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Parametric study of the dispersion of inertial ellipsoidal particles in a wave-current flow

Laura K. C. Sunberg1, Michelle H. DiBenedetto2, Nicholas T. Ouellette3, and Jeffrey R. Koseff3

  • 1Institute of Arctic and Alpine Research, University of Colorado Boulder, Boulder, Colorado 80303, USA
  • 2Department of Mechanical Engineering, University of Washington, Seattle, Washington 98115, USA
  • 3The Bob and Norma Street Environmental Fluid Mechanics Laboratory, Department of Civil and Environmental Engineering, Stanford University, Stanford, California 94305, USA

Phys. Rev. Fluids 9, 034302 – Published 4 March, 2024

DOI: https://doi.org/10.1103/PhysRevFluids.9.034302

Abstract

The degree to which particles such as larvae, seagrass pollen, and microplastics are dispersed by waves and currents influences many ecologically important aspects of their transport and fate. Particle transport models often assume dispersion is simply a function of the local turbulence, but there are many additional parameters related to both the particle characteristics and the flow dynamics that can impact how particles disperse. Here, we perform a parametric study of solutions to the Maxey-Riley equation and Euler's equation for rigid body motion for negatively buoyant, ellipsoidal particles dispersing in a wave-current flow. We systematically examine the impact of a comprehensive set of parameters on particle dispersion: the ratio between the time scales associated with particle settling and the waves, the Archimedes number, the particle eccentricity, the wave steepness, the Keulegan-Carpenter number, and the Stokes number. Our results show that no parameters can be discounted, but that the settling-wave time scale ratio has the largest influence on particle dispersion.

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References (44)

  1. B. Daly, C. Parada, T. Loher, S. Hinckley, A. J. Hermann, and D. Armstrong, Red king crab larval advection in bristol bay: Implications for recruitment variability, Fish. Oceanogr. 29, 505 (2020).
  2. G. A. Kendrick, M. Waycott, T. J. Carruthers, M. L. Cambridge, R. Hovey, S. L. Krauss, P. S. Lavery, D. H. Les, R. J. Lowe, O. M. I. Vidal et al., The central role of dispersal in the maintenance and persistence of seagrass populations, Bioscience 62, 56 (2012).
  3. E. van Sebille, S. Aliani, K. L. Law, N. Maximenko, J. M. Alsina, A. Bagaev, M. Bergmann, B. Chapron, I. Chubarenko, A. Cózar et al., The physical oceanography of the transport of floating marine debris, Environ. Res. Lett. 15, 023003 (2020).
  4. W. S. Arnold, G. L. Hitchcock, M. E. Frischer, R. Wanninkhof, and Y. Peter Sheng, Dispersal of an introduced larval cohort in a coastal lagoon, Limnol. Oceanogr. 50, 587 (2005).
  5. A. de Vos, L. Aluwihare, S. Youngs, M. H. DiBenedetto, C. P. Ward, A. P. Michel, B. C. Colson, M. G. Mazzotta, A. N. Walsh, R. K. Nelson et al., The M/V X-press Pearl nurdle spill: Contamination of burnt plastic and unburnt nurdles along Sri Lanka's beaches, ACS Environ. Au 2, 128 (2022).
  6. M. Bouvard and S. Petkovic, Vertical dispersion of spherical, heavy particles in turbulent open channel flow, J. Hydraul. Res. 23, 5 (1985).
  7. V. Onink, M. L. Kaandorp, E. van Sebille, and C. Laufkötter, Influence of particle size and fragmentation on large-scale microplastic transport in the Mediterranean Sea, Environ. Sci. Technol. 56, 15528 (2022).
  8. W. W. Willmarth, N. E. Hawk, and R. L. Harvey, Steady and unsteady motions and wakes of freely falling disks, Phys. Fluids 7, 197 (1964).
  9. F. Auguste, J. Magnaudet, and D. Fabre, Falling styles of disks, J. Fluid Mech. 719, 388 (2013).
  10. F. Candelier and B. Mehlig, Settling of an asymmetric dumbbell in a quiescent fluid, J. Fluid Mech. 802, 174 (2016).
  11. J. B. Will, V. Mathai, S. G. Huisman, D. Lohse, C. Sun, and D. Krug, Kinematics and dynamics of freely rising spheroids at high Reynolds numbers, J. Fluid Mech. 912, A16 (2021).
  12. F. Zhao, W. K. George, and B. G. M. Van Wachem, Four-way coupled simulations of small particles in turbulent channel flow: The effects of particle shape and Stokes number, Phys. Fluids 27, 083301 (2015).
  13. G. A. Voth and A. Soldati, Anisotropic particles in turbulence, Annu. Rev. Fluid Mech. 49, 249 (2017).
  14. N. Pujara and E. A. Variano, Rotations of small, inertialess triaxial ellipsoids in isotropic turbulence, J. Fluid Mech. 821, 517 (2017).
  15. T. B. Oehmke, A. D. Bordoloi, E. Variano, and G. Verhille, Spinning and tumbling of long fibers in isotropic turbulence, Phys. Rev. Fluids 6, 044610 (2021).
  16. L. J. Baker and F. Coletti, Experimental investigation of inertial fibres and disks in a turbulent boundary layer, J. Fluid Mech. 943, A27 (2022).
  17. L. Esteban, J. Shrimpton, and B. Ganapathisubramani, Disks settling in turbulence, J. Fluid Mech. 883, A58 (2020).
  18. M. Shin and D. L. Koch, Rotational and translational dispersion of fibres in isotropic turbulent flows, J. Fluid Mech. 540, 143 (2005).
  19. T. X. Thoman, T. Kukulka, and K. Gamble, Dispersion of buoyant and sinking particles in a simulated wind- and wave-driven turbulent coastal ocean, J. Geophys. Res.: Oceans 126, e2020JC016868 (2021).
  20. G. G. Stokes, On the theory of oscillatory waves, Trans. Cambridge Philos. Soc. 8, 441 (1847).
  21. I. Eames, Settling of particles beneath water waves, J. Phys. Oceanogr. 38, 2846 (2008).
  22. A. W. K. Law, Taylor dispersion of contaminants due to surface waves, J. Hydraul. Res. 38, 41 (2000).
  23. J. Pearson, I. Guymer, J. West, and L. Coates, Effect of wave height on cross-shore solute mixing, J. Waterway, Port, Coastal, Ocean Eng. 128, 10 (2002).
  24. M. H. DiBenedetto, N. T. Ouellette, and J. R. Koseff, Transport of anisotropic particles under waves, J. Fluid Mech. 837, 320 (2018).
  25. M. H. DiBenedetto, L. K. Clark, and N. Pujara, Enhanced settling and dispersion of inertial particles in surface waves, J. Fluid Mech. 936, A38 (2022).
  26. L. K. Clark, M. H. DiBenedetto, N. T. Ouellette, and J. R. Koseff, Dispersion of finite-size, non-spherical particles by waves and currents, J. Fluid Mech. 954, A3 (2023).
  27. P. L. Forsberg, D. Sous, A. Stocchino, and R. Chemin, Behaviour of plastic litter in nearshore waters: First insights from wind and wave laboratory experiments, Mar. Pollut. Bull. 153, 111023 (2020).
  28. N. B. Kerpen, T. Schlurmann, A. Schendel, J. Gundlach, D. Marquard, and M. Hüpgen, Wave-induced distribution of microplastic in the surf zone, Front. Mar. Sci. 7, 590565 (2020).
  29. T. Kukulka and K. Brunner, Passive buoyant tracers in the ocean surface boundary layer: 1. Influence of equilibrium wind-waves on vertical distributions, J. Geophys. Res.: Oceans 120, 3837 (2015).
  30. K. Brunner, T. Kukulka, G. Proskurowski, and K. L. Law, Passive buoyant tracers in the ocean surface boundary layer: 2. Observations and simulations of microplastic marine debris, J. Geophys. Res.: Oceans 120, 7559 (2015).
  31. M. Shapiro and M. Goldenberg, Deposition of glass fiber particles from turbulent air flow in a pipe, J. Aerosol Sci. 24, 65 (1993).
  32. M. R. Maxey and J. J. Riley, Equation of motion for a small rigid sphere in a nonuniform flow, Phys. Fluids 26, 883 (1983).
  33. H. Lamb, Hydrodynamics (Dover Publications, New York, 1945), pp. 153–154.
  34. I. Gallily and A.-H. Cohen, On the orderly nature of the motion of nonspherical aerosol particles. II. inertial collision between a spherical large droplet and an axially symmetrical elongated particle, J. Colloid Interface Sci. 68, 338 (1979).
  35. C. Siewert, R. Kunnen, M. Meinke, and W. Schröder, Orientation statistics and settling velocity of ellipsoids in decaying turbulence, Atmos. Res. 142, 45 (2014).
  36. A. Oberbeck, Ueber stationäre flüssigkeitsbewegungen mit berücksichtigung der inneren reibung, J. Reine Angew. Math. (1876).
  37. H. Brenner, The stokes resistance of an arbitrary particle–II: An extension, Chem. Eng. Sci. 19, 599 (1964).
  38. E. Loth, Drag of non-spherical solid particles of regular and irregular shape, Powder Technol. 182, 342 (2008).
  39. G. B. Jeffery, The motion of ellipsoidal particles immersed in a viscous fluid, Proc. R. Soc. London Ser. A 102, 161 (1922).
  40. V. Dabade, N. K. Marath, and G. Subramanian, Effects of inertia and viscoelasticity on sedimenting anisotropic particles, J. Fluid Mech. 778, 133 (2015).
  41. K. Gustavsson, M. Sheikh, A. Naso, A. Pumir, and B. Mehlig, Effect of particle inertia on the alignment of small ice crystals in turbulent clouds, J. Atmos. Sci. 78, 2573 (2021).
  42. F. Jiang, L. Zhao, H. I. Andersson, K. Gustavsson, A. Pumir, and B. Mehlig, Inertial torque on a small spheroid in a stationary uniform flow, Phys. Rev. Fluids 6, 024302 (2021).
  43. A. Hazzab, A. Terfous, and A. Ghenaim, Measurement and modeling of the settling velocity of isometric particles, Powder Technol. 184, 105 (2008).
  44. B. Efron and R. Tibshirani, Bootstrap methods for standard errors, confidence intervals, and other measures of statistical accuracy, Statist. Sci. 1, 54 (1986).

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