Skip to main content Accessibility help

Multi-particle dispersion during entrainment in turbulent free-shear flows

  • Tomoaki Watanabe (a1), Carlos B. da Silva (a2) and Koji Nagata (a1)


Multi-particle dispersion is studied using direct numerical simulations of temporally evolving mixing layers and planar jets for tetrahedra consisting of four fluid particles which are seeded in the turbulent regions or in the non-turbulent regions near the turbulent/non-turbulent interface (TNTI). The modified Richardson law for decaying turbulence is observed for particle pairs. The size dependence of the mean and relative motions of the entrained tetrahedra indicates that the characteristic length scale of the entrained lumps of fluid is approximately 10 times the Kolmogorov microscale. When the tetrahedra move within the TNTI layer they are flattened and elongated by vortex stretching at a deformation rate that is characterized by the Kolmogorov time scale. The shape evolutions of the tetrahedra show that in free-shear flows, thin-slab structures of advected scalars are generated within the TNTI layers.


Corresponding author

Email address for correspondence:


Hide All
Bourgoin, M., Ouellette, N. T., Xu, H., Berg, J. & Bodenschatz, E. 2006 The role of pair dispersion in turbulent flow. Science 311 (5762), 835838.
Brethouwer, G., Hunt, J. C. R. & Nieuwstadt, F. T. M. 2003 Micro-structure and Lagrangian statistics of the scalar field with a mean gradient in isotropic turbulence. J. Fluid Mech. 474, 193225.
Corrsin, S. & Kistler, A. L.1955 Free-stream boundaries of turbulent flows. NACA Tech. Rep. No. TN-1244.
Holzner, M., Liberzon, A., Nikitin, N., Lüthi, B., Kinzelbach, W. & Tsinober, A. 2008 A Lagrangian investigation of the small-scale features of turbulent entrainment through particle tracking and direct numerical simulation. J. Fluid Mech. 598, 465475.
Ishihara, T. & Kaneda, Y. 2002 Relative diffusion of a pair of fluid particles in the inertial subrange of turbulence. Phys. Fluids 14 (11), L69L72.
Ishihara, T., Kaneda, Y. & Hunt, J. C. R. 2013 Thin shear layers in high Reynolds number turbulence – DNS results. Flow Turbul. Combust. 91 (4), 895929.
Larcheveque, M. & Lesieur, M. 1981 The application of eddy-damped Markovian closures to the problem of dispersion of particle pairs. J. Méc. 20 (1), 113134.
Mahrt, L. 1999 Stratified atmospheric boundary layers. Boundary-Layer Meteorol. 90 (3), 375396.
Mazzitelli, I. M., Toschi, F. & Lanotte, A. S. 2014 An accurate and efficient Lagrangian sub-grid model. Phys. Fluids 26 (9), 095101.
Ott, S. & Mann, J. 2000 An experimental investigation of the relative diffusion of particle pairs in three-dimensional turbulent flow. J. Fluid Mech. 422, 207223.
Pumir, A., Shraiman, B. I. & Chertkov, M. 2001 The Lagrangian view of energy transfer in turbulent flow. Europhys. Lett. 56 (3), 379385.
Robert, P., Roux, A., Harvey, C. C., Dunlop, M. W., Daly, P. W. & Glassmeier, K. H. 1998 Tetrahedron geometric factors. Anal. Meth. Multi-Spacecraft Data 323348.
Schumacher, J. 2009 Lagrangian studies in convective turbulence. Phys. Rev. E 79 (5), 056301.
da Silva, C. B., Dos Reis, R. J. N. & Pereira, J. C. F. 2011 The intense vorticity structures near the turbulent/non-turbulent interface in a jet. J. Fluid Mech. 685, 165190.
da Silva, C. B., Hunt, J. C. R., Eames, I. & Westerweel, J. 2014 Interfacial layers between regions of different turbulence intensity. Annu. Rev. Fluid Mech. 46, 567590.
da Silva, C. B. & Pereira, J. C. F. 2008 Invariants of the velocity-gradient, rate-of-strain, and rate-of-rotation tensors across the turbulent/nonturbulent interface in jets. Phys. Fluids 20 (5), 055101.
Taveira, R. R., Diogo, J. S., Lopes, D. C. & da Silva, C. B. 2013 Lagrangian statistics across the turbulent–nonturbulent interface in a turbulent plane jet. Phys. Rev. E 88 (4), 043001.
Taveira, R. R. & da Silva, C. B. 2013 Kinetic energy budgets near the turbulent/nonturbulent interface in jets. Phys. Fluids 25, 015114.
Taveira, R. R. & da Silva, C. B. 2014 Characteristics of the viscous superlayer in shear free turbulence and in planar turbulent jets. Phys. Fluids 26 (2), 021702.
Thorpe, S. A. 1978 The near-surface ocean mixing layer in stable heating conditions. J. Geophys. Res. 83 (C6), 28752885.
Watanabe, T. & Nagata, K. 2016 Mixing model with multi-particle interactions for Lagrangian simulations of turbulent mixing. Phys. Fluids 28 (8), 085103.
Watanabe, T., Sakai, Y., Nagata, K., Ito, Y. & Hayase, T. 2015 Turbulent mixing of passive scalar near turbulent and non-turbulent interface in mixing layers. Phys. Fluids 27 (8), 085109.
Watanabe, T., da Silva, C. B., Sakai, Y., Nagata, K. & Hayase, T. 2016 Lagrangian properties of the entrainment across turbulent/non-turbulent interface layers. Phys. Fluids 28 (3), 031701.
Westerweel, J., Fukushima, C., Pedersen, J. M. & Hunt, J. C. R. 2009 Momentum and scalar transport at the turbulent/non-turbulent interface of a jet. J. Fluid Mech. 631, 199230.
Xu, H., Ouellette, N. T. & Bodenschatz, E. 2008 Evolution of geometric structures in intense turbulence. New J. Phys. 10 (1), 013012.
MathJax is a JavaScript display engine for mathematics. For more information see

JFM classification

Multi-particle dispersion during entrainment in turbulent free-shear flows

  • Tomoaki Watanabe (a1), Carlos B. da Silva (a2) and Koji Nagata (a1)


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed