Dominant spanwise Fourier modes, and the existence of very large scale coherence in turbulent boundary layers

Multiple plane stereo PIV results and data from a rake of ten hot-wire probes are used to investigate the largest scale structures in a zero-pressure-gradient turbulent boundary layer. Instantaneous vector fields from stereo PIV in spanwisestreamwise planes reveal long lowand high-speed regions, with a length that often exceeds the viewing window (> 2δ). Also evident is a remarkable degree of spanwise organisation, that manifests as a persistent spanwise stripiness in the u component of the PIV vector field. Almost all trace of such spanwise organisation is lost in the mean statistics, presumably due to the multitude of scales naturally present in wall-bounded turbulence. This can be overcome by ‘de-jittering’ the instantaneous vector fields. By sorting the data according to dominant spanwise fourier modes, and then applying simple statistical tools to the sorted subsets, we are able to extract a clear view of spanwise organisation. Results are confirmed in the various PIV data-sets. Since the PIV fails to adequately capture the full streamwise extent of the low-speed regions, a rake of hot-wire probes is also employed to capture a continuous view of the spanwise coherence. It is found that the low-speed regions are in fact extremely persistent in the streamwise direction, often exceeding 20 δ in length. The fact that these long features meander appreciably in the spanwise direction will limit the overall streamwise length-scale as witnessed by a single probe or single point statistic. For instance, premultiplied one-dimensional spectra of the streamwise velocity (kxΦuu) at this z/δ show a peak contribution for characteristic lengthscales of 5−7δ.