Hot-wire measurements were conducted in the very near wake (x/d<. 10) of a circular cylinder at a Reynolds number based on cylinder diameter, Red of 3900. Measurements of the streamwise velocity component with the use of single sensor hot-wire probes were found to be inaccurate for such flowfields where high flow angles are present. An X-array probe provided detailed streamwise and lateral velocity component statistics. Frequency spectra of these two velocity components are also presented. Measurements with a 4-sensor hot-wire probe confirmed that the very near wake region is dominantly two-dimensional, thus validating the accuracy of the present X-array data.

An experimental study of a turbulent boundary layer at Rθ≈1070 and Rτ≈543 was conducted. Detailed measurements of the velocity vector and the velocity gradient tensor within the near-wall region were performed at various distances from the wall, ranging from approximately y+=14 to y+=89. The measured mean statistical properties of the fluctuating velocity and vorticity components agree well with previous experimental and numerically simulated data. These boundary layer measurements were used in a joint probability density analysis of the various component vorticity and vorticity–velocity gradient products that appear in the instantaneous vorticity and enstrophy transport equations. The vorticity filaments that contribute most to the vorticity covariance Ω[bar]xΩ [bar]y in this region were found to be oriented downstream with angles of inclination to the wall, when projected on the streamwise (x, y)-plane, that decrease with distance moving from the buffer to the logarithmic layer. When projected on the planview (x, z)- and cross-stream (y, z)-planes, the vorticity filaments that most contribute to the vorticity covariances Ω [bar]xΩ [bar]z and Ω [bar]yΩ [bar]z have angles of inclination to the z-ordinate axis that increase with distance from it. All the elements of the ΩiΩj ∂Ui/∂xj term in the enstrophy transport equation, i.e. the term that describes the rate of increase or decrease of the enstrophy by vorticity filament stretching or compression by the strain-rate field, have been examined. On balance, the average stretching of the vorticity filaments is greater than compression at all y+ locations examined here. However, some individual velocity gradient components compress the vorticity filaments, on average, more than they stretch them.

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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Measurements of the velocity and vorticity field with a 12-sensor hot-wire probe were carried out in the boundary layer of the test section ceiling of the NASA Ames 80ϫ 120 ft 2 wind tunnel at a turbulence Reynolds number of R Ϸ 875. Tests of local isotropy were applied to the data obtained at y / ␦ = 0.1. In the inertial subrange, which extended over a decade of wave numbers for this experiment, both the velocity and vorticity component one-dimensional k x spectra agree well with the isotropic spectra of Kim and Antonia ͓J. Fluid Mech. 251, 219 ͑1993͔͒. This agreement extends into the dissipation range up to wave numbers at which the accuracy of the measurements is limited because of spatial resolution and other sources of error. Additional tests of local isotropy, from the characteristics of the Reynolds shear stress correlation coefficient cospectrum and from the isotropic relationships between the k x spectra of the streamwise velocity and vorticity components with the k x spectra of the respective cross-stream components, also show evidence of local isotropy at these higher wave numbers.