Reynolds Number Influence on Turbulent Blocking Effects of a Rigid Plane Boundary (1st Report, Linear Analysis Using the Rapid Distortion Theory)

Abstract

The effects of Reynolds number on turbulent blocking effect by a rigid plane boundary are studied using a boundary-layer theory and a linear theory based on rapid distortion theory (RDT).The three-dimensional energy spectrum for low Reynolds number flows is applied to the linear theory developed for shear-free boundary layer by Hunt & Graham (1978). Fully analytical solutions for the three-component turbulent intensities of velocity fluctuations are obtained. The one-dimensional power spectra are also obtained analytically. The results are compared with the previous analysis at high and moderate Reynolds numbers and laboratory measurement at low Reynolds number. The results show that the blocking effects by the surface become more significant at low Reynolds numbers when the viscous damping is small : the vertical velocity fluctuations decrease and streamwise and spanwise velocity fluctuations increase faster than those at high Reynolds numbers. The spectra are amplified in the higher wavenumber region compared with the high Reynolds case. The solution in the viscous layer explains why the data at low Reynolds numbers show no amplification of turbulence intensities near the surface.