Correcting hot-wire spatial resolution effects in third- and fourth-order velocity moments in wall-bounded turbulence

Spatial averaging, resulting from the finite size of a hot-wire probe, significantly affects the accuracy of velocity measurements in turbulent flows close to walls. Here, we extend the theoretical model, introduced in Segalini et al. (Meas Sci Technol 22:104508, 2011) quantifying the effect of a linear spatial filter of hot-wire probes on the mean and the variance of the streamwise velocity in turbulent wall-bounded flows, to describe the effect of the spatial filtering on the third- and fourth-order moments of the same velocity component. The model, based on the three-(four) point velocity-correlation function for the third-(fourth-) order moment, shows that the filtering can be related to a characteristic length scale which is an equivalent of the Taylor transverse microscale for the second-order moment. The capacity of the model to accurately describe the attenuation is validated against direct numerical simulation (DNS) data of a zero pressure-gradient turbulent boundary layer. The DNS data allow the filtering effect to be appraised for different wire lengths and for the different moments. The model shows good accuracy except for the third-order moment in the region where a zero-crossing of the third-order function is observed and where the equations become ill-conditioned. An “a posteriori” correction procedure, based on the developed model, to correct the measured third- and fourth-order velocity moments is also presented. This procedure, based on combining the measured data by two single hot-wire sensors with different wire lengths, is a natural extension of the one introduced by Segalini et al. (Exp Fluids 51:693–700, 2011) to evaluate both the turbulence intensity and the transverse Taylor microscale in turbulent flows. The technique is validated against spatially averaged simulation data showing a good capacity to correct the actual profiles over the entire height of the boundary layer except, as expected, for the third-order moment in the region where the latter exhibits a zero-crossing. Moreover, the proposed method has been tested on experimental data from turbulent pipe flow experiments.