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

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, phi, and degree of exposure, e, of the test particle. The effectiveness of shear flow in mobilizing surface particles will change with e and phi, or collectively, eta = e/tan phi, yielding a wide range of critical Shields parameter, theta(c), values. The use of eta is better suited for describing local bed geometry as both e and phi values will change simultaneously during substrate rearranging processes. Furthermore, the range of theta(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, alpha, to establish such connections between the global and local flow shear intensities. These results provide a unique perspective to examine typical theta(c) data obtained from both Stokes and turbulence regimes. For the case of a single-particle entrainment under given grain protrusion, Stokes flow-based theta(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 theta(c) between the two regimes. In part, we attribute this significant theta(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.