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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46

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"'"

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0:::

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o

r/TL

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Figure 3.6

Autocorrelation Functions from an aircraft (RA)',
Eulerian (RE) and Lagrangian (RL) frame of

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Values of S vary from 1 to 5. Tennekes and Lumley (1972) have shm.;rn that

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S = 1 for homogeneous turbulence in an incompressible fluid. Panofsky and

Mizuno (1974) concluded that S varies from 2.0 to 4.5 based on data from

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multiple tOloJers in Nebraska. In this study, S Hill be assumed to be 3.

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L L
It may be shown that E, (~) and R, (l) are a fourier tr2.nsform pair ~oJhere
l l
E~ (w) is the Langrangian power density spectrum per unit frequency in the i
l

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direction.

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2 ,2 foo }{L (T) l' WT
EL (w) = ? d
i - n Ui 0 i e T

(3.7)

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,2
2 ui TL
n 1 + (w TL)2

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It is implicit in these results that the power density spectrum is

not frequency (w) to the -5/3, but rather w to the -6/3 or -2. Later,

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we "li11 examine the pOloJer density spectrum data and determine Hhether the

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clatc! fits the -5/3 or -2 pmoJer law.

Substituting the empirically determined Lagrangian exponential auto-

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correlation function (Equation 3.~) into the modified Taylor's diffusion