The surface boundary layer as a part of the overlying convective layer
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This paper extends previous work developing a mechanistic theory of the convective boundary layer to the forced convective region between the base of the plumes and the surface. It is shown that a simple model based on specifying the entrainment between adjacent layers, gives quantitative relations between temperature at plume height and the surface temperature, and the shearing stress and the turbulence, thus completing the specifications of the surface boundary needed for the convective planetary boundary layer plume model, by describing the surface boundary layer without constants determined to match boundary layer measurements.
The formulae are deduced in terms of the entrainment constanta=1/12, and the turbulent decay constantA=1, by mechanistic reasoning, without the introduction of any adjustable empirical constants.
Rough surface conditions also allow the wind and the temperature excess at ten meters or so above the surface to be derived. In these conditionsv=(A/2a)1/2i, andTsurface−Taverage at plume base=H/(ϱCpai). When the surface is not very rough, an additional roughness parameter is required to specify the number of layers needed to make the transition from the plume to the surface, and its function is examined. These formulae all compare well with published measured values.
It is shown by means of a fully descriptive theory, that the shear in the plume layer is very small.
Key wordsBoundary layer Convection
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