A spectral budget model for the longitudinal turbulent velocity in the stable atmospheric surface layer

A spectral budget model is developed to describe the scaling behavior of the longitudinal turbulent velocity variance σ2u with the stability parameter ζ=z/L and the normalized height z/δ in an idealized stably stratified atmospheric surface layer (ASL), where z is the height from the surface, L is the Obukhov length, and δ is the boundary layer height. The proposed framework employs Kolmogorov's hypothesis for describing the shape of the longitudinal velocity spectra in the inertial subrange, Heisenberg's eddy viscosity as a closure for the pressure redistribution and turbulent transfer terms, and the Monin-Obukhov similarity theory (MOST) scaling for linking the mean longitudinal velocity and temperature profiles to ζ. At a given friction velocity u*, σu reduces with increasing ζ as expected. The model is consistent with the disputed z-less stratification when the stability correction function for momentum increases with increasing ζ linearly or as a power law with the exponent exceeding unity. For the Businger-Dyer stability correction function for momentum, which varies linearlywith ζ, the limit of the z-less onset is ζ≈2. The proposed framework explains why σu does not follow MOST scaling even when the mean velocity and temperature profiles may follow MOST in the ASL. It also explains how d ceases to be a scaling variable in more strongly stable (although well-developed turbulent) ranges.

Duke Scholars

Author Gabriel G. Katul Civil and Environmental Engineering