Puff with No Wind

The solution to Equation 5-17 in spherical coordinates1 is and in rectangular coordinates it is 

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Case 5 Puff with No Wind and Eddy Diffusivity Is a Function of Direction... 

Case 8 Puff with No Wind and with Source on Ground... 

Input Requirements and Availability. Input requirements for Gaussian plume or puff modeling are straightforward. The source emission in terms of mass rate (plume) or mass (puff) must be defined. Wind speed and atmospheric stability must be specified. Wind speed should be appropriate for the height of the center line. The standard equation assumes a point source with no deposition, reaction, or absorption of vapors. Alternative equations exist for line, area and volume sources, with deposition, reaction or absorption, if relevant (Pasquill and Smith, 1983 Turner, 1970). 

The dispersion coefficients above are not necessarily those evaluated with respect to the dispersion of a continuous source at a fixed point in space. (See Chapter 48 for more details.) This equation can be simplified for centerline concentrations and ground-level emissions by setting y — 0 and H = 0, respectively. The dispersion coefficients in the above equation refer to dispersion statistics following the motion of the expanding puff. The is the standard deviation of the concentration distribution in the puff in the downwind direction, and t is the time after release. Note that there is essentially no dilution in the downwind direction by wind speed. The speed of the wind mainly serves to give the downwind position of the center of the puff, as shown by examination of the exponential term involving In general, one should expect the (7 value to be about the same as... 

Here Qr represents the total mass of the release, the a s refer to dispersion coefficients following the motion of the expanding puff, and the 2 in the numerator accounts for assumed ground reflection, which is consistent with the continuous plume models. Note that there is no dilution in the downwind direction by the wind. The wind serves to move the centerline of the puff in the downwind direction. This motion is accounted for by the product u t term in the exponential involving a. In the term u t, t is the time after release and u is the average wind speed in the X direction. Thus, m t is the distance down wind the puff has traveled after release. 

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