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.

Application of a Novel Laser-Doppler Velocimeter for Turbulence: Structural Measurements in Turbulent Boundary Layers

“…Similar studies to Klebanoff's were repeated with elaborate hot-wire arrangements by Balint et al (1991) and Honkan and Andreopoulos (1997) among others. These studies measured all-nine components of the velocity gradient tensor in low Reynolds number turbulent boundary layer flows, but with probe-sizes that were several times the Kolmogorov length scales in the low Reynolds number flows.…”

“…Analogous data are plotted for the higher Reynolds number 2DFPTBL in Figure 4.44. The underestimation of TKE dissipation rate in near-wall TBLs using single-point spectral data has been documented a number of times (Sandbom and Braun 1956;Balint et al 1991). Surprisingly, the lower-Reynolds number case follows the spectral value for the lowest y+ value reported.…”

“…Several researchers have utilized HWA in multiple-wire configurations to achieve velocity gradient measurements (Balint et al 1991, Wallace and Foss 1995, Honkan and Andreopoulos 1997, Wang and Sen 1999, Honkan and Andreopoulos 2001, and Kholmyansky et al 2001. Although able to measure three components of vorticity, these techniques are intrusive, thus preventing near-wall measurements, and spatially unresolved, with probe sizes no smaller than twice the size of the smallest scales of turbulence in their flows.…”

A Laser Vorticity Probe for the Characterization and Control of Turbulent Boundary Layers

“…Eckelmann et al (1977) proposed a five sensor arrangement in order to obtain, simultaneously, the two components of vorticity. Wassman and Wallace (1979), Vukoslavcevic et al (1991), Balint e; a/ (1991) and Andreopoulos and Honkan (1996), among others, attempted three component simultaneous measurements of the vorticity vector using various configurations of clusters of hot-wire sensors, the latter three using nine independent wires in groups of three at spatially distinct locations. Hot wire-based vorticity and velocity gradient techniques are comparatively less intrusive that those discussed earlier, however, the existence of a physical probe in the flow not only disturbs the flow but also is vulnerable in hostile flow environments.…”

Orthogonal Wavelet-Decomposed 3-D Vorticity of a Turbulent Cylinder Wake

“…There have been many attempts to measure these quantities simultaneously in various flows since the first measurements of all three components of the vorticity fluctuations by Wassman and Wallace (1979) (1) using a nine-sensor probe. Convectional statistical analysis on the three vorticity components have been performed in some turbulent flows, such as a turbulent boundary layer (2) , grid and boundary layer turbulence (3) and wake flows (e.g. Refs.…”