Hostname: page-component-76c49bb84f-qtd2s Total loading time: 0 Render date: 2025-07-07T05:22:14.189Z Has data issue: false hasContentIssue false
  • English
  • Français

Acceleration statistics of tracer particles in filtered turbulent fields

Published online by Cambridge University Press:  29 May 2018

Cristian C. Lalescu Open the ORCID record for Cristian C. Lalescu [Opens in a new window]  and
Michael Wilczek Open the ORCID record for Michael Wilczek [Opens in a new window]
Cristian C. Lalescu*
Affiliation:
Max Planck Institute for Dynamics and Self-Organization, 37077 Göttingen, Germany
Michael Wilczek
Affiliation:
Max Planck Institute for Dynamics and Self-Organization, 37077 Göttingen, Germany
*
†Email address for correspondence: Cristian.Lalescu@ds.mpg.de
Get access Rights & Permissions [Opens in a new window]

Abstract

We present results from direct numerical simulations of tracer particles advected in filtered velocity fields to quantify the impact of the scales of turbulence on Lagrangian acceleration statistics. Systematically removing spatial scales reduces the frequency of extreme acceleration events, consistent with the notion that they are rooted in the small-scale structure of turbulence. We also find that acceleration variance and flatness as a function of filter scale closely resemble experimental results of neutrally buoyant, finite-sized particles, corroborating the picture that particle size determines the scale on which turbulent fluctuations are sampled.

JFM classification

Turbulent Flows: Intermittency Multiphase and Particle-laden Flows: Multiphase and Particle-laden Flows Turbulent Flows: Turbulent Flows

Information

Type
JFM Rapids
Information
Journal of Fluid Mechanics , Volume 847 , 25 July 2018 , R2
Check for updates
Copyright
© 2018 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.)

Article purchase

Temporarily unavailable

References

Biferale, L., Boffetta, G., Celani, A., Devenish, B. J., Lanotte, A. & Toschi, F. 2004 Multifractal statistics of Lagrangian velocity and acceleration in turbulence. Phys. Rev. Lett. 93 (6), 064502.Google Scholar
Brown, R. D., Warhaft, Z. & Voth, G. A. 2009 Acceleration statistics of neutrally buoyant spherical particles in intense turbulence. Phys. Rev. Lett. 103, 194501.CrossRefGoogle ScholarPubMed
Buzzicotti, M., Bhatnagar, A., Biferale, L., Lanotte, A. S. & Ray, S. S. 2016 Lagrangian statistics for Navier–Stokes turbulence under Fourier-mode reduction: fractal and homogeneous decimations. New J. Phys. 18 (11), 113047.CrossRefGoogle Scholar
Buzzicotti, M., Linkmann, M., Aluie, H., Biferale, L., Brasseur, J. & Meneveau, C. 2018 Effect of filter type on the statistics of energy transfer between resolved and subfilter scales from a priori analysis of direct numerical simulations of isotropic turbulence. J. Turbul. 19 (2), 167–197.CrossRefGoogle Scholar
Calzavarini, E., Volk, R., Bourgoin, M., Lévêque, E., Pinton, J.-F. & Toschi, F. 2009 Acceleration statistics of finite-sized particles in turbulent flow: the role of Faxén forces. J. Fluid Mech. 630, 179–189.Google Scholar
Chevillard, L., Roux, S. G., Levêque, E., Mordant, N., Pinton, J.-F. & Arneodo, A. 2003 Lagrangian velocity statistics in turbulent flows: effects of dissipation. Phys. Rev. Lett. 91, 214502.CrossRefGoogle ScholarPubMed
Cisse, M., Homann, H. & Bec, J. 2013 Slipping motion of large neutrally buoyant particles in turbulence. J. Fluid Mech. 735, R1.CrossRefGoogle Scholar
Cisse, M., Saw, E.-W., Gibert, M., Bodenschatz, E. & Bec, J. 2015 Turbulence attenuation by large neutrally buoyant particles. Phys. Fluids 27 (6), 061702.Google Scholar
Eyink, G. L.2007 Turbulence theory course notes. The Johns Hopkins University, 2007–2008, http://www.ams.jhu.edu/∼eyink/Turbulence/, accessed: 2018-05-11.Google Scholar
Germano, M. 1992 Turbulence: the filtering approach. J. Fluid Mech. 238, 325–336.Google Scholar
Gotoh, T. & Fukayama, D. 2001 Pressure spectrum in homogeneous turbulence. Phys. Rev. Lett. 86, 3775–3778.CrossRefGoogle ScholarPubMed
Homann, H. & Bec, J. 2010 Finite-size effects in the dynamics of neutrally buoyant particles in turbulent flow. J. Fluid Mech. 651, 81–91.Google Scholar
Homann, H., Kamps, O., Friedrich, R. & Grauer, R. 2009 Bridging from Eulerian to Lagrangian statistics in 3D hydro- and magnetohydrodynamic turbulent flows. New J. Phys. 11 (7), 073020.CrossRefGoogle Scholar
Hou, T. Y. & Li, R. 2007 Computing nearly singular solutions using pseudo-spectral methods. J. Comput. Phys. 226, 379–397.CrossRefGoogle Scholar
Hunter, J. D. 2007 Matplotlib: a 2D graphics environment. Comput. Sci. Engng 9 (3), 90–95.CrossRefGoogle Scholar
Ishihara, T., Kaneda, Y., Yokokawa, M., Itakura, K. & Uno, A. 2003 Spectra of energy dissipation, enstrophy and pressure by high-resolution direct numerical simulations of turbulence in a periodic box. J. Phys. Soc. Japan 72 (5), 983–986.CrossRefGoogle Scholar
Ishihara, T., Kaneda, Y., Yokokawa, M., Itakura, K. & Uno, A. 2007 Small-scale statistics in high-resolution direct numerical simulation of turbulence: Reynolds number dependence of one-point velocity gradient statistics. J. Fluid Mech. 592, 335–366.Google Scholar
Kamps, O., Friedrich, R. & Grauer, R. 2009 Exact relation between Eulerian and Lagrangian velocity increment statistics. Phys. Rev. E 79, 066301.Google ScholarPubMed
Klein, S., Gibert, M., Bérut, A. & Bodenschatz, E. 2013 Simultaneous 3D measurement of the translation and rotation of finite-size particles and the flow field in a fully developed turbulent water flow. Meas. Sci. Technol. 24 (2), 024006.Google Scholar
Lalescu, C. C. & Wilczek, M. 2018 How tracer particles sample the complexity of turbulence. New J. Phys. 20 (1), 013001.Google Scholar
La Porta, A., Voth, G. A., Crawford, A. M., Alexander, J. & Bodenschatz, E. 2001 Fluid particle accelerations in fully developed turbulence. Nature 409 (6823), 1017–1019.CrossRefGoogle ScholarPubMed
Lehmann, B., Nobach, H. & Tropea, C. 2002 Measurement of acceleration using the laser Doppler technique. Meas. Sci. Technol. 13 (9), 1367–1381.Google Scholar
Lundgren, T. S. 2003 Linearly forced isotropic turbulence. In Annual Research Briefs (Center for Turbulence Research, Stanford, CA), pp. 461–473.Google Scholar
Maxey, M. 2017 Simulation methods for particulate flows and concentrated suspensions. Annu. Rev. Fluid Mech. 49, 171–193.Google Scholar
Mazzitelli, I. M., Toschi, F. & Lanotte, A. S. 2014 An accurate and efficient Lagrangian sub-grid model. Phys. Fluids 26 (9), 095101.Google Scholar
Mordant, N., Levêque, E. & Pinton, J.-F. 2004 Experimental and numerical study of the Lagrangian dynamics of high Reynolds turbulence. New J. Phys. 6, 116.Google Scholar
Naso, A. & Prosperetti, A. 2010 The interaction between a solid particle and a turbulent flow. New J. Phys. 12 (3), 033040.Google Scholar
Ott, S. & Mann, J. 2000 An experimental investigation of the relative diffusion of particle pairs in three-dimensional turbulent flow. J. Fluid Mech. 422, 207–223.Google Scholar
Pearson, B. R. & Antonia, R. A. 2001 Reynolds-number dependence of turbulent velocity and pressure increments. J. Fluid Mech. 444, 343–382.Google Scholar
Qureshi, N. M., Bourgoin, M., Baudet, C., Cartellier, A. & Gagne, Y. 2007 Turbulent transport of material particles: an experimental study of finite size effects. Phys. Rev. Lett. 99, 184502.Google Scholar
Reynolds, A. M., Mordant, N., Crawford, A. M. & Bodenschatz, E. 2005 On the distribution of Lagrangian accelerations in turbulent flows. New J. Phys. 7 (1), 58.Google Scholar
Sato, Y. & Yamamoto, K. 1987 Lagrangian measurement of fluid–particle motion in an isotropic turbulent field. J. Fluid Mech. 175, 183–199.CrossRefGoogle Scholar
Sawford, B. L. & Yeung, P. K. 2015 Direct numerical simulation studies of Lagrangian intermittency in turbulence. Phys. Fluids 27 (6), 065109.Google Scholar
Sawford, B. L., Yeung, P. K., Borgas, M. S., Vedula, P., La Porta, A., Crawford, A. M. & Bodenschatz, E. 2003 Conditional and unconditional acceleration statistics in turbulence. Phys. Fluids 15 (11), 3478–3489.Google Scholar
Shaw, R. A. 2003 Particle–turbulence interactions in atmospheric clouds. Annu. Rev. Fluid Mech. 35, 183–227.Google Scholar
Snyder, W. H. & Lumley, J. L. 1971 Some measurements of particle velocity autocorrelation functions in a turbulent flow. J. Fluid Mech. 48 (1), 41–71.CrossRefGoogle Scholar
Toschi, F., Biferale, L., Boffetta, G., Celani, A., Devenish, B. J. & Lanotte, A. 2005 Acceleration and vortex filaments in turbulence. J. Turbul. 6, N15.Google Scholar
Toschi, F. & Bodenschatz, E. 2009 Lagrangian properties of particles in turbulence. Annu. Rev. Fluid Mech. 41 (1), 375–404.Google Scholar
Tsuji, Y. & Ishihara, T. 2006 Statistical property of pressure fluctuation in fully developed turbulence. In IUTAM Symposium on Elementary Vortices and Coherent Structures: Significance in Turbulence Dynamics (ed. Kida, S.), Fluid Mechanics and Its Applications, vol. 79, p. 163+. Springer.CrossRefGoogle Scholar
Uhlmann, M. & Chouippe, A. 2017 Clustering and preferential concentration of finite-size particles in forced homogeneous-isotropic turbulence. J. Fluid Mech. 812, 991–1023.Google Scholar
Vedula, P. & Yeung, P. K. 1999 Similarity scaling of acceleration and pressure statistics in numerical simulations of isotropic turbulence. Phys. Fluids 11 (5), 1208–1220.CrossRefGoogle Scholar
Virant, M. & Dracos, T. 1997 3D PTV and its application on Lagrangian motion. Meas. Sci. Technol. 8 (12), 1539.Google Scholar
Volk, R., Calzavarini, E., Lévêque, E. & Pinton, J.-F. 2011 Dynamics of inertial particles in a turbulent von Kármán flow. J. Fluid Mech. 668, 223–235.Google Scholar
Volk, R., Calzavarini, E., Verhille, G., Lohse, D., Mordant, N., Pinton, J.-F. & Toschi, F. 2008a Acceleration of heavy and light particles in turbulence: comparison between experiments and direct numerical simulations. Physica D 237 (14), 2084–2089.Google Scholar
Volk, R., Mordant, N., Verhille, G. & Pinton, J.-F. 2008b Laser Doppler measurement of inertial particle and bubble accelerations in turbulence. Europhys. Lett. 81 (3), 34002.Google Scholar
Voth, G. A., La Porta, A., Crawford, A. M., Alexander, J. & Bodenschatz, E. 2002 Measurement of particle accelerations in fully developed turbulence. J. Fluid Mech. 469, 121–160.CrossRefGoogle Scholar
Voth, G. A., Satyanarayan, K. & Bodenschatz, E. 1998 Lagrangian acceleration measurements at large Reynolds numbers. Phys. Fluids 10 (9), 2268–2280.Google Scholar
Xu, H. & Bodenschatz, E. 2008 Motion of inertial particles with size larger than Kolmogorov scale in turbulent flows. Physica D 237 (14), 2095–2100.Google Scholar
Yeung, P. K. & Pope, S. B. 1989 Lagrangian statistics from direct numerical simulations of isotropic turbulence. J. Fluid Mech. 207, 531–586.Google Scholar
Zhou, Z., Chen, J. & Jin, G. 2017 Prediction of Lagrangian dispersion of fluid particles in isotropic turbulent flows using large-eddy simulation method. Acta Mech. 228, 3203–3222.Google Scholar