Dispersion parameters, Gaussian

Method of Moments The first step in the analysis of chromatographic systems is often a characterization of the column response to sm l pulse injections of a solute under trace conditions in the Henry s law limit. For such conditions, the statistical moments of the response peak are used to characterize the chromatographic behavior. Such an approach is generally preferable to other descriptions of peak properties which are specific to Gaussian behavior, since the statisfical moments are directly correlated to eqmlibrium and dispersion parameters. Useful references are Schneider and Smith [AJChP J., 14, 762 (1968)], Suzuki and Smith [Chem. Eng. ScL, 26, 221 (1971)], and Carbonell et al. [Chem. Eng. Sci., 9, 115 (1975) 16, 221 (1978)]. 

Pasquill s dispersion parameters were restated in terms of a-y and Cj by Gifford (14, 15) to allow their use in the Gaussian plume equations. The... 

As an example of the use of the Gaussian plume equations using the Pasquill-Gifford dispersion parameters, assume that a source releases 0.37 g s of a pollutant at an effective height of 40 m into the atmosphere with the wind blowing at 2 m s . What is the approximate distance of the maximum concentration, and what is the concentration at this point if the atmosphere is appropriately represented by Pasquill stability class B ... 

However, we must keep in mind the limitations of this approach, especially the transfer of consistent sets of dispersion parameters to the propagation of air pollution in the vicinity of a source. The Gaussian plume formula should be used only for those downwind distances for which the empirical diffusion coefficients have been determined by standard diffusion experiments. Because we are interested in emissions near ground level and immissions nearby the source, we use those diffusion parameters which are based on the classification of Klug /12/ and Turner /13/. The parameters are expressible as power functions,... 

Based on the manner of derivation of the Gaussian equations in Section III, we see that the dispersion parameters a-y and are originally defined for an instantaneous release and are functions of travel time from release. Since the puff equations depend on the travel time of individual puffs or releases, the dispersion coefficients depend on this time, i.e., these coefficients describe the growth of each puff about its own center. This is basically a Lagrangian formulation. 

The basic Gaussian plume dispersion parameters are ay and a. The essential theoretical result concerning the dependence of these parameters on travel time is for stationary, homogeneous turbulence (Taylor, 1921). Consider marked particles that are released from the origin in a stationary, homogeneous turbulent flow with a mean flow in the x direction. The y component, y, of the position of a fluid particle satisfies the equation... 

The results just obtained for < y) are, however, rarely used in applications because (v ) and T are generally not known. The Gaussian dispersion parameters aj and al are, in a sense, generalizations of (Cj) and particle displacement variances o-y and a-] are not calculated by Eq. (8.8). Rather, they are treated as empirical dispersion coefficients the functional forms of which are determined by matching the Gaussian solution to data. In that way, the empirically determined a-y and deviations from stationary, homogeneous conditions which are inherent in the assumed Gaussian distribution. 

Coefficients in Gaussian Plume Dispersion Parameter Correlations"... 

Weber, A. H. (1976). Atmospheric Dispersion Parameters in Gaussian Plume Modeling, EPA-600/4-76-030A. U.S. Environ. Prot. Agency, Washington, D.C. 

It is apparent from equations 3.2.4-3.2.7 that the determination of the concentration field is dependent on the values of the Gaussian dispersion parameters a, (or Oy in the fully coupled puff model). Drawing on the fundamental result provided by Taylor (1923), it would be expected that these parameters would relate directly to the statistics of the components of the fluctuating element of the flow velocity. In a neutral atmosphere, the factors affecting these components can be explored by considering the fundamental equations of fluid motion in an incompressible fluid (for airflows less than 70% of the speed of sound, airflows can reasonably be modeled as incompressible) when the temperature of the atmosphere varies with elevation, the fluid must be modeled as compressible (in other words, the density is treated as a variable). The set of equations governing the flow of an incompressible Newtonian fluid at any point at any instant is as follows ... 

This equation represents a Gaussian distribution, where C (Bq.m 3) represents the radionuclide concentration, Q (Bq.s1) the source strength, and H (m) the corrected source released height. Dispersion parameters, ay (m) and az (m), are the standard deviations of the plume concentration in the horizontal and vertical directions respectively. The atmospheric transport is done at wind-speed (height-independent), u (m.s1), to a sampling position located at surface elevation, z (m), and transverse horizontal distance, y (m), from the plume centre. 

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