The Vertical Transfer of Heat and the Chan_??_e of Air Temperature by Turbulence

Abstract

In 1915 .G. I. Taylor obtained a formula expressing the rate of the vertical transfer of heat by turbulence. In obtaining this he assumed that there is no resultant transfer of mass across any horizontal plane. However, when the heat is transferred vertically and the vertical distribution of temperature changes, the change of the vertical distribution of pressure. will follow. This means that the mass is transferred vertically and so Taylor's assumption is not correct. We obtained an equation which expresses the rate of the vertical transfer of heat and the change of the temperature of the air taking the transfer of mass into consideration and compared this with the results obtained by observations.
The equation expressing the rate of change of temperature was given by where K is the eddy conductivity and _??_ is the dry adiabatic lapse rate of the air temperature. The second term of the right-hand side of the above equation arises due to the effect of the vertical transport of air being taken into consideration.
As an example the diurnal variation of the upper air temperature was obtained from the above equation and it was compared with the result from Taylor's equation and the observed values at Lindenberg. In the above table, K was assumed to be 10⁵.
From the above table we can find that Taylor's result holds only below 500m and the discrepancy increases with height. On the contrary, our result holds fairly good up to higher levels even if K is assumed to be constant.
Details will be published in the Science Report of Tohoku University Series V, Vol. 1. No 3.