Journal of Fluid Mechanics


Dimensionality and morphology of particle and bubble clusters in turbulent flow


a1 Physics of Fluids Group, Department of Science and Technology, J.M. Burgers Center for Fluid Dynamics, and Impact-Institute, University of Twente, PO Box 217, 7500 AE Enschede, The Netherlands

a2 Mathematisches Institut, Ludwig-Maximilians-Universität, Theresienstrasse 39, D-80333 München, Germany

a3 IAC-CNR, Istituto per le Applicazioni del Calcolo, Viale del Policlinico 137, I-00161 Roma, Italy and INFN, via Saragat 1, I-44100 Ferrara, Italy

a4 International Collaboration for Turbulence Research


We conduct numerical experiments to investigate the spatial clustering of particles and bubbles in simulations of homogeneous and isotropic turbulence. On varying the Stokes parameter and the densities, striking differences in the clustering of the particles can be observed. To quantify these visual findings we use the Kaplan–Yorke dimension. This local scaling analysis shows a dimension of approximately 1.4 for the light bubble distribution, whereas the distribution of very heavy particles shows a dimension of approximately 2.6. However, clearly different parameter combinations yield the same dimensions. To overcome this degeneracy and to further develop the understanding of clustering, we perform a morphological (geometrical and topological) analysis of the particle distribution. For such an analysis, Minkowski functionals have been successfully employed in cosmology, in order to quantify the global geometry and topology of the large-scale distribution of galaxies. In the context of dispersed multiphase flow, these Minkowski functionals – being morphological order parameters – allow us to discern the filamentary structure of the light particle distribution from the wall-like distribution of heavy particles around empty interconnected tunnels. Movies are available with the online version of the paper.

(Received October 08 2007)

(Revised April 09 2008)

Key words

  • Turbulent flows;
  • Particle-laden flows