The velocity and vorticity vector fields of a turbulent boundary layer. Part 2. Statistical properties

Abstract

Many of the statistical properties of both the velocity and the vorticity fields of a nominally zero-pressure-gradient turbulent boundary layer at Rδ = 27650 (Rθ = 2685) have been simultaneously measured. The measurements were made with a small nine-sensor hot-wire probe which can resolve the turbulence to within about six Kolmogorov microscales just above the sublayer. The statistical properties of the velocity vector field compare very well with other laboratory measurements and with direct numerical simulations when Reynolds-number dependence is taken into account. The statistical properties of the vorticity field are also in generally good agreement with the few other measurements and with the direct numerical simulations available for comparison. Near the wall, r.m.s. measurements show that the fluctuating spanwise vorticity is the dominant component, but in the outer part of the boundary layer all the component r.m.s. values are nearly equal. R.m.s. measurements of the nine individual velocity gradients show that the gradients normal to the wall of all three velocity components are the largest, with peaks occurring near the wall as expected. Gradients in the streamwise direction are everywhere small. One-dimensional spectra of the vorticity components show the expected shift of the maximum energy to higher wavenumbers compared to spectra of the velocity components at the same location in the flow. The budget of the transport equation for total enstrophy indicates that the viscous dissipation rate is primarily balanced by the viscous diffusion rate in the buffer layer and by the rotation and stretching rate in the logarithmic layer.