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Horizontal diffusion in the atmosphere as determined by geostrophic trajectories

Published online by Cambridge University Press:  28 March 2006

C. S. Durst ,
A. F. Crossley  and
N. E. Davis
C. S. Durst
Affiliation:
7 Alton Road, London, S.W. 15
A. F. Crossley
Affiliation:
Meteorological Office, Air Ministry, London, W.C. 2
N. E. Davis
Affiliation:
Meteorological Office, Air Ministry, London, W.C. 2
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Abstract

If a series of air trajectories is drawn from a fixed point at a certain height above the earth's surface, the end-points of the superimposed trajectories, after each has been followed for a time t, will have a standard vector deviation S. The purpose of this paper is to discuss the form of S. One expression is obtained by relating S empirically to the magnitude of the mean vector position [x] of the ends of the trajectories, so that $S = CL |[X|L]|^a,$

where L is a certain length and C and a are dimensionless constants; a is found to be about 0·870 and C is nearly proportional to $\surd T$, where T is the total period over which the series of trajectories is initiated.

A more satisfying expression for S connects it with the variability of the wind during the priod of initiation of the trajectories, i.e. with the standard vector deviation of wind (ω) which is itself dependent on T. The relationship involves the Lagrangian correlation coefficient r(t) of wind with time along the trajectories. It is found that the variation of S with time t agrees well with that deduced from the exponential formula r(t) = e-αt. Moreover, α, the reciprocal of the characteristic time of the ‘eddies’, is identified with ω2/K where K is the coefficient of eddy viscosity for lateral mixing.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 6 , Issue 3 , October 1959 , pp. 401 - 422
Copyright
© 1959 Cambridge University Press

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