Unsteadiness as a cause of non-equality of eddy diffusivities for heat and vapour at the base of an advective inversion

This paper examines the effect of non-stationarity of the wind on similarity of the eddy diffusivities for heat and vapour within a stable layer at the bottom of an internal boundary layer formed downwind of a dry-to-wet transition. First, we present some experimental data taken above a rice crop downwind of very extensive dry range lands at Warrawidgee, NSW, Australia. These data establish that periods of higher wind speed were associated with periods of higher saturation deficit in the canopy of the rice crop, and lower Bowen ratio. It is shown that Bowen ratios calculated for 30-second sub-intervals varied three-fold within a single 20-minute averaging period. Thus periods of higher wind speed corresponded to periods of higher moisture flux and smaller sensible heat flux. An idealized situation is then analysed theoretically. It is assumed that the time scale of the slow variations of the wind is long compared with the surface-layer time scale and that fetch is sufficient that the air near the ground is in continuous equilibrium with the surface. Using a two-scale Reynolds decomposition of the fluctuating wind and scalar variables into active and inactive components, it is shown that unsteadiness can lead to an eddy diffusivity for saturation deficit, calculated as the ratio of average flux to average gradient, that is larger than that for total energy calculated in a similar way. Using this ratio to calculate the ratio of diffusivities for temperature and humidity, K-T/K-q, it is found that the latter can be much larger than one if the Bowen ratio is small and negative. Despite this, assuming K-T = K-q and using the Bowen ratio method to calculate surface energy fluxes will usually incur only minor errors.