A THEORETICAL AND EXPERIMENTAL INVESTIGATION OF ENERGY-CONTAINING SCALES IN THE DYNAMIC SUBLAYER OF BOUNDARY-LAYER FLOWS

The existence of universal power laws at low wavenumbers (K) in the en ergy spectrum (E-u) of the turbulent longitudinal velocity (u) is exam ined theoretically and experimentally for the near-neutral atmospheric surface layer. Newly derived power-law solutions to Tchen's approxima te integral spectral budget equation are tested for strong-and weak-in teraction cases between the mean flow and turbulent vorticity fields. To verify whether these solutions reproduce the measured E-u at low wa venumbers, velocity measurements were collected in the dynamic sublaye r of the atmosphere at three sites and in the inner region of a labora tory open channel. The atmospheric surface layer measurements were car ried out using triaxial sonic anemometers over tall corn, short grass, and smooth desert-like sandy soil. The open channel measurements were performed using a two-dimensional boundary-layer probe above a smooth stainless steel bed. Comparisons between the proposed analytical solu tion for E-u, the dimensional analysis by Kader and Yaglom, and the me asured Haar wavelet E-u spectra are presented. It is shown that when s trong interaction between the mean flow and turbulent vorticity field occurs, wavelet spectra measurements, predictions by the analytical so lution, and predictions by the dimensional analysis of Kader-Yaglom (K Y) are all in good agreement and confirm the existence of a -1 power l aw in E-u(= CuuU(2) K-1, where C-uu is a constant and u* is the frict ion velocity). The normalized upper wavenumber limit of the -1 power l aw (Kz = 1, where z is the height above the zero-plane displacement) i s estimated using two separate approaches and compared to the open cha nnel and atmospheric surface-layer measurements. It is demonstrated th at the measured upper wavenumber limit is consistent with Tchen's budg et but not with the KY assumptions. The constraints as to whether the mean flow and turbulent vorticity strongly interact are considered usi ng a proposed analysis by Panchev. It is demonstrated that the argumen ts by Panchev cannot be consistent with surface-layer turbulence. Usin g dimensional analysis and Heisenberg's turbulent viscosity model, new constraints are proposed. The new constraints agree with the open cha nnel and atmospheric surface-layer measurements, Townsend's 'inactive eddy motion hypothesis', and the Ferry et al. analysis.