## Abstract

A radioactive vapour of thorium-*B *(lead-212) has been used to measure the vertical flux of a gas to grass and similar surfaces in a wind tunnel, as a function of the difference in vapour concentration between the air and the surface. Experiments were done over a range of values of the parameters friction velocity (u) and roughness length (z_{o}). The results have been analysed in term s of the reciprocal sublayer Stanton number B^{-1}of Owen & Thomson (1963), which is a measure of the degree to which Reynolds’s analogy between transport of momentum and matter (or heat) breaks down at the surface. B^{-1} is equal to the difference between the dimensionless resistances of the boundary layer for momentum and for mass. Experiments with grass and other surfaces having roughness elements of a fibrous character gave values of B^{-1} in the range 6 to 12. Some variation of B^{-1} with u* was found, but less than expected from Owen & Thomson’s work. Little effect of variation in z0 was found. For values of u* and z_{0} applicable in normal conditions to vapour transport to or from short grass in the field, B^{-1} was found to equal 8 ± 1. Experiments with a surface of rough glass, having roughnesses of a pyramidal nature, confirmed Owen & Thomson’s results, and gave values of B^{-1} in the range 20 to 40. The dependence of B^{-1} on the shape of the roughness elements, suggested by Owen & Thomson, was strongly exhibited in the present work, and R~x cannot be considered to be a single function of the roughness Reynolds number u*z_{0}/v. Comparative experiments were done on the rate of evaporation of water from two of the surfaces (artificial grass and towelling) used in the experiments with thorium-*B*, in order to obtain an estimate of the dependence of B^{-1} on the molecular properties of the vapour. The ratio of the molecular diffusivity of water vapour to that of thorium-*B* vapour is 4.4:1. The ratio of values of *B*^{-1} was found to be 1:1.6, with some variation according to the surface and the wind speed. Under average conditions of evaporation in the field, a value about 5 is suggested for *B*^{-1}, but this may not apply for values of z_{0} outside the range of the experiments. The dimensionless resistance for momentum, between a height z_{1} and the surface, is and if z_{1} is of order 1 m, this term is several times larger than *B*^{-1}. Since it is the sum of u_{1}/u* and *B*-1 which enters into the formula for the rate of evaporation, it is sufficient to obtain *B*-1 to a moderate accuracy. The wetted artificial grass, subjected to forced evaporation in the wind tunnel, could be considered as a wet-bulb thermometer, and the surface temperature was found to approximate very closely to the wet-bulb temperature of the air, especially a t high wind speeds, when the transport of heat to the surface by radiation from above or conduction from below was relatively small. I t follows from this that the eddy diffusivities of heat and vapour in the boundary layer are equal, at least to within 10 %. Moreover the molecular diffusivity of water vapour is not very different from the thermometric conductivity of air at room temperature, and therefore nearly the same values of *B*-1 should apply to the transport of heat and water vapour. Temperature profiles obtained by Pasquill and Rider over short grassland at Cambridge are shown to give values of *B*-1 of 5.7 and 3.9, in good agreement with the results from the wind tunnel.

## Footnotes

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- Received May 14, 1965.

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