Hostname: page-component-5cf477f64f-bmd9x Total loading time: 0 Render date: 2025-04-07T20:48:44.206Z Has data issue: false hasContentIssue false
  • English
  • Français

Lagrangian network analysis of turbulent mixing

Published online by Cambridge University Press:  20 February 2019

Giovanni Iacobello Open the ORCID record for Giovanni Iacobello [Opens in a new window] ,
Stefania Scarsoglio Open the ORCID record for Stefania Scarsoglio [Opens in a new window] ,
J. G. M. Kuerten Open the ORCID record for J. G. M. Kuerten [Opens in a new window]  and
Luca Ridolfi Open the ORCID record for Luca Ridolfi [Opens in a new window]
Giovanni Iacobello*
Affiliation:
Department of Mechanical and Aerospace Engineering, Politecnico di Torino, 10129 Turin, Italy
Stefania Scarsoglio
Affiliation:
Department of Mechanical and Aerospace Engineering, Politecnico di Torino, 10129 Turin, Italy
J. G. M. Kuerten
Affiliation:
Department of Mechanical Engineering, Eindhoven University of Technology, 5600 Eindhoven, The Netherlands
Luca Ridolfi
Affiliation:
Department of Environmental, Land and Infrastructure Engineering, Politecnico di Torino, 10129 Turin, Italy
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

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 classification

Mathematical Foundations: Mathematical Foundations Turbulent Flows: Turbulent Flows Mixing: Turbulent mixing
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 865 , 25 April 2019 , pp. 546 - 562
Copyright
© 2019 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Balasuriya, S., Ouellette, N. T. & Rypina, I. I. 2018 Generalized Lagrangian coherent structures. Physica D 372, 31–51.10.1016/j.physd.2018.01.011Google Scholar
Barrat, A., Barthélemy, M. & Vespignani, A. 2004 Weighted evolving networks: coupling topology and weight dynamics. Phys. Rev. Lett. 92 (22), 228701.10.1103/PhysRevLett.92.228701Google Scholar
Bianchi, S., Biferale, L., Celani, A. & Cencini, M. 2016 On the evolution of particle-puffs in turbulence. Eur. J. Mech. (B/Fluids) 55, 324–329.10.1016/j.euromechflu.2015.06.009Google Scholar
Boccaletti, S., Latora, V., Moreno, Y., Chavez, M. & Hwang, D. U. 2006 Complex networks: structure and dynamics. Phys. Rep. 424 (4–5), 175–308.10.1016/j.physrep.2005.10.009Google Scholar
Charakopoulos, A. K., Karakasidis, T. E., Papanicolaou, P. N. & Liakopoulos, A. 2014 The application of complex network time series analysis in turbulent heated jets. Chaos 24 (2), 024408.10.1063/1.4875040Google Scholar
Dimotakis, P. E. 2005 Turbulent mixing. Annu. Rev. Fluid Mech. 37, 329–356.10.1146/annurev.fluid.36.050802.122015Google Scholar
Donner, R. V., Hernández-García, E. & Ser-Giacomi, E. 2017 Introduction to focus issue: complex network perspectives on flow systems. Chaos 27 (3), 035601.10.1063/1.4979129Google Scholar
Elder, J. W. 1959 The dispersion of marked fluid in turbulent shear flow. J. Fluid Mech. 5 (4), 544–560.10.1017/S0022112059000374Google Scholar
Falkovich, G., Gawdzki, K. & Vergassola, M. 2001 Particles and fields in fluid turbulence. Rev. Mod. Phys. 73 (4), 913–975.10.1103/RevModPhys.73.913Google Scholar
Fernando, H. J. S. 2012 Handbook of Environmental Fluid Dynamics, Volume Two: Systems, Pollution, Modeling, and Measurements. CRC Press.Google Scholar
Fischer, H. B. 1973 Longitudinal dispersion and turbulent mixing in open-channel flow. Annu. Rev. Fluid Mech. 5 (1), 59–78.10.1146/annurev.fl.05.010173.000423Google Scholar
Geurts, B. J. & Kuerten, J. G. M. 2012 Ideal stochastic forcing for the motion of particles in large-eddy simulation extracted from direct numerical simulation of turbulent channel flow. Phys. Fluids 24 (8), 081702.10.1063/1.4745857Google Scholar
Hadjighasem, A., Farazmand, M., Blazevski, D., Froyland, G. & Haller, G. 2017 A critical comparison of lagrangian methods for coherent structure detection. Chaos 27 (5), 053104.10.1063/1.4982720Google Scholar
Hadjighasem, A., Karrasch, D., Teramoto, H. & Haller, G. 2016 Spectral-clustering approach to lagrangian vortex detection. Phys. Rev. E 93 (6), 063107.Google Scholar
Holme, P. & Saramäki, J. 2012 Temporal networks. Phys. Rep. 519 (3), 97–125.10.1016/j.physrep.2012.03.001Google Scholar
Iacobello, G., Scarsoglio, S., Kuerten, J. G. M. & Ridolfi, L. 2018 Spatial characterization of turbulent channel flow via complex networks. Phys. Rev. E 98 (1), 013107.Google Scholar
Kim, D., Hussain, F. & Gharib, M. 2013 Vortex dynamics of clapping plates. J. Fluid Mech. 714, 5–23.10.1017/jfm.2012.445Google Scholar
Kuerten, J. G. M. & Brouwers, J. J. H. 2013 Lagrangian statistics of turbulent channel flow at Re 𝜏 = 950 calculated with direct numerical simulation and Langevin models. Phys. Fluids 25 (10), 105108.10.1063/1.4824795Google Scholar
Martin, S., Brown, W. M., Klavans, R. & Boyack, K. W. 2011 OpenOrd: an open-source toolbox for large graph layout. In Visualization and Data Analysis, vol. 7868, p. 786806. International Society for Optics and Photonics.Google Scholar
Murugesan, M. & Sujith, R. I. 2015 Combustion noise is scale-free: transition from scale-free to order at the onset of thermoacoustic instability. J. Fluid Mech. 772, 225–245.10.1017/jfm.2015.215Google Scholar
Newman, M. 2018 Networks, 2nd edn. Oxford University Press.10.1093/oso/9780198805090.001.0001Google Scholar
Nguyen, Q. & Papavassiliou, D. V. 2018 Scalar mixing in anisotropic turbulent flow. AIChE J. 64 (7), 2803–2815.10.1002/aic.16104Google Scholar
Opsahl, T., Agneessens, F. & Skvoretz, J. 2010 Node centrality in weighted networks: generalizing degree and shortest paths. Soc. Networks 32 (3), 245–251.10.1016/j.socnet.2010.03.006Google Scholar
Padberg-Gehle, K. & Schneide, C. 2017 Network-based study of Lagrangian transport and mixing. Nonlinear Process. Geophys. 24 (4), 661.10.5194/npg-24-661-2017Google Scholar
Pasquill, F. & Smith, F. B. 1983 Atmospheric Diffusion: Study of the Dispersion of Windborne Material from Industrial and Other Sources. Wiley.Google Scholar
Pitton, E., Marchioli, C., Lavezzo, V., Soldati, A. & Toschi, F. 2012 Anisotropy in pair dispersion of inertial particles in turbulent channel flow. Phys. Fluids 24 (7), 073305.10.1063/1.4737655Google Scholar
Polanco, J. I., Vinkovic, I., Stelzenmuller, N., Mordant, N. & Bourgoin, M. 2018 Relative dispersion of particle pairs in turbulent channel flow. Intl J. Heat Fluid Flow 71, 231–245.10.1016/j.ijheatfluidflow.2018.04.007Google Scholar
Rypina, I. I. & Pratt, L. J. 2017 Trajectory encounter volume as a diagnostic of mixing potential in fluid flows. Nonlinear Process. Geophys. 24 (2), 189–202.10.5194/npg-24-189-2017Google Scholar
Salazar, J. P. & Collins, L. R. 2009 Two-particle dispersion in isotropic turbulent flows. Annu. Rev. Fluid Mech. 41, 405–432.10.1146/annurev.fluid.40.111406.102224Google Scholar
Sawford, B. 2001 Turbulent relative dispersion. Annu. Rev. Fluid Mech. 33 (1), 289–317.10.1146/annurev.fluid.33.1.289Google Scholar
Scarsoglio, S., Iacobello, G. & Ridolfi, L. 2016 Complex networks unveiling spatial patterns in turbulence. Intl J. Bifurcation Chaos 26 (13), 1650223.10.1142/S0218127416502230Google Scholar
Schlueter-Kuck, K. L. & Dabiri, J. O. 2017 Coherent structure colouring: identification of coherent structures from sparse data using graph theory. J. Fluid Mech. 811, 468–486.10.1017/jfm.2016.755Google Scholar
Schneide, C., Pandey, A., Padberg-Gehle, K. & Schumacher, J. 2018 Probing turbulent superstructures in Rayleigh–Bénard convection by Lagrangian trajectory clusters. Phys. Rev. Fluids 3 (11), 113501.10.1103/PhysRevFluids.3.113501Google Scholar
Ser-Giacomi, E., Rossi, V., López, C. & Hernandez-Garcia, E. 2015 Flow networks: a characterization of geophysical fluid transport. Chaos 25 (3), 036404.10.1063/1.4908231Google Scholar
Seuront, L. & Schmitt, F. G. 2004 Eulerian and Lagrangian properties of biophysical intermittency in the ocean. Geophys. Res. Lett. 31 (3).10.1029/2003GL018185Google Scholar
Sreenivasan, K. R. & Schumacher, J. 2010 Lagrangian views on turbulent mixing of passive scalars. Phil. Trans. R. Soc. Lond A 368 (1916), 1561–1577.10.1098/rsta.2009.0140Google Scholar
Taira, K., Nair, A. G. & Brunton, S. L. 2016 Network structure of two-dimensional decaying isotropic turbulence. J. Fluid Mech. 795.10.1017/jfm.2016.235Google Scholar
Toschi, F. & Bodenschatz, E. 2009 Lagrangian properties of particles in turbulence. Annu. Rev. Fluid Mech. 41, 375–404.10.1146/annurev.fluid.010908.165210Google Scholar
Warhaft, Z. 2000 Passive scalars in turbulent flows. Annu. Rev. Fluid Mech. 32 (1), 203–240.10.1146/annurev.fluid.32.1.203Google Scholar
Warnatz, J., Maas, U. & Dibble, R. W. 1996 Combustion: Physical and Chemical Fundamentals, Modeling and Simulation, Experiments, Pollutant Formation. Springer.10.1007/978-3-642-97668-1Google Scholar

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 2.5 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