Hostname: page-component-848d4c4894-x5gtn Total loading time: 0 Render date: 2024-05-24T05:43:03.783Z Has data issue: false hasContentIssue false

Preferential orientation of spheroidal particles in wavy flow

Published online by Cambridge University Press:  12 October 2018

Michelle H. DiBenedetto
Affiliation:
The Bob and Norma Street Environmental Fluid Mechanics Laboratory, Department of Civil and Environmental Engineering, Stanford University, Stanford, CA 94305, USA
Nicholas T. Ouellette*
Affiliation:
The Bob and Norma Street Environmental Fluid Mechanics Laboratory, Department of Civil and Environmental Engineering, Stanford University, Stanford, CA 94305, USA
*
Email address for correspondence: nto@stanford.edu

Abstract

We report a theoretical study of the angular dynamics of small, non-inertial spheroidal particles in a linear wave field. We recover the observation recently reported by DiBenedetto et al. (J. Fluid Mech., vol. 837, 2018, pp. 320–340) that the orientation of these spheroids tends to a stable limit cycle consisting of a preferred value with a superimposed oscillation. We show that this behaviour is a consequence of finite wave amplitude and is the angular analogue of Stokes drift. We derive expressions for both the preferred orientation of the particles, which depends only on particle shape, and the amplitude of the oscillation about this preferred value, which additionally depends on the wave parameters and the depth of the particle in the water column.

Type
JFM Papers
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.)

References

Andersson, H. I. & Soldati, A. 2013 Anisotropic particles in turbulence: status and outlook. Acta Mech. 224, 22192223.Google Scholar
Balachandar, S. & Eaton, J. K. 2010 Turbulent dispersed multiphase flow. Annu. Rev. Fluid Mech. 42, 111133.Google Scholar
van den Bremer, T. S. & Breivik, Ø. 2017 Stokes drift. Phil. Trans. R. Soc. Lond. A 376 (2111), 20170104.Google Scholar
Brown, R. D., Warhaft, Z. & Voth, G. A. 2009 Acceleration statistics of neturally buoyant spherical particles in intense turbulence. Phys. Rev. Lett. 103, 194501.Google Scholar
Byron, M., Einarsson, J., Gustavsson, K., Voth, G., Mehlig, B. & Variano, E. 2015 Shape-dependence of particle rotation in isotropic turbulence. Phys. Fluids 27, 035101.Google Scholar
de Carolis, G., Olla, P. & Pignagnoli, L. 2005 Effective viscosity of grease ice in linearized gravity waves. J. Fluid Mech. 535, 369381.Google Scholar
Challabotla, N. R., Zhao, L. & Andersson, H. I. 2015a Orientation and rotation of inertial disk particles in wall turbulence. J. Fluid Mech. 766, R2.Google Scholar
Challabotla, N. R., Zhao, L. & Andersson, H. I. 2015b Shape effects on dynamics of inertia-free spheroids in wall turbulence. Phys. Fluids 27, 061703.Google Scholar
Chubarenko, I., Bagaev, A., Zobkov, M. & Esiukova, E. 2016 On some physical and dynamical properties of microplastic particles in marine environment. Mar. Pollut. Bull. 108, 105112.Google Scholar
Chubarenko, I. & Stepanova, N. 2017 Microplastics in sea coastal zone: lessons learned from the Baltic amber. Environ. Pollut. 224, 243254.Google Scholar
DiBenedetto, M. H., Ouellette, N. T. & Koseff, J. R. 2018 Transport of anisotropic particles under waves. J. Fluid Mech. 837, 320340.Google Scholar
Gay, N. C. 1968 The motion of rigid particles embedded in a viscous fluid during pure shear deformation of the fluid. Tectonophysics 5, 8188.Google Scholar
Guha, A. 2008 Transport and deposition of particles in turbulent and laminar flow. Annu. Rev. Fluid Mech. 40, 311341.Google Scholar
Hinata, H., Mori, K., Ohno, K., Miyao, Y. & Kataoka, T. 2017 An estimation of the average residence times and onshore–offshore diffusivities of beached microplastics based on the population decay of tagged meso- and macrolitter. Mar. Pollut. Bull. 122, 1726.Google Scholar
Homann, H. & Bec, J. 2010 Finite-size effects in the dynamics of neutrally buoyant particles in turbulent flow. J. Fluid Mech. 651, 8191.Google Scholar
Isobe, A., Kubo, K., Tamura, Y., Kako, S., Nakashima, E. & Fujii, N. 2014 Selective transport of microplastics and mesoplastics by drifting in coastal waters. Mar. Pollut. Bull. 89, 324330.Google Scholar
Jeffery, G. B. 1922 The motion of ellipsoidal particles imnmersed in a viscous fluid. Proc. R. Soc. Lond. A 102, 161179.Google Scholar
Kukulka, T., Proskurowski, G., Morét-Ferguson, S., Meyer, D. W. & Law, K. L. 2012 The effect of wind mixing on the vertical distribution of buoyant plastic debris. Geophys. Res. Lett. 39, L07601.Google Scholar
Kundu, P. K., Cohen, I. M. & Dowling, D. R. 2016 Fluid Mechanics. Academic Press.Google Scholar
Lundell, F., Söderberg, L. D. & Alfredsson, P. H. 2011 Fluid mechanics of papermaking. Annu. Rev. Fluid Mech. 43, 195217.Google Scholar
Maximenko, N., Hafner, J. & Niiler, P. 2012 Pathways of marine debris derived from trajectories of Lagrangian drifters. Mar. Pollut. Bull. 65, 5162.Google Scholar
Mortensen, P. H., Andersson, H. I., Gillissen, J. J. J. & Boersma, B. J. 2008a Dynamics of prolate ellipsoidal particles in a turbulent channel flow. Phys. Fluids 20, 093302.Google Scholar
Mortensen, P. H., Andersson, H. I., Gillissen, J. J. J. & Boersma, B. J. 2008b On the orientation of ellipsoidal particles in a turbulent shear flow. Intl J. Multiphase Flow 64, 678683.Google Scholar
Ni, R., Kramel, S., Ouellette, N. T. & Voth, G. A. 2015 Measurements of the coupling between the tumbling of rods and the velocity gradient tensor in turbulence. J. Fluid Mech. 766, 202225.Google Scholar
Ni, R., Ouellette, N. T. & Voth, G. A. 2014 Alignment of vorticity and rods with Lagrangian fluid stretching in turbulence. J. Fluid Mech. 743, R3.Google Scholar
Olla, P. 2006 Orientation dynamics of weakly Brownian particles in periodic viscous flows. Phys. Rev. E 73, 041406.Google Scholar
Ouellette, N. T., O’Malley, P. J. J. & Gollub, J. P. 2008 Transport of finite-sized particles in chaotic flow. Phys. Rev. Lett. 101, 174504.Google Scholar
Parsa, S., Calzavarini, E., Toschi, F. & Voth, G. A. 2012 Rotation rate of rods in turbulent fluid flow. Phys. Rev. Lett. 109, 134501.Google Scholar
Pinsky, M. B. & Khain, A. P. 1998 Some effects of cloud turbulence on water–ice and ice–ice collisions. Atmos. Res. 47–48, 6986.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
Reed, L. J. & Tryggvason, E. 1974 Preferred orientations of rigid particles in a viscous matrix deformed by pure shear and simple shear. Tectonophysics 24, 8598.Google Scholar
Ryan, P. G., Moore, C. J., van Franeker, J. A. & Moloney, C. L. 2009 Monitoring the abundance of plastic debris in the marine environment. Phil. Trans. R. Soc. Lond. B 364, 19992012.Google Scholar
Sherman, P. & Van Sebille, E. 2016 Modeling marine surface microplastic transport to assess optimal removal locations. Environ. Res. Lett. 11, 014006.Google Scholar
Shin, M. & Koch, D. L. 2005 Rotational and translational dispersion of fibres in isotropic turbulent flows. J. Fluid Mech. 540, 143173.Google Scholar
Stickel, J. J. & Powell, R. L. 2005 Fluid mechanics and rheology of dense suspensions. Annu. Rev. Fluid Mech. 37, 129149.Google Scholar
Toschi, F. & Bodenschatz, E. 2009 Lagrangian properties of particles in turbulence. Annu. Rev. Fluid Mech. 41, 375404.Google Scholar
Voth, G. A. & Soldati, A. 2017 Anisotropic particles in turbulence. Annu. Rev. Fluid Mech. 49, 249276.Google Scholar