Spatio-temporal analysis of wall-bounded turbulence: A multidisciplinary perspective via complex networks

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Complex Networks Unveiling Spatial Patterns in Turbulence

Numerical and experimental turbulence simulations are nowadays reaching the size of the so-called big data, thus requiring refined investigative tools for appropriate statistical analyses and data mining. We present a new approach based on the complex network theory, offering a powerful framework to explore complex systems with a huge number of interacting elements. Although interest on complex networks has been increasing in the last years, few recent studies have been applied to turbulence. We propose an investigation starting from a two-point correlation for the kinetic energy of a forced isotropic field numerically solved. Among all the metrics analyzed, the degree centrality is the most significant, suggesting the formation of spatial patterns which coherently move with similar vorticity over the large eddy turnover time scale. Pattern size can be quantified through a newly-introduced parameter (i.e., average physical distance) and varies from small to intermediate scales. The network analysis allows a systematic identification of different spatial regions, providing new insights into the spatial characterization of turbulent flows. Based on present findings, the application to highly inhomogeneous flows seems promising and deserves additional future investigation.Comment: 12 pages, 7 figures, 3 table

A review on turbulent and vortical flow analyses via complex networks

Turbulent and vortical flows are ubiquitous and their characterization is crucial for the understanding of several natural and industrial processes. Among different techniques to study spatio-temporal flow fields, complex networks represent a recent and promising tool to deal with the large amount of data on turbulent flows and shed light on their physical mechanisms. The aim of this review is to bring together the main findings achieved so far from the application of network-based techniques to study turbulent and vortical flows. A critical discussion on the potentialities and limitations of the network approach is provided, thus giving an ordered portray of the current diversified literature. The present review can boost future network-based research on turbulent and vortical flows, promoting the establishment of complex networks as a widespread tool for turbulence analysis

New insights into spatial characterization of turbulent flows: a complex network-based analysis

Despite much progress has been made, several mechanisms about turbulence dynamics are still unclear. We propose an innovative approach based on complex networks theory, which combines elements from graph theory and statistical physics, providing a powerful framework to investigate complex systems.The network is built on a forced isotropic turbulent field, by evaluating the temporal correlation of the kinetic energy for pairs of nodes within the Taylor microscale, λ. Among all the parameters analyzed, the degree centrality, k, is one of the most meaningful, representing how a node is linked to the others. We observe 3D patterns of high k values, which can be interpreted as regions of spatial coherence. The turbulent network exhibits typical behaviors of real and spatial networks (scale-free property). Similarly to other physical systems where complex networks successfully apply, our approach can give new insights for the spatial characterization of turbulence

Large-to-small scale frequency modulation analysis in wall-bounded turbulence via visibility networks

Scale interaction is studied in wall-bounded turbulence by focusing on the frequency modulation (FM) mechanism of large scales on small scale velocity fluctuations. Differently from amplitude modulation analysis, frequency modulation has been less investigated also due to the difficulty to develop robust tools for broadband signals. To face this issue, the natural visibility graph approach is proposed in this work to map the full velocity signals into complex networks. We show that the network degree centrality is able to capture the signal structure at local scales directly from the full signal, thereby quantifying FM. Velocity signals from numerically-simulated turbulent channel flows and an experimental turbulent boundary layer are investigated at different Reynolds numbers. A correction of Taylor's hypothesis for time-series is proposed to overcome the overprediction of near-wall frequency modulation obtained when local mean velocity is used as the convective velocity. Results provide network-based evidences of the large-to-small FM features for all the three velocity components in the near-wall region, with a reversal mechanism emerging far from the wall. Additionally, scaling arguments in the view of the quasi-steady quasi-homogeneous hypothesis are discussed, and a delay-time between large and small scales very close to the near-wall cycle characteristic time is detected. Results show that the visibility graph is a parameter-free tool that turns out to be effective and robust to detect FM in different configurations of wall-bounded turbulent flows. Based on present findings, the visibility network-based approach can represent a reliable tool to systematically investigate scale interaction mechanisms in wall-bounded turbulence

Visibility network analysis of large-scale intermittency in convective surface layer turbulence

Large-scale intermittency is a widely observed phenomenon in convective surface layer turbulence that induces non-Gaussian temperature statistics, while such signature is not observed for velocity signals. Although approaches based on probability density functions have been used so far, those are not able to explain to what extent the signals' temporal structure impacts the statistical characteristics of the velocity and temperature fluctuations. To tackle this issue, a visibility network analysis is carried out on a field-experimental dataset from a convective atmospheric surface layer flow. Through surrogate data and network-based measures, we demonstrate that the temperature intermittency is related to strong non-linear dependencies in the temperature signals. Conversely, a competition between linear and non-linear effects tends to inhibit the temperature-like intermittency behaviour in streamwise and vertical velocities. Based on present findings, new research avenues are likely to be opened up in studying large-scale intermittency in convective turbulence.Comment: 4 figure

Spatial characterization of turbulent channel flow via complex networks

A network-based analysis of a turbulent channel flow numerically solved at $Re_\tau=180$ is proposed as an innovative perspective for the spatial characterization of the flow field. Two spatial networks corresponding to the streamwise and wall-normal velocity components are built, where nodes represent portions of volume of the physical domain. For each network, links are active if the correlation coefficient of the corresponding velocity component between pairs of nodes is sufficiently high, thus unveiling the strongest kinematic relations. Several network measures are studied in order to explore the interrelations between nodes and their neighbors. Specifically, long-range links are localized between near-wall regions and associated with the temporal persistence of coherent patterns, namely high and low speed streaks. Furthermore, long-range links play a crucial role as intermediary for the kinematic information flow, as emerges from the analysis of indirect connections between nodes. The proposed approach provides a framework to investigate spatial structures of the turbulent dynamics, showing the full potential of complex networks. Although the network analysis is based on the two-point correlation, it is able to advance the level of information, by exploiting the texture created by active links in all directions. Based on the observed findings, the current approach can pave the way for an enhanced spatial interpretation of the turbulence dynamics