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The inertial response of a particle to turbulent flows is a problem of relevance to a wide range of environmental and engineering problems. The equation most often used to describe the force balance is the Maxey-Riley equation, which includes in addition to buoyancy and steady drag forces, an unsteady Basset drag force related to past particle acceleration. Here we provide a historical review of how the Maxey-Riley equation was developed and how it is only suited for studies where the Reynolds number is less than unity. Revisiting the innovative mathematical methods employed by Basset (1888), we introduce an alternative formulation for the unsteady drag for application to a broader range of particle motions. While the Basset unsteady drag is negligible at higher Reynolds numbers, the revised unsteady drag is not.
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Dynamics of inertial particles on the ocean surface with unrestricted reserve buoyancy
The purpose of this note is to present an enhancement to a Maxey–Riley theory proposed in recent years for the dynamics of inertial particles on the ocean surface [Beron-Vera et al., “Building a Maxey–Riley framework for surface ocean inertial particle dynamics,” Phys. Fluids 31, 096602 (2019)]. This updated model removes constraints on the reserve buoyancy, defined as the fraction of the particle volume above the ocean surface. The refinement results in an equation that correctly describes both the neutrally buoyant and fully buoyant particle scenarios.
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- Award ID(s):
- 2148499
- PAR ID:
- 10587253
- Publisher / Repository:
- American Institute of Physics
- Date Published:
- Journal Name:
- Physics of Fluids
- Volume:
- 36
- Issue:
- 10
- ISSN:
- 1070-6631
- Page Range / eLocation ID:
- 101702
- 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/10.1063/5.0226779
