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.

A nine-sensor hot-wire probe is described which is capable of simultaneously measuring the velocity and vorticity vectors with a spatial resolution of about six Kolmogorov microscales just above the viscous sublayer in a thick turbulent boundary layer at a Reynolds number of Rθ = 2685. Results from tests of the probe performance are presented to show that the three velocity components at each of its three arrays are measured with sufficient accuracy to allow determination of velocity gradients and from them the vorticity vector. Measurements with this probe of statistical properties of the velocity and vorticity fields of the turbulent boundary layer are given in Part 2 of this paper. When compared to the results of others, they further demonstrate the capability of this probe to measure simultaneously the velocity and vorticity vectors in turbulent flows of low to moderate Reynolds numbers.

Databases for a turbulent boundary layer at Rθ=2685, a turbulent two-stream mixing layer at Rθ=5800, and a turbulent grid flow at RM=23 400 have been examined for properties of the relative helicity density, h=(U⋅Ω)/‖U‖‖Ω‖. The velocity and vorticity vectors U and Ω were simultaneously measured in these flows using a miniature probe with nine hot-wire sensors with a spatial resolution of a few Kolmogorov microscales. The results of this analysis are in generally good agreement with a similar analysis of a direct numerical channel flow simulation of Rogers and Moin [Phys. Fluids 30, 2662 (1987)]. The results do not support the suggestion that there is a high probability for the flows locally to achieve a Beltrami-like state with the velocity and vorticity vectors often nearly aligned. Such preferred alignment does not occur in the grid flow and only slightly occurs in regions of the shear flows where it is known that the mean velocity is somewhat aligned with coherent vortices. A joint probability analysis does provide some indication that alignment of the vectors is associated with lower turbulent kinetic energy dissipation. Residual mean helicity density, which previously has been explained by conjectured ‘‘spontaneous symmetry breaking,’’ is shown here likely to be due to small measurement errors. Joint probability density plots show that the two parts of the convective acceleration term in the Navier–Stokes equation, the Lamb vector, Ω×U, and ∇[(U⋅U)/2], are highly correlated with each other and are similarly associated with the turbulent kinetic energy dissipation.

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The results of large eddy simulation (LES) of the Navier–Stokes equations are used to evaluate the validity of Taylor’s hypothesis of frozen turbulence, which states that the time derivative of some instantaneous quantity is proportional to its derivative in the streamwise direction, for incompressible plane channel flow. Time and space derivatives in the streamwise direction of the velocity components are, in fact, found to be well correlated. Root-mean-square fluctuations of the terms in Taylor’s hypothesis also support the validity of this hypothesis above the buffer layer. The good agreement between LES and experimental results indicates that errors in the evaluation of derivatives in the streamwise direction are due mostly to insufficient resolution.