Hydrodynamic Resistance on Oscillating Planar Interfacial Bodies
Abstract
We study the unsteady dynamics of floating planar bodies undergoing lateral oscillations along an air--water interface. Scaling arguments indicate that when the viscous penetration depth and oscillation amplitude are both small compared to the body size, the flow beneath the body can be approximated by an oscillatory Stokes boundary layer, yielding a leading-order description of the hydrodynamic resistance. Using magnetic actuation, we drive the interfacial bodies harmonically and measure the amplitude response and phase lag in steady state over a range of frequencies, masses, sizes, and shapes. This frequency-response framework enables direct extraction of effective added mass and damping coefficients, which we find to be consistent with oscillatory boundary-layer theory in the limit of small interfacial deformation. The transient behavior during startup is also shown to be accurately predicted by a history integral that captures the development of the oscillatory boundary layer beneath the body. This work also establishes a simple experimental platform for quantifying unsteady hydrodynamic forces at fluid interfaces.
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BibTeX
@misc{ho2026hydrodynamic,
title = {{Hydrodynamic Resistance on Oscillating Planar Interfacial Bodies}},
author = {Ian Ho and Ajay Harishankar Kumar and Daniel M. Harris},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2606.12570},
eprint = {2606.12570},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.12570},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Hydrodynamic Resistance on Oscillating Planar Interfacial Bodies
AU - Ian Ho
AU - Ajay Harishankar Kumar
AU - Daniel M. Harris
PY - 2026
DA - 2026/09/18
PB - arXiv
DO - 10.48550/arxiv.2606.12570
UR - https://arxiv.org/abs/2606.12570
AB - We study the unsteady dynamics of floating planar bodies undergoing lateral oscillations along an air--water interface. Scaling arguments indicate that when the viscous penetration depth and oscillation amplitude are both small compared to the body size, the flow beneath the body can be approximated by an oscillatory Stokes boundary layer, yielding a leading-order description of the hydrodynamic resistance. Using magnetic actuation, we drive the interfacial bodies harmonically and measure the amplitude response and phase lag in steady state over a range of frequencies, masses, sizes, and shapes. This frequency-response framework enables direct extraction of effective added mass and damping coefficients, which we find to be consistent with oscillatory boundary-layer theory in the limit of small interfacial deformation. The transient behavior during startup is also shown to be accurately predicted by a history integral that captures the development of the oscillatory boundary layer beneath the body. This work also establishes a simple experimental platform for quantifying unsteady hydrodynamic forces at fluid interfaces.
ER -