The growth of the atmospheric internal boundary layer

When air, whose wind profile is in equilibrium with an underlying surface, passes to another surface with different roughness, a layer is formed in which the air has adjusted to the new surface. Generally this layer will grow in depth downwind. Assuming the logarithmic wind‐speed distribution and Karman's integral equation the height of this layer is computed theoretically as a function of distance. A dimensional argument is also presented which qualitatively confirms the result that the boundary layer grows as the ⅘ power of the distance downwind and is independent of wind speed. The effect of thermal stability is estimated and found to be relatively small, raising the height of the layer in lapse conditions and lowering it in inversions. Some data are discussed which qualitatively confirm those results but which cannot be considered to be conclusive.