WMOD00400

• Contract/Permit #: 14-06-D-6801
• Title: Structure and Seedability of San Juan Storms
• Date: 11/1/1976
• Weather Modification - Doc Type: Report

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(Equation 3.3) and integrating one obtains:

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2
0i (t)

2 ui,2 [TLt(l - e-t/TL) + TL2 ((t/TL + l)e-t/TL -1)]

(3.9)

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Taking the limit as t

~co
,

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2
0. (t)
1.

2 ,2
u i TL t

(3.10)

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The ratio of Equation 3.9 to Equation 3.10 for various values of t is given

in Table 3.3 It may be noted that ui,2 TL is the Lagrangian eddy diffusion
L
coefficient, K. The results in Table 3.3 show that the K-theory has validity

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for t > TL.

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t 0 TL 2 TL 4 TL 7 TL
Eq. 3.9/Eq. 3.10 0 0.61 0.75 0.87 0.92
Table 3.3. Ratio of Equation 3.9 to Equation 3.10 for
various values of t.

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The so-called mixing length theories are commonly used to predict dispersion.

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They postualte an analogy between molecular diffusion and atmospheric eddy

diffusion, i.e., the flux is proportional to the gradient of concentration.

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Tennekes and Lumley (1972) have shown that the mixing length theories

are

fundamentally incorrect and have no real value in the physical sense

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since the diffusing mechanism is the same scale as the property being

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diffused.

In summary, the procedure for computing the Lagrangian diffusion from

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airciaft-derived turbulence data is as follows:

1. Block the aircraft data into time segments in which the aircraft Has

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flown in straight and level flight through homogeneous turbulence fields.

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