of the mean velocity at the point (denoted by the overbar) and the fluctuating element of the velocity (denoted by the lowercase m). To permit the use of the Einstein summation convention, the component of the instantaneous velocity in direction i at a point is written as the sum of the mean and fluctuating components of the velocity in that direction. 

It is the fluctuating element of the velocity in a turbulent flow that drives the dispersion process. The foundation for determining the rate of dispersion was set out in papers by G. 1. Taylor, who first noted the ability of eddy motion in the atmosphere to diffuse matter in a manner analogous to molecular diffusion (though over much larger length scales) (Taylor 1915), and later identified the existence of a direct relation between the standard deviation in the displacement of a parcel of fluid (and thus any affinely transported particles) and the standard deviation of the velocity (which represents the root-mean-square value of the velocity fluctuations) (Taylor 1923). Roberts (1924) used the molecular diffusion analogy to derive concentration profiles 

The assumption of a Gaussian concentration prohle permits the construction of relatively straightforward equations to describe the concentration prohle of puffs and plumes. For a continuous point source in a uniform flow having homogeneous turbulence, the plume concentration prohle is given by (Arya 1999), 

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