Terminal fall velocity: The legacy of Stokes from the perspective of fluvial hydraulics

Article Type

Research Article

Publication Title

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences


This review article, dedicated to the bicentenary celebration of Sir George Gabriel Stokes’ birthday, presents the state-of-the-science of terminal fall velocity, highlighting his rich legacy from the perspective of fluvial hydraulics. It summarizes the fluid drag on a particle and the current status of the drag coefficient from both the theoretical and empirical formulations, highlighting the three major realms—Stokesian, transitional and Newtonian realms. The force system that drives the particle motion falling through a fluid is described. The response of terminal fall velocity to key factors, which include particle shape, hindered settling and turbulence (nonlinear drag, vortex trapping, fast tracking and effects of loitering), is delineated. The article puts into focus the impact of terminal fall velocity on fluvial hydraulics, discussing the salient role that the terminal fall velocity plays in governing the hydrodynamics of the sediment threshold, bedload transport and suspended load transport. Finally, an innovative perspective is presented on the subject’s future research track, emphasizing open questions.



Publication Date



Open Access, Green