Generalized Non-dimensional Wind and Temperature Gradients in the Surface Layer

Abstract

We propose a single generalized function for dimensionless wind and temperature gradients in stable and unstable conditions based on Monin–Obukhov similarity theory. The proposed function may be matched with the currently accepted universal functions for the dimensionless wind-speed and temperature gradients using the empirical coefficients a and b to yield differences within ± 14% for both wind and temperature gradients in the interval of $$-2$$ < z/L < 0.5 (z is height and L is the Obukhov length). In neutral conditions, wind and temperature profiles are the same as the standard log-law profile. Under unstable conditions, the differences are smaller than 1.5%; conversely, under stable conditions, the differences reach up to $$-~5.2$$%. The coefficients a and b are analyzed here to evaluate the limits of this proposed semi-empirical function and possible physical characteristics are discussed. Although we use the same theoretical assumptions and limitations of Monin–Obukhov similarity theory in the surface layer, the proposed function has the flexibility of adjusting the wind and temperature gradients for specific sites using the empirical coefficients a and b within the range 0–1, with stable and unstable conditions able to be described by a single general function.