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Lagrangian network analysis of turbulent mixing

Published online by Cambridge University Press:  20 February 2019

Giovanni Iacobello*
Department of Mechanical and Aerospace Engineering, Politecnico di Torino, 10129 Turin, Italy
Stefania Scarsoglio
Department of Mechanical and Aerospace Engineering, Politecnico di Torino, 10129 Turin, Italy
J. G. M. Kuerten
Department of Mechanical Engineering, Eindhoven University of Technology, 5600 Eindhoven, The Netherlands
Luca Ridolfi
Department of Environmental, Land and Infrastructure Engineering, Politecnico di Torino, 10129 Turin, Italy
Email address for correspondence:


A temporal complex network-based approach is proposed as a novel formulation to investigate turbulent mixing from a Lagrangian viewpoint. By exploiting a spatial proximity criterion, the dynamics of a set of fluid particles is geometrized into a time-varying weighted network. Specifically, a numerically solved turbulent channel flow is employed as an exemplifying case. We show that the time-varying network is able to clearly describe the particle swarm dynamics, in a parametrically robust and computationally inexpensive way. The network formalism enables us to straightforwardly identify transient and long-term flow regimes, the interplay between turbulent mixing and mean flow advection and the occurrence of proximity events among particles. Thanks to their versatility and ability to highlight significant flow features, complex networks represent a suitable tool for Lagrangian investigations of turbulent mixing. The present application of complex networks offers a powerful resource for Lagrangian analysis of turbulent flows, thus providing a further step in building bridges between turbulence research and network science.

JFM Papers
© 2019 Cambridge University Press 

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Iacobello et al. supplementary movie 1

The movie shows the temporal evolution of (left panel) particle positions in a streamwise-wall normal view (x-y plane), and the time-varying network as (top right panel) weight matrices, $W_{i,j}$, for $K^u$, and (bottom right panel) network topology. Particles in the left panel, as well as network nodes in the bottom right panel, are coloured according to their corresponding initial $y^+$ level. For the left panel, an increasing range of $x^+/L_x^+$ values in the horizontal axis is adopted, where $L_x^+$ is the streamwise DNS domain length.

Download Iacobello et al. supplementary movie 1(Video)
Video 3 MB

Iacobello et al. supplementary movie 2

The movie shows the temporal evolution of (top panel) particle positions in a streamwise-wall normal view (x-y plane), and (bottom panel) the probability distribution of the streamwise particle positions, $x^+$. Particles in the top panel are coloured according to their corresponding initial $y^+$ level. Please note the increasing range of $x^+/L_x^+$ values in the horizontal axis, where $L_x^+$ is the streamwise DNS domain length.

Download Iacobello et al. supplementary movie 2(Video)
Video 4 MB