The “Inactive” Eddy Motion and the Large-Scale Turbulent Pressure Fluctuations in the Dynamic Sublayer

Abstract

The statistical structure of the turbulent pressure fluctuations was measured in the dynamic sublayer of a large grass-covered forest clearing by a free air static pressure probe and modeled using Townsend's hypothesis. Townsend's hypothesis states that the eddy motion in the equilibrium layer can be decomposed into an active component, which is only a function of the ground shear stress and height, and an inactive component, which is produced by turbulence in the outer region. It is demonstrated that the inactive eddy motion contributes significantly to the pressure and longitudinal velocity power spectra for wavenumbers much smaller than that corresponding to the height above the ground surface. Because of the importance of this inactive eddy motion contribution, it was possible to derive and validate a scaling law for the pressure power spectrum at low wavenumbers. The root-mean-square pressure was derived from the ground shear stress using simplifications to the Poisson equation that relate the Laplacian of the pressure fluctuations to the divergence of momentum. The theoretically derived and experimentally measured root-mean-square pressure values were in close agreement with other theoretical predictions and numerous laboratory measurements for wall pressure fluctuations. The relation between the root-mean-square pressure and the ground shear stress was also used to determine the similarity constant for the large-scale pressure spectrum. From considerations of the integral representation of the Poisson equation, previous laboratory measurements, and the present data, it was shown that this similarity constant does not vary appreciably with the roughness of the boundary layer. Finally, it was demonstrated that the inactive eddy motion does not contribute to the vertical velocity power spectrum in agreement with Monin and Obukhov surface-layer similarity theory.