# Drag and heat transfer relations for the planetary boundary layer

## Authors

- Received:

DOI: 10.1007/BF02186087

- Cite this article as:
- Long, R.R. & Guffey, L.J. Boundary-Layer Meteorol (1977) 11: 363. doi:10.1007/BF02186087

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## Abstract

A theory is offered for the drag and heat transfer relations in the statistically steady, horizontally homogeneous, diabatic, barotropic planetary boundary layer. The boundary layer is divided into three regions*R*_{1},*R*_{2}, and*R*_{3}, in which the heights are of the order of magnitude of*z*_{0},*L*, and*h*, respectively, where*z*_{0} is the roughness length for either momentum or temperature,*L* is the Obukhov length, and*h* is the height of the planetary boundary layer. A matching procedure is used in the overlap zones of regions*R*_{1} and*R*_{2} and of regions*R*_{2} and*R*_{3}, assuming that*z*_{0} ≪*L* ≪*h*. The analysis yields the three similarity functions*A*(μ),*B*(μ), and*C*(μ) of the stability parameter, μ = ϰ*u*_{*}/*fL*, where ϰ is von Kármán's constant,*u*_{*} is the friction velocity at the ground and*f* is the Coriolis parameter. The results are in agreement with those previously found by Zilitinkevich (1975) for the unstable case, and differ from his results only by the addition of a universal constant for the stable case. Some recent data from atmospheric measurements lend support to the theory and permit the approximate evaluation of universal constants.