Fluid memory beyond creeping flow: a history kernel for a sphere at finite Reynolds numbers

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.