Fluid memory beyond creeping flow: a history kernel for a sphere at finite Reynolds numbers
Abstract
Predicting the history force on a sphere beyond the creeping-flow limit remains challenging. Existing formulations have been derived or calibrated for selected flow histories, with limited evidence of their predictive accuracy under more general conditions. We develop a systematic approach to extract the history kernel of a fixed sphere in spatially uniform, unsteady flow from axisymmetric Navier-Stokes simulations of finite-duration acceleration and deceleration ramps at initial Reynolds numbers from 0.2 to 200. The resulting kernel surface recovers the Basset limit at short lags and in the creeping-flow limit and is continued beyond the resolved lags using far-wake asymptotics. At higher Reynolds numbers, the kernel develops non-monotonic behaviour at intermediate lags, associated with delayed adjustment of the boundary layer and wake. For the cases tested, the present kernel substantially improves history-force predictions for finite ramps, oscillatory forcing and non-periodic composite velocity histories relative to the literature formulations considered, without case-specific adjustment. These findings indicate that lag and Reynolds number capture the dominant memory response.
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BibTeX
@misc{lasica2026fluid,
title = {{Fluid memory beyond creeping flow: a history kernel for a sphere at finite Reynolds numbers}},
author = {M. D. Łasica and J. G. M. Kuerten and S. K. F. Stoter},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.04606},
eprint = {2611.04606},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.04606},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Fluid memory beyond creeping flow: a history kernel for a sphere at finite Reynolds numbers
AU - M. D. Łasica
AU - J. G. M. Kuerten
AU - S. K. F. Stoter
PY - 2026
DA - 2026/11/03
PB - arXiv
DO - 10.48550/arxiv.2611.04606
UR - https://arxiv.org/abs/2611.04606
AB - Predicting the history force on a sphere beyond the creeping-flow limit remains challenging. Existing formulations have been derived or calibrated for selected flow histories, with limited evidence of their predictive accuracy under more general conditions. We develop a systematic approach to extract the history kernel of a fixed sphere in spatially uniform, unsteady flow from axisymmetric Navier-Stokes simulations of finite-duration acceleration and deceleration ramps at initial Reynolds numbers from 0.2 to 200. The resulting kernel surface recovers the Basset limit at short lags and in the creeping-flow limit and is continued beyond the resolved lags using far-wake asymptotics. At higher Reynolds numbers, the kernel develops non-monotonic behaviour at intermediate lags, associated with delayed adjustment of the boundary layer and wake. For the cases tested, the present kernel substantially improves history-force predictions for finite ramps, oscillatory forcing and non-periodic composite velocity histories relative to the literature formulations considered, without case-specific adjustment. These findings indicate that lag and Reynolds number capture the dominant memory response.
ER -