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

It is well known that spatial averaging, resulting from the nite size of a hot-wire probe, signicantly aects the accuracy of such measurements in turbulent ows close to the wall. Here, a theoretical model which describes the eect of the spatial ltering 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 ltering 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 ltering eect to be appraised for dierent wire lengths and for the dierent moments. A procedure, based on the developed model, to correct the measured moments in turbulent ows is nally presented. The method is applied by combining the response of two single hot-wire sensors with dierent wire lengths. The technique has also been validated against spatially averaged DNS data showing a good capacity to reconstruct the actual proles over the entire height of the boundary layer except, for the third order moment, in the region where the latter is close to zero.