Threshold of Motion Conditions Under Stokes Flow Regime and Comparison With Turbulent Flow Data

Abstract

The present study numerically investigates the effects of bed geometrical properties on particle entrainment driven by Stokes flow. We use different substrate arrangements to alter two important factors: The angle of repose, φ, and degree of exposure, e, of the test particle. The effectiveness of shear flow in mobilizing surface particles will change with e and φ, or collectively, η = e/tanφ, yielding a wide range of critical Shields parameter, θ c , values. The use of η is better suited for describing local bed geometry as both e and φ values will change simultaneously during substrate rearranging processes. Furthermore, the range of θ c values obtained in this study stems from the limitation of this parameter to relate the applied force variation to local flow and bed conditions. We therefore propose an effective shear ratio, α, to establish such connections between the global and local flow shear intensities. These results provide a unique perspective to examine typical θ c data obtained from both Stokes and turbulence regimes. For the case of a single-particle entrainment under given grain protrusion, Stokes flow-based θ c values are found to be 2 to 3 times larger than the counterpart turbulence data. For the case of channel bed mobility, however, the Shields curve suggests an order of magnitude difference in θ c between the two regimes. In part, we attribute this significant θ c variation to turbulent flow fluctuations in the first case and varied bed mobility levels in the second, given their distinct theoretical and empirical nature, respectively.

The Physics of Sediment Transport Initiation, Cessation, and Entrainment Across Aeolian and Fluvial Environments

“…For example, the transition point (Θ, Q * ) ≈ (0.05, 0.007) at which the function Q * (Θ) measured in the gravel-bed experiments by Paintal (1971) changed from Q * ∝ Θ 16 to Q * ∝ Θ 2.5 (see section 1) is indistinguishable from the reference threshold for the same conditions within measurement uncertainty. In particular, a close examination of Paintal's and other gravel bed data has revealed that Paintal's power-16 region can actually be subdivided into two regions (Dey & Ali, 2019, Figure 5) (see also Shih and Diplas, 2019, Figure 8b): one region (Θ ≲ 0.04) with a milder power law and one with a stronger power law (0.04 ≲ Θ ≲ 0.05), which includes a jump of Q * by an order of magnitude at Θ ≃ 0.04. Such a jump is consistent with exceeding the rebound threshold Θ Rb t because transported particles suddenly become able to move along the surface for comparably long times before being captured by the bed.…”

“…Thus, the yield stress of the bulk granular material may at least play some role in setting the scatter in . In this context, it is worth noting that, for the entrainment of particles resting on an idealized substrate by a laminar flow, threshold Shields numbers range from zero to very large values depending on the packing arrangement (Agudo et al, ; Deskos and Diplas, ; Shih and Diplas, ; Topic et al, ).…”

Simulation of aerodynamic entrainment with interparticle cohesions based on discrete element method

“…The calculation of F D that act on a partly exposed particle without resolving the flow field has been one of the most challenging issues. In this study (Shih & Diplas, 2019), we first define the exposure e as where A e and A t are the exposed and total particle areas projected on a plane perpendicular to the flow, respectively.…”

“…For intermediate states (0 < e < 1), Shih & Diplas (2019) showed that the fluid drag force increases linearly with exposure. Thus, the fluid drag force can be expressed as …”

“…For a partly exposed particle (0 < e < 1), the point of action of the fluid drag force is set at the middle height of the exposed portion. Here, the lift force is neglected owing to its smaller order of magnitude than the gravitational and drag forces (Shih & Diplas, 2019).…”