## 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$_0$). The results have been analysed in terms 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 z$_0$ 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 $\pm$ 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 B$^{-1}$ 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 u$_1$/u$_*$, 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 at high wind speeds, when the transport of heat to the surface by radiation from above or conduction from below was relatively small. It 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.