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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1. Turbulent diffusion thec~

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Turbulence theory has been classically formulated for stationary turbu-

1ence. Fundamental to this theory is the assumption that any measured flow

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can be partitioned into a mean component and a perturbation component where

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the mean component. does not change \vith time and the mean of the perturbation

quantities is zero. This statement expressed mathematically is:

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U.
1.

u. + u. " \vhere u. 10 f (t) and ~
1. 1. J. i

o

(3.1)

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Spectra of kinetic energy in the atmosphere have been sho\Vll to be continuous

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up to planetary scales of motion.. Therefore, even though the concept of

partitioning the flow into a mean and a perturbation quantity is not strictly

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applicable, it is common practice out of necessity.

Monin and Yag10n (1971) have reviewed the classical l-D diffusion theory

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of Taylor (1921) for homogeneous turbulence. Taylor's equation extended to

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3-D is:

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2
cr. (t)
1.

'2 ft fS
= 2 u. R~ (T) dTds
1. 001.

(3.2)

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cr.2 (t) is the mean squared displacement of particles diffused about the
1.
center of mass in the i direction after time t, R~ (T) is the Lagrangian
1.

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autocorrelation function between turbulent velocities in the i direction

and u. ,2 is the covariance of the u., i.e., perturbatiOn quantity squared.
1. 1.

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The equation is for a typical parcel at times separated by T. Kampe de Feriet

(1939) reformulated Taylor's equation in an equivalent manner as:

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2
cr. (t)
1.

ft
2 u. ,2 (t - T) R~ (T) dT
1. 0 1.

(3.3)

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