The Cessation Threshold of Nonsuspended Sediment Transport Across Aeolian and Fluvial Environments

Abstract

Using particle‐scale simulations of nonsuspended sediment transport for a large range of Newtonian fluids driving transport, including air and water, we determine the bulk transport cessation threshold normalΘtr by extrapolating the transport load as a function of the dimensionless fluid shear stress (Shields number) Θ to the vanishing transport limit. In this limit, the simulated steady states of continuous transport can be described by simple analytical model equations relating the average transport layer properties to the law of the wall flow velocity profile. We use this model to calculate normalΘtr for arbitrary environments and derive a general Shields‐like threshold diagram in which a Stokes‐like number replaces the particle Reynolds number. Despite the simplicity of our hydrodynamic description, the predicted cessation threshold, both from the simulations and analytical model, quantitatively agrees with measurements for transport in air and viscous and turbulent liquids despite not being fitted to these measurements. We interpret the analytical model as a description of a continuous rebound motion of transported particles and thus normalΘtr as the minimal fluid shear stress needed to compensate the average energy loss of transported particles during an average rebound at the bed surface. This interpretation, supported by simulations near normalΘtr, implies that entrainment mechanisms are needed to sustain transport above normalΘtr. While entrainment by turbulent events sustains intermittent transport, entrainment by particle‐bed impacts sustains continuous transport. Combining our interpretations with the critical energy criterion for incipient motion by Valyrakis and coworkers, we put forward a new conceptual picture of sediment transport intermittency.

Large Effects of Particle Size Heterogeneity on Dynamic Saltation Threshold

“…Hence, if splash‐sustained transport required that all size classes are equally susceptible to splash entrainment (as it likely does Martin & Kok, ), this assumption would also explain why the relationship between u * and U ∞ tends to be described by equation at shear velocities u * that are not too far above , as splash‐sustained transport is the origin of the strong particle‐flow feedback causing the roughness increase described by equation (section ). However, note that the shift from equation to equation does not always happen immediately (e.g., there is an obvious transitional region for Sample 5 in Figure ), which is also consistent with the rebound hypothesis (in the sustained‐rebound picture, the splash entrainment threshold is always larger than the rebound threshold; Pähtz & Durán, ).…”

“…Because such particles have a harder job to maintain their bouncing motion than the median particle, since they experience less fluid drag acceleration during their hops, this assumption automatically explains why is larger for heterogeneous sand beds than for homogeneous ones. Furthermore, we would like to emphasize that the ability of a certain particle class to rebound is probably strongly tied to its ability to eject particles of the same size class via splash (Pähtz & Durán, , section 4.2.1). Hence, if splash‐sustained transport required that all size classes are equally susceptible to splash entrainment (as it likely does Martin & Kok, ), this assumption would also explain why the relationship between u * and U ∞ tends to be described by equation at shear velocities u * that are not too far above , as splash‐sustained transport is the origin of the strong particle‐flow feedback causing the roughness increase described by equation (section ).…”

“…Such a linear transport law is currently favored among most aeolian transport physicists (Creyssels et al, ; Durán et al, ; Ho et al, ; Kok et al, ; Martin & Kok, , ). However, discrete element‐based simulations of saltation transport suggest a nonlinear transport law because of midair collisions (Carneiro et al, ), which can be parametrized via (see Figure S1 in the supporting information, which shows data from numerical discrete element method‐based simulations of sediment transport that have been experimentally validated in a number of recent studies; Durán et al, , , ; Pähtz & Durán, , , ) where κ =0.4 is the von Kármán constant, μ b =0.63 the bed friction coefficient (i.e., the ratio between granular shear stress and normal‐bed pressure at the sand bed surface), and M c =0.13 the critical value of the nondimensionalized transport load M (Θ) above which midair collisions become significant in dissipating energy. In fact, equation is linear in Θ only for M ≤ M c , and the linearity of M with the Shields number Θ (shown and discussed by Pähtz & Durán, ) is the reason why we have used Θ to parametrize aeolian transport in the first place.…”

“…That is, if we defined u t indirectly through a saltation transport law (which is the assumed definition whenever one uses a saltation transport law to predict Q ), u t should convey information about the saturated state even though transport near u t is intermittent and thus undersaturated (Martin & Kok, ). According to recent studies (Pähtz & Durán, , ), transport saturates because splash entrainment of bed sediment supplies the transport layer nearly continuously with bed sediment until the flow becomes so strongly suppressed by the negative feedback of the particle motion that it can no longer compensate energy losses of rebounding particles, resulting in a sudden strong increase of deposition that compensates splash entrainment. Consistent with this hypothesis, experiments revealed that, for saturated transport, the local wind velocities near the surface decrease with u * because of this feedback (Walter et al, ).…”

Resistance Is Not Futile: Grain Resistance Controls on Observed Critical Shields Stress Variations

“…For each scenario, we also used these resulting median τ * c values in a bedload equation (Meyer‐Peter & Müller, ) to determine the sediment flux ( q s ; see Supporting Information S1). These calculated τ * c values are approximations of the actual entrainment threshold rather than of a higher reference shear stress that is part of the original bedload equation (Pähtz & Durán, ). In this sediment transport equation, b 50 is the representative grain size that is used for q s calculations for the entire bed of sediment.…”