Journal of the Meteorological Society of Japan. Ser. II
Online ISSN : 2186-9057
Print ISSN : 0026-1165
ISSN-L : 0026-1165
On the Numerical Calculation of Eddy Flux
Y. Takahasi
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1942 Volume 20 Issue 1 Pages 18-28

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Abstract
Assuming that a small mass of air, which occupies a certain position, say x1, at time t, is diffused by eddy into its surrounding air within the limits of x1-s to x1+s at the next time t+τ, it was found that the eddy flux of any physical quantity per unit area for the time from t to t+τ can be calculated numerically by the formula (6), if the distribution of the quantity at time t is known.
By the Simpson's 1/3 rule the formula (6) can be transformed into more convenient formula such as (71), (711), or (7111). Further these formulae can be also transformed into the formula (8), where A is the Austausch coefficient and _??_τ (x, t) the mean gradient of the distribution of the quantity for the time from t to t+τ. Fig. 3, I, II and III show how to determine the mean gradient from the curve of the distribution of the quantity, corresponding respectively to the formulae (71), (711), and (7111).
In the case when τ is not small, it will be better to use the formula (13).
In the tables 1 and 2 are compared the results of the theoretical and the numerical calculations for some exercises.
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