Eddy diffusion coefficient

The value of 0/ is calculated from Eq. (14-142). The term Dg is an eddy-diffusion coefficient that is obtained from experimental measurements. For sieve plates, Barker and Self [Chem. E/ig. Sci., 17,, 541 (1962)] obtained the Following correlation ... 

Modeling pollutant concentration between source and worker prediction of small-scale dispersion of contaminants using data collected with a high-resolution three-axis sonic anemometer. The ultimate goal is to convert information collected by the anemometer into eddy diffusion coefficients, which can be used to estimate contaminant concentrations at any point within indoor environments. 

If we define AT as the eddy diffusivity for momentum, the vertictil eddy diffusion coefficient under unstable conditions can be expressed as... 

Eq. 7.2, where is then the eddy diffusion coefficient (Taylor and Spencer 1990). The height of the turbulent zone, within the atmospheric boundary layer, is orders of magnitude greater than that of the laminar flow layer, and dispersion of contaminant vapors in the turbulent zone is relatively rapid. 

This was obtained from Equation (7), where D is an eddy diffusion coefficient. Thus, we have no assurance that = 0 in this case. 

There are many transport conditions where experiments are needed to determine coefficients to be used in the solution. Examples are an air-water transfer coefficient, a sediment-water transfer coefficient, and an eddy diffusion coefficient. These coefficients are usually specific to the type of boundary conditions and are determined from empirical characterization relations. These relations, in turn, are based on experimental data. 

Figure 5.4. Eddy formation at the edge of a jet issuing into a tank illustrates the importance of velocity gradients in eddy diffusion coefficient.

Here, it is easier to simply give the experimental relation for eddy diffusion coefficient ... 

Figure 5.7 gives some relationships for eddy diffusion coefficient profiles under different conditions that will be handy in applications of turbulent diffusive transport. 

Figure 5.7. Profiles of eddy diffusion coefficient for various types of applications.

We will apply equation (5.20) to solve for the concentration profile of suspended sediment in a river, with some simplifying assumptions. Suspended sediment is generally considered similar to a solute, in that it is a scalar quantity in equation (5.20), except that it has a settling velocity. We will also change our notation, in that the bars over the temporal mean values will be dropped. This is a common protocol in turbulent transport and will be followed here for conformity. Thus, if an eddy diffusion coefficient, e, is in the transport equation,... 

The mean lateral eddy diffusion coefficient is much greater than the diffusion coefficient for any compound, Sy D. 

We are using an equivalent vertical-mean eddy diffusion coefficient because we are computing a vertical mean concentration. 

It is interesting to compare equations (6.32) and (6.33) with those for a fully developed laminar flow, equations (6.29) and (6.30). In Example 5.1, we showed that eddy diffusion coefficient in a turbulent boundary layer was linearly dependent on distance from the wall and on the wall shear velocity. If we replace the diffusion coefficient in equation (6.30) with an eddy diffusion coefficient that is proportional to hu, we get... 

Interfacial transfer of chemicals provides an interesting twist to our chemical fate and transport investigations. Even though the flow is generally turbulent in both phases, there is no turbulence across the interface in the diffusive sublayer, and the problem becomes one of the rate of diffusion. In addition, temporal mean turbulence quantities, such as eddy diffusion coefficient, are less helpful to us now. The unsteady character of turbulence near the diffusive sublayer is crucial to understanding and characterizing interfacial transport processes. 

The eddy diffusion coefficients that we introduced in Chapter 5 were steady quantities, using mean turbulence quantities (e.g., the temporal mean of u C). This temporal mean character of eddy diffusion coefficients can be misleading in determining the thickness of a diffusive boundary layer because of the importance of unsteady characteristics. We will review some conceptual theories of mass transfer that have been put forward to describe the interaction of the diffusive boundary layer and turbulence. 

Turbulent flow means that, superimposed on the large-scale flow field (e.g., the Gulf Stream), we find random velocity components along the flow (longitudinal turbulence) as well as perpendicular to the flow (transversal turbulence). The effect of the turbulent velocity component on the transport of a dissolved substance can be described by an expression which has the same form as Fick s first law (Eq. 18-6), where the molecular diffusion coefficient is replaced by the so-called turbulent or eddy diffusion coefficient, E. For instance, for transport along the x-axis ... 

The coefficient Ex is called the turbulent (or eddy) diffusion coefficient it has the same dimension as the molecular diffusion coefficient [L2 1]. The index x indicates the coordinate axis along which the transport occurs. Note that the turbulentjliffusion coefficient can be interpreted as the product of a mean transport distance Lx times a mean velocity v = (Aa At) l Egex, as found in the random walk model, Eq. 18-7. 

If the lake is stratified, vertical transport is commonly the time-limiting step for complete mixing. This was the reason for applying the two-box model to the case of PCE in Greifensee (Illustrative Example 21.5). Now we go one step further. We consider a vertical water column of mean depth h with a constant vertical eddy diffusion coefficient Ez. The flux Fa/VJ of PCE escaping to the atmosphere is given by Eq. 20-la ... 

Mechanisms and rates of transport of nuclear test debris in the upper and lower atmosphere are considered. For the lower thermosphere vertical eddy diffusion coefficients of 3-6 X 106 cm.2 sec. 1 are estimated from twilight lithium enhancement observations. Radiochemical evidence for samples from 23 to 37 km. altitude at 31° N indicate pole-ward mean motion in this layer. Large increases in stratospheric debris in the southern hemisphere in 1963 and 1964 are attributed to debris from Soviet tests, transported via the mesosphere and the Antarctic stratosphere. Most of the carbon-14 remains behind in the Arctic stratosphere. 210Bi/ 210Pb ratios indicate aerosol residence times of only a few days at tropospheric levels and only several weeks in the lower stratosphere. Implications for the inventory and distribution of radioactive fallout are discussed. 

Above 120 km. the atmosphere is essentially in diffusive equilibrium (34). For the altitude interval between 80 and 120 km. Colegrove et al. (6) estimated an average vertical eddy diffusion coefficient of 4 X 106 cm.2 sec."1 by a careful evaluation of the 0/02 concentration ratio profile over this altitude interval. Using their eddy diffusion coefficient and following the procedure of Kellogg (22) it is estimated that molecular... 

The pattern of eddy mixing in the mesosphere apparently may be highly nonisotropic, similar to that indicated for the lower thermosphere. The upper limit of vertical eddy diffusion coefficients for the mesosphere... 

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