Change of terrain roughness and the wind profile

Abstract

SIJMMARYTo describe the distribution of wind with height in hydrostatically-neutral air following a change h terrain roughness, a theory is constructed by assurnin2 that only the air below an internal boundary is affected by the chanxe and that air above the boundary is moving with the speed and Reynolds stress that it had upwind of the change of roughness. Unlike in tlic closely related theory of Elliott, the assumed velocity distribution in the lower layer is consistent, not with stress independent of height, but with continuous variation of stress from the surface to the boundarv \vIicre the stress is that in the original layer. The condition of overall conservation of momentum then leads to relations between surface stress, boundary height and fetch. The theory is compared with observations at a variety of locations, and the agreement with measurements is satisfactory. In particular, a fairly sharp boundary separates the masses of air influenced by the two types of terrain; for micrometeorological distanccs, the slope of this interface is of order 1/10.

Aerodynamic Characteristics of Atmospheric Boundary Layers.

“…Panofsky and Townsend (1964) reasoned that the most unrealistic feature of Elliott's model is the condition, apparently imphed by the logarithmic profile in the internal boundary layer, that the shear stress jumps discontinuously at z = 5 from u*2 to uJi. This criticism is, however, not entirely justified because it requires the mixing-length relation between shear stress and velocity profile: r = uJ=(Kz)^(|f-y (4.24)…”

Numerical Study on. Atmospheric Boundary Layer Flow over Inhomogeneous Terrain

“…Using the method of boundary layer theory, Elliott (1958) and Panofsky and Townsend (1964) obtained the wind profile downstream of the Toughness discontinuity. They assumed that the wind field upstream from the discontinuity and above the internal boundary is unaffected by the change of roughness.…”

“…Theoretical investigations of Elliott (1958), Taylor (1962), Panofsky and Townsend (1964), and Townsend (1965) assume the formation of an internal boundary, which separates the air underneath, which has been influenced by the roughness of the underlying surface, from the air above which has not yet been modified. All theories agree in assuming that the internal surface is fairly sharp, and observations by Lettau et al (1962) confirm this assumption.…”

Could Crop Height Affect the Wind Resource at Agriculturally Productive Wind Farm Sites?

“…When one roughness regime gives way to another, the flow near the ground gradually adjusts to the new surface characteristics. This process is often represented mathematically by local internal boundary layers (IBLs), which grow vertically downstream of a roughness boundary (Elliott 1958;Panofsky and Townsend 1964;Townsend 1965;Peterson 1969;Blom and Wartena 1969).…”