Transport of gases to and from grass and grass-like surfaces

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.