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Particulate matter in the environment, such as sediment, marine debris and plankton, is transported by surface waves. The transport of these inertial particles is different from that of fluid parcels described by Stokes drift. In this study, we consider the transport of negatively buoyant particles that settle in flow induced by surface waves as described by linear wave theory in arbitrary depth. We consider particles that fall under both a linear drag regime in the low Reynolds number limit and in a nonlinear drag regime in the transitional Reynolds number range. Based on an analysis of typical applications, we find that the nonlinear regime is the most widely applicable. From an expansion in the particle Stokes number, we find kinematic expressions for inertial particle motion in waves, and from a multiscale expansion in the dimensionless wave amplitude, we find expressions for the wave-averaged drift velocities. These drift velocities are analogous to Stokes drift and can be used in large-scale models that do not resolve surface waves. We find that the horizontal drift velocity is reduced relative to the Stokes drift of fluid parcels and that the vertical drift velocity is enhanced relative to the particle terminal settling velocity. We also demonstrate that a cloud of settling particles released simultaneously will disperse in the horizontal direction. Finally, we discuss the accuracy of our expressions by comparing against numerical simulations, which show excellent agreement, and against experimental data, which show the same trends.
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Revisiting Brenner's method for Stokes resistance of a deformed sphere
We revisit Brenner's seminal work on the Stokes resistance of a slightly deformed sphere (Chem. Engng Sci., vol. 19, 1964, p. 519), evaluate its range of validity and extend its applicability to higher deformations for axisymmetric particles, using hydrodynamic radius as the measure of Stokes resistance. Brenner's method solves the flow around a slightly deformed sphere through two mapping steps: the first mapping translates the surface velocity on the deformed sphere to that over a reference sphere of arbitrary radius using an asymptotic expansion of the flow field in terms of deformation amplitude and a Taylor expansion of the velocity field around the surface of the reference sphere. Subsequently, the second mapping extrapolates the velocity field from the surface of the reference sphere to any point in the fluid using Lamb's general solution for Stokes flow. While the original work addresses slightly deformed spheres to a linear order in deformation amplitude, we demonstrate that the first mapping, in combination with axisymmetric spectral modes (J. Fluid Mech., vol. 936, 2022, R1), can accommodate significant deformations to arbitrary orders of perturbation, and thus is not limited to slightly deformed spheres. Also, while first-order analysis is suitable for nearly spherical particles, second-order terms can provide a reasonable range for significantly higher deformations.
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- Award ID(s):
- 2238915
- PAR ID:
- 10574934
- Publisher / Repository:
- Cambridge University Press
- Date Published:
- Journal Name:
- Journal of Fluid Mechanics
- Volume:
- 994
- ISSN:
- 0022-1120
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1017/jfm.2024.610
