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A CONTRIBUTION TO THE PROBLEM OF STRATOSPHERIC DIFFUSION BY LARGE-SCALE MIXING

RICHARD J. REEDUniversity of Washington, Seattle, Wash.

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KENNETH E. GERMANUniversity of Washington, Seattle, Wash.

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Abstract

The assumption is commonly made in stratospheric diffusion studies that the large-scale eddy flux of various properties obeys the Fickian law which requires that the flux in a coordinate direction is proportional to and in the direction of the gradient. Measurements of eddy fluxes of ozone and sensible heat reveal, however, that the law is violated in the lower stratosphere where the meridional fluxes are countergradient at most latitudes.

Use is made of the mixing length hypothesis to derive a more general expression for the large-scale eddy flux which is able to account for the phenomenon of countergradient flux. It is found that the critical parameter in determining whether the horizontal flux is in the gradient or countergradient direction is the ratio of the mean slope of the mixing path (or surface) to the mean slope of the isopleths of the property being considered.

A procedure is outlined for evaluating the coefficients needed to solve the derived diffusion equation. Although exact solutions to the equation can be obtained only by numerical methods, it is possible, by use of a number of simplifying assumptions, to achieve a crude analytical solution. Only the results of the analytical solution are presented here. These pertain to the tungsten-185 injected into the lower equatorial stratosphere during the Hardtack nuclear test series of 1958. Good correspondence is obtained between the gross features of the predicted and observed distributions two months following the time of injection.

Abstract

The assumption is commonly made in stratospheric diffusion studies that the large-scale eddy flux of various properties obeys the Fickian law which requires that the flux in a coordinate direction is proportional to and in the direction of the gradient. Measurements of eddy fluxes of ozone and sensible heat reveal, however, that the law is violated in the lower stratosphere where the meridional fluxes are countergradient at most latitudes.

Use is made of the mixing length hypothesis to derive a more general expression for the large-scale eddy flux which is able to account for the phenomenon of countergradient flux. It is found that the critical parameter in determining whether the horizontal flux is in the gradient or countergradient direction is the ratio of the mean slope of the mixing path (or surface) to the mean slope of the isopleths of the property being considered.

A procedure is outlined for evaluating the coefficients needed to solve the derived diffusion equation. Although exact solutions to the equation can be obtained only by numerical methods, it is possible, by use of a number of simplifying assumptions, to achieve a crude analytical solution. Only the results of the analytical solution are presented here. These pertain to the tungsten-185 injected into the lower equatorial stratosphere during the Hardtack nuclear test series of 1958. Good correspondence is obtained between the gross features of the predicted and observed distributions two months following the time of injection.

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