Similarity of instantaneous and filtered velocity fields in the near wall region of zero-pressure gradient boundary layer

Abstract

Instantaneous velocity distributions in the viscous and roughness sublayers and in the lower parts of the logarithmic-law region of flat-plate boundary layers over smooth and rough surfaces are measured using a hot-wire rake consisting of two X-wire and nine single-sensor probes in order to investigate the turbulence structure and similarity of the instantaneous and filtered velocity profiles near the wall. The results can provide useful information as to the treatment of flow in this region in a large-eddy type simulation of high Reynolds-number flows over smooth and rough walls. The instantaneous velocity profiles feature large-scale structures but random fluctuations of considerable amplitude are superimposed and no similarity that is applicable to instantaneous unconditioned profiles can be derived. Conditionally averaged profiles based on the magnitudes of the wall shear and normal velocity in the buffer layer, however, show trends related to the sweep-ejection type events. The filtered profiles normalized by the filtered instantaneous friction velocity show similarity that progressively extends its region from the immediate neighborhood of the wall to the log layer as the filter size is increased. The minimum streamwise length of the filter size required to show logarithmic similarity is found to be as large as 1800 wall units. Similar results are obtained for rough-wall boundary layers if the instantaneous friction velocity is replaced by the equivalent velocity scale implied by the velocity just outside the roughness-influenced sublayer at about 10 viscous units from the wall, or about 1.5 times the height of the roughness bars from the wall. The sub-grid stress components have are obtained from the data and implication for modeling is discussed.