Developing an Impulse-Based Intermittent Particle Entrainment Mechanism in Turbulent Flows Using a Multivariate Random Process

The Shields parameter, dimensionless time-averaged bed shear stress, has been widely used to predict the onset of bed load particle motion and the magnitude of time-averaged bed load sediment flux in open channel flows. Nevertheless, the limitation of a time-averaged approach becomes evident when addressing near-threshold transport problems, potentially leading to the neglect of critical factors. Studies reported that the impulse criterion (force times its duration) is more effective than the Shields criterion under low-shear conditions.

This study focuses on developing an impulse-based entrainment mechanism, incorporating turbulent fluctuation, bed load transport intermittency, and force duration from an instantaneous viewpoint. We characterized the random impulse events time series, covering random intensity, random event duration, and random arrival time, as the energy imparted to particles by turbulent flow. The joint probability density function (PDF) models the event intensity and duration, while the Poisson process governs the random arrivals of impulse events. The essential parameters are extracted from a Direct Numerical Simulation (DNS) data set. A work-based criterion is applied to determine whether a particle will be entrained by the energy it receives. The time-averaged bed load sediment flux is obtained through an existing linkage between impulse events and the sediment flux. The model will be validated using the stress transport relation, where the time-averaged sediment flux is expected to be proportional to the 16th power of time-averaged shear stress at low shear conditions and the 1.5th power of time-averaged shear stress at high shear conditions.

This study offers valuable insights into near-threshold transport problems from various perspectives in a stochastic manner. For instance, statistical properties of impulse event duration, intensity, and mean arrival rate that transit from high to low shear conditions are investigated. Furthermore, from a macroscopic and time-averaged view, the stress-transport relation with the uncertainty of time-averaged sediment flux is obtained, showing an increased variability when near the critical threshold. Moreover, from a microscopic and instantaneous view, this study developed a physical-based approach to address particle resting time from a Lagrangian viewpoint. The impulse event random process can be applied as the entrainment mechanism to a Lagrangian stochastic bed load particle tracking model (PTM) to predict the local inception of particles at any instant. The statistical properties of near-bed particle dynamics, such as the particle hopping distance, resting time, and anomalous advection and diffusion, can be comprehensively investigated once a bed load PTM is equipped with the proposed model that considers a physical-based intermittent entrainment random process.