Visibility graph analysis of wall turbulence time-series

Abstract

The spatio-temporal features of the velocity field of a fully-developed turbulent channel flow are investigated through the natural visibility graph (NVG) method, which is able to fully map the intrinsic structure of the time-series into complex networks. Time-series of the three velocity components, (u,v,w), are analyzed at fixed grid-points of the whole three-dimensional domain. Each time-series was mapped into a network by means of the NVG algorithm, so that each network corresponds to a grid-point of the simulation. The degree centrality, the transitivity and the here proposed mean link-length were evaluated as indicators of the global visibility, inter-visibility, and mean temporal distance among nodes, respectively. The metrics were averaged along the directions of homogeneity (x, z) of the flow, so they only depend on the wall-normal coordinate, y^+. The visibility-based networks, inheriting the flow field features, unveil key temporal properties of the turbulent time-series and their changes moving along y^+. Although intrinsically simple to be implemented, the visibility graph-based approach offers a promising and effective support to the classical methods for accurate time-series analyses of inhomogeneous turbulent flows

Experimental investigation of vertical turbulent transport of a passive scalar in a boundary layer: Statistics and visibility graph analysis

“…Differently from classical statistics tools, different temporal arrangements of the same time-series generate different visibility networks (e.g., a shuffled series maintains the same statistics of the originating series, but exhibits a different temporal structure and visibility-network). Since the network metrics evaluated from the visibility graph approach are able to characterize the temporal structure of the time-series, they carry high-order and nonlinear information of the signal [21]. As a result, the visibility graph approach is proposed to shed light on the temporal structure -in terms of extreme events and their relative intensity -of the turbulent transport time-series.…”

“…In order to characterize the structure of complex networks, several metrics have been proposed so far [15]. In a previous work on the investigation of velocity time-series in a turbulent channel flow, three metrics were exploited [21]: the transitivity, the mean linklength and the degree centrality. Among these three metrics, the transitivity and the mean link-length are able to highlight the presence of small variations in the series and the occurrence of peaks, respectively.…”

“…Among these three metrics, the transitivity and the mean link-length are able to highlight the presence of small variations in the series and the occurrence of peaks, respectively. On the other hand, the degree centrality cannot be uniquely related to a specific temporal feature, since the degree accounts for both the recurrence of peaks and the presence of small variations in the series [21]. Therefore, to extract information on the characterization of extreme events of the plume dynamics we here exploited two specific network metrics: the mean link-length, and the assortativity coefficient.…”

“…Therefore, to extract information on the characterization of extreme events of the plume dynamics we here exploited two specific network metrics: the mean link-length, and the assortativity coefficient. The mean link-length, d i , was proposed by Iacobello et al [21] as a local measure to characterize the temporal occurrence of peaks in a series, defined as…”

“…Although different research fields have taken advantage of network science during last decades (e.g., social, biological, or technological networks [15]), only recently complex networks have emerged as an effective framework also to study fluid flows. The main applications of network science to fluid flows involve the study of two-phase flows [16,17], turbulent jets [18,19], isotropic and wall-bounded turbulence [20][21][22], reacting flows [23,24], Lagrangian mixing [25,26] and geophysical flows [27,28]. Among several techniques that have been developed so far to study time-series by means of complex networks [29], the visibility graph approach [30] was here adopted since it is a simple but powerful tool to extract non-trivial insights into the non-linear process from which the time-series are obtained [29].…”