# The surface boundary layer as a part of the overlying convective layer

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## Abstract

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 constant*a*=1/12, and the turbulent decay constant*A*=1, by mechanistic reasoning, without the introduction of any adjustable empirical constants.

*i*is the total turbulence such that

*i*

^{2}=σ

_{u}

^{2}+

_{v}

^{2}+

_{w}

^{2}, given that the σ are the standard deviations of the air velocity along each axis. Von Karman's constant is

*k*=0.4, and

*L*is the Obukhov scale length.

Rough surface conditions also allow the wind and the temperature excess at ten meters or so above the surface to be derived. In these conditions*v*=(A/2a)^{1/2}i, and*T*_{surface}−*T*_{average at plume base}=*H/(ϱC*_{p}*ai*). 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 words

Boundary layer Convection## Preview

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### References

- Deardorff, James W. (1972),
*Numerical investigation on neutral and unstable planetary boundary layers*, J. Atmos. Sci.*29*, 91–115.Google Scholar - Kaimal, J. C., Wyngaard, J. C., Haugen, D. A., Cote, O. R., Izuml, Y., Caughey, S. J. andReadings, C. J. (1976),
*Turbulence structure in the convective boundary layer*, J. Atmos. Sci.*33*, 2152–2169.Google Scholar - Kazanskiy, A. B. andMonin, A. S. (1957),
*Shape of Smoke Plumes*, Izvestiya AN USSR, Ser. Geofiz,*8*, 1020–1033.Google Scholar - Lumley, J. L. andPanofsky, H. A. (1964),
*The Structure of Atmospheric Turbulence*(New York, Wiley, 1964), 239 pp.Google Scholar - Monin, A. S., andYaglom, A. M. (1971),
*Statistical Fluid Mechanics: Mechanics of Turbulence*, Vol. 1, (The MIT Press, 1971), 769 pp.Google Scholar - Panofsky, H. A. andMcCormick, R. A. (1954),
*Properties of spectra of atmospheric turbulence at 100 meters*, Quart. J. Roy Meteorol. Soc.*80*, 546.Google Scholar - Pasquill, F. (1972),
*Some aspects of boundary layer description*, Quart. J. Roy. Meteorol. Soc.*98*, 469–494.Google Scholar - Telford, J. W., I. (1966),
*The convective mechanism in clear air*, J. Atmos. Sci.*23*, 652–666.Google Scholar - Telford, J. W., II, (1970),
*Convective plumes in a convective field*, J. Atmos. Sci.*24*, 347–358.Google Scholar - Telford, J. W., III. (1972),
*A plume theory for the convective field in clear air*, J. Atmos. Sci.*29*, 128–134.Google Scholar - Telford, J. W., IV. (1975),
*The effects of compressibility and dissipation heating on boundary layer plumes*, J. Atmos. Sci.*32*, 108–115.Google Scholar - Telford, J. W., V. (1975),
*Turbulence, entrainment and mixing in cloud dynamics*, Pure. Appl. Geophys.*113*, 1067–1084.Google Scholar