Insights into the initiation of motion of spheres on a rough bed in a turbulent boundary layer

Abstract

A crucial problem in earth surface science and engineering is that of determining the rate at which sediment is transported in riverine environments due to the flowing water. Essential to this is the threshold at which sediment particles begin to move from the periphery of the channel. At a fundamental level, the flowing river and the sediment bed can be approximated as a turbulent boundary layer over a bed composed of spheres. In order for a sediment particle or sphere to dislodge (herein referred to as ‘migrate’), it must move from its rest position to the next interstice formed by adjacent spheres. The hydrodynamic impulse or work imparted to a sphere during its trajectory have been proposed as criteria for determining the conditions leading to the sphere’s migration from its own pocket.

In this doctoral research project, a number of experiments have been completed to investigate these criteria. The conducted experiments encompassed flow conditions both at, and above, the threshold of motion for a sphere positioned on a rough bed, within turbulent, open channel flow. In contrast to conventional approaches that predominantly rely on stationary spheres or the local flow velocity to estimate hydrodynamic forces, this study is the first to track the motion of the sphere in its pocket and concurrently determine the hydrodynamic forces causing its motion and the local flow velocities.

Observations of the intermittent motion of the sphere due to the turbulent flow revealed substantial variability in the critical hydrodynamic impulse required for its migration by the flow, even under consistent experimental parameters. Notably, the average critical hydrodynamic impulse decreased as the migration rate of the sphere increased. An alternative approach proposing a hydrodynamic impulse threshold that demarcates the recorded hydrodynamic impulses of migration events and events where the sphere simply oscillates (oscillations) in its pocket was explored. However, it was demonstrated that this boundary also varies with the migration rate of the sphere, thus complicating the establishment of a straightforward demarcation between the two types of events (migrations and oscillations), unless empirically determined for a specific set of experimental parameters.

The study uncovered no trend between the hydrodynamic work and impulse imparted to the sphere for individual migration and oscillation events for a given time-averaged, near-bed flow velocity. Furthermore, as expected, with an increase in the time-averaged, near-bed flow velocity, the average hydrodynamic work exerted on the sphere naturally increased too. However, there was a tendency for the average hydrodynamic impulse to diminish despite this increase in hydrodynamic work–though the observed decrease in the impulse was slight despite the large range of near-bed flow velocities tested here. The hydrodynamic impulse, however, did exhibit a notable, positive trend with the duration of migration and oscillation events. It was additionally observed that in all cases where the sphere oscillated in its pocket, it displayed limited maximum displacement. That is, after the sphere’s displacement reached a certain value, it was extremely unlikely to return to the initial rest position. This enabled the definition of an initial hydrodynamic work threshold defining the point of no return of the sphere. While an alternative expression for estimating the hydrodynamic work done to the sphere based on low angular displacements was investigated, its sensitivity to the predicted net force on the sphere hindered its accuracy.

Finally, a comparative analysis of hydrodynamic drag forces estimated using static and dynamic (that follow the sphere during motion) fluid velocity probes revealed minimal discrepancies between the two approaches, while neglecting the sphere’s velocity in drag force determination also had only a small effect on the calculated drag force. However, the differences in the drag force parameterisations yielded a more notable variation in hydrodynamic work estimates due to the sensitivity to the predicted net force on the sphere previously discussed.

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Identifiers

ORCID for Will Crawford-Jones: orcid.org/0000-0002-2836-2922

ORCID for Sergio Maldonado: orcid.org/0000-0001-6072-122X

ORCID for Gustavo De Almeida: orcid.org/0000-0002-3291-3985

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