Buoyancy effects on the integral lengthscales and mean velocity profile in atmospheric surface layer flows

Within the diabatic atmospheric surface layer (ASL) under quasi-stationary and horizontal homogeneous conditions, the mean velocity profile deviates from its conventional logarithmic shape by a height-dependent universal stability correction function φ{symbol}m(ζ) that varies with the stability parameter ζ. The ζ parameter measures the relative importance of mechanical to buoyant production or destruction of turbulent kinetic energy (TKE) within the ASL. A link between φ{symbol}m(ζ) and the spectrum of turbulence in the ASL was recently proposed by Katul et al. ["Mean velocity profile in a sheared and thermally stratified atmospheric boundary layer," Phys. Rev. Lett.107, 268502 (2011)]. By accounting for the stability-dependence of TKE production, Katul et al. were able to recover scalings for φ{symbol}m with the anticipated power-law exponents for free convective, slightly unstable, and stable conditions. To obtain coefficients for the φ{symbol}m(ζ) curve in good agreement with empirical formulas, they introduced a correction for the variation of the integral lengthscale of vertical velocity with ζ estimated from the Kansas experiment. In the current work, the link between the coefficients in empirical curves for φ{symbol}m(ζ) and stability-dependent properties of turbulence in the ASL, including the variation with ζ of the integral lengthscale and the anisotropy of momentum transporting eddies is investigated using data from the Advection Horizontal Array Turbulence Study. The theoretical framework presented by Katul et al. is revised to account explicitly for these effects. It is found that the coefficients in the φ{symbol}m(ζ) curve for unstable and near-neutral conditions can be explained by accounting for the stability-dependence of the integral lengthscale and anisotropy of momentum-transporting eddies; however, an explanation for the observed φ{symbol}m(ζ) curve for stable conditions remains elusive. The effect of buoyancy on the horizontal and vertical integral lengthscales is also analyzed in detail. © 2013 AIP Publishing LLC.

Duke Scholars

Author Gabriel G. Katul Civil and Environmental Engineering