Bursting-process modulation in a turbulent boundary layer via the natural visibility graph method

Abstract

This study proposes a new method for detecting bursting events based on a natural visibility graph and reveals the amplitude modulation of the large-scale to small-scale bursting processes. Through hot-wire measurements of the turbulent boundary layer, velocity signal sequences with different normal heights are obtained. First, a natural visibility graph method is used to map the velocity signal into a visibility network to obtain a time series of the network degree centrality. Next, a statistical analysis of the degree centrality shows that it can reflect hidden structural characteristics. Moreover, the degree centrality signals have a comparable spatial/temporal scale to the Taylor microscale, which indicates that the degree centrality could provide a potential method to characterize the instantaneous wavenumber/frequency information of small-scales. Then, a new method for detecting bursting events is provided based on the degree centrality values. Characterizations of small-scale bursting events are investigated, providing results for the amplitude modulation between large-scale and small-scale bursting processes. These results show that, in the near-wall region, an increase in amplitudes of a small-scale bursting process is induced for intervals of positive large-scale fluctuations and vice versa for negative large-scale fluctuations. The outer zone shows opposite. The phenomenon of temporal shifting of the amplitude modulation is then investigated and shows that the high-speed large-scales lag behind the small-scale bursting process in the near-wall region, while the outer region shows the opposite. The distance of the small-scale bursting processes leading to the large-scales in the near-wall space is log-linear with the wall-normal height.