A method to correct third and fourth order moments in turbulent flows

It is well known that spatial averaging, resulting from the finite size of a hot-wire probe, significantly affects the accuracy of such measurements in turbulent flows close to the wall. Here, a theoretical model which describes the effect of the spatial filtering of hot-wire probes on the third and fourth order moments of the streamwise velocity is presented. The model, which is 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 micro-scale 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. A procedure, based on the developed model, to correct the measured moments in turbulent flows is finally presented. The method is applied by combining the response of two single hot-wire sensors with different wire lengths. The technique has also been validated against spatially averaged DNS data showing a good capacity to reconstruct the actual profiles over the entire height of the boundary layer except, for the third order moment, in the region where the latter is close to zero.