All first-order spatial derivatives of the turbulent velocity fluctuations were measured using a pair of X hot-wire probes. Measurements were performed in the self-preserving region of a turbulent plane wake downstream of a cylinder and in an axisymmetric wake behind the sphere. Good spatial resolution of the measurements was ensured by choosing small values for the cylinder/sphere diameter and a low flow speed. Errors due to the finite hot-wire length and the wire and probe separation were analyzed using Wyngaard’s correction method. The derived corrections were verified experimentally. The measuring technique and the experimental results were systematically checked and compared with the results available in the literature. The assumptions of local isotropy and local axisymmetry were examined. Both investigated flows deviate only moderately from local isotropy and local axisymmetry. Support for the measured results is provided by plotting the data on an anisotropy invariant map. The budgets of the turbulent kinetic energy were computed from the measured data. In contrast to the results obtained in the plane wake, where the pressure transport is nearly negligible, in the axisymmetric wake it was found to play an important role and closely follows the estimate made by Lumley,
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