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 energy spectrum (E(u)) of the turbulent longitudinal velocity (u) is examined theoretically and experimentally for the near-neutral atmospheric surface layer. Newly derived power-law solutions to Tchen's approximate integral spectral budget equation are tested for strong-and weak-interaction cases between the mean flow and turbulent vorticity fields. To verify whether these solutions reproduce the measured E(u) at low wavenumbers, velocity measurements were collected in the dynamic sublayer of the atmosphere at three sites and in the inner region of a laboratory open channel. The atmospheric surface layer measurements were carried 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 solution for E(u), the dimensional analysis by Kader and Yaglom, and the measured Haar wavelet E(u) spectra are presented. It is shown that when strong interaction between the mean flow and turbulent vorticity field occurs, wavelet spectra measurements, predictions by the analytical solution, and predictions by the dimensional analysis of Kader-Yaglom (KY) are all in good agreement and confirm the existence of a -1 power law in E(u)(= C(uu)U*(2) K(-1), where C(uu) is a constant and u* is the friction velocity). The normalized upper wavenumber limit of the -1 power law (Kz = 1, where z is the height above the zero-plane displacement) is estimated using two separate approaches and compared to the open channel and atmospheric surface-layer measurements. It is demonstrated that the measured upper wavenumber limit is consistent with Tchen's budget but not with the KY assumptions. The constraints as to whether the mean flow and turbulent vorticity strongly interact are considered using a proposed analysis by Panchev. It is demonstrated that the arguments by Panchev cannot be consistent with surface-layer turbulence. Using dimensional analysis and Heisenberg's turbulent viscosity model, new constraints are proposed. The new constraints agree with the open channel and atmospheric surface-layer measurements, Townsend's 'inactive eddy motion hypothesis', and the Ferry et al. analysis.