Turbulent boundary layer profiles over uniform rough surfaces

Abstract

Historically, atmospheric boundary layer profiles have been most commonly expressed by logarithmic and power law forms. This paper examines several ways in which the wind profile can be “derived” and shows that all the methods lead either to logarithmic or power law expressions. The logarithmic form is seen to be best near the surface, with the power law a better fit at greater heights or over a larger range of elevations. Results show that the power law exponent is a function of the boundary layer thickness and the surface roughness. The various expressions obtained are compared with the log-polynomial profile proposed by Deaves and Harris (CIRIA Rep. 76, 1978) since it has been verified with many atmospheric profiles measured to as much as half the boundary layer thickness. When compared over the entire boundary layer, the power law agrees with the Deaves and Harris model to within a maximum of 5% and generally much less; a weighted log-power law expression agrees with the Deaves and Harris expression to within 1%. The velocity defect forms of the several expressions are examined, and all show similar values and variation.