Scales of collective entrainment and intermittent transport in collision-driven bed load

Abstract

Abstract. Fluvial bed-load transport is notoriously unpredictable, especially near the threshold of motion where stochastic fluctuations in sediment flux are large. A general statistical mechanics framework has been developed to formally average these fluctuations, and its application requires an intimate understanding of the probabilistic motion of individual particles. Laboratory and field observations suggest that particles are entrained collectively, but this behavior is not well resolved. Collective entrainment introduces new length and time scales of correlation into probabilistic formulations of bed-load flux. We perform a 5 series of experiments to directly quantify spatially-clustered movement of particles (i.e., collective motion), using a steep-slope 2D flume in which centimeter-scale marbles are fed at varying rates into a shallow and turbulent water flow. We observe that entrainment results exclusively from particle collisions and is generally collective, while particles deposit independently of each other. The size distribution of collective motion events is roughly exponential and constant across sediment feed rates.The primary effect of changing feed rate is simply to change the entrainment frequency, although the relation between these 10 two diverges from the expected linear form in the slowly-driven limit. The total displacement of all particles entrained in a collision event is proportional to the kinetic energy deposited into the bed by the impactor. The first-order picture that emerges is similar to generic avalanching dynamics in sandpiles: "avalanches" (collective entrainment events) of a characteristic size relax with a characteristic timescale regardless of feed rate, but the frequency of avalanches increases in proportion to the feed rate. The transition from intermittent to continuous bed-load transport then results from the progressive merger of entrainment 15 avalanches with increasing transport rate. As most bed-load transport occurs in the intermittent regime, the length scale of collective entrainment should be considered a fundamental addition to any probabilistic bed-load framework.

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

“…One mechanism is the cumulative effect of successive particle‐bed impacts, which causes a fluctuation motion of bed surface particles that makes them more susceptible for entrainment in a continuous rebound state. Note that recent numerical and experimental studies indicate that impact entrainment dominates direct fluid entrainment in turbulent bedload transport (Lee & Jerolmack, ; Pähtz & Durán, ; Vowinckel et al, ). The impact entrainment threshold also marks the transition between intermittent and continuous transport. Below , turbulent events sustain transport on an intermittent basis, where the intermittency characteristics depend on whether the Shields number Θ is above or below the rebound threshold (Figure ). Sediment transport rate relations like equation are only applicable to steady, continuous transport of nonsuspended sediment (i.e., ) but fail to describe intermittent transport (i.e., ), which explains why bedload transport formulae like equation fail when (Meyer‐Peter & Müller, ; Recking et al, ) and why one should therefore only use data representing bulk transport when testing such relations (Bunte & Abt, ; Shih & Diplas, ; Singh et al, ).…”

“…One mechanism is the cumulative effect of successive particle-bed impacts, which causes a fluctuation motion of bed surface particles that makes them more susceptible for entrainment in a continuous rebound state. Note that recent numerical and experimental studies indicate that impact entrainment dominates direct fluid entrainment in turbulent bedload transport [Vowinckel et al, 2016;Pähtz and Durán, 2017;Lee and Jerolmack, 2018]. 7.…”

“…In contrast, when Θ r t < Θ < Θ e t , particles entrained by turbulent events continuously rebound for comparably longer periods before they deposit again, giving rise to intermittent bulk transport and significant transport autocorrelations, as often observed in aeolian (Bauer & Davidson-Arnott, 2014;Baas & Sherman, 2005;Carneiro et al, 2015;Dupont et al, 2013;Ellis et al, 2012;Lee, 1987;Martin et al, 2013;Pfeifer & Schönfeldt, 2012;Rasmussen & Sørensen, 1999;Sherman et al, 2018;Spies et al, 2000;Stout & Zobeck, 1997) and fluvial systems (Ancey et al, 2006(Ancey et al, , 2008Dinehart, 1999;Drake et al, 1988;Heathershaw & Thorne, 1985;Heyman et al, 2013;Lee & Jerolmack, 2018). The closer Θ comes to the impact entrainment threshold Θ e t , the more such continuously rebounding particles the flow can carry, which increases the probability of impact entrainment events (section 4.2) and thus further enhances transport autocorrelation.…”

“…This cumulative effect of successive particle-bed impacts, which has been neglected in most previous studies of impact entrainment Haff , 1988, 1991;Haff and Anderson, 1993;Rioual et al, 2000Rioual et al, , 2003Oger et al, 2005Oger et al, , 2008Beladjine et al, 2007;Crassous et al, 2007;Ammi et al, 2009;Kok and Renno, 2009;Valance and Crassous, 2009;Ho et al, 2012;Comola and Lehning, 2017;Huang et al, 2017;Tanabe et al, 2017; and in numerous theoretical studies that link properties of aeolian saltation transport to the splash of isolated particle-bed impacts [Andreotti, 2004;Creyssels et al, 2009;Kok and Renno, 2009;Kok, 2010a;Jenkins et al, 2010;Lämmel et al, 2012;Pähtz et al, 2012;Huang et al, 2014;Valance, 2014, 2018;Zheng, 2014, 2015;Berzi et al, 2016Berzi et al, , 2017Bo et al, 2017;, increases with the frequency of particlebed impacts and thus with Θ − Θ r t [equation ( 1)]. Consistently, Lee and Jerolmack [2018], who investigated bedload transport intermittency in a water flume as a function of the rate at which particles are fed at the flume entrance, reported a change in the velocity distribution of transported particles that is qualitatively very similar to the one shown in Figure 9: a bimodal distribution at low feeding rate (i.e., low impact frequency) turns into a unimodal distribution at high feeding rate (i.e., high impact frequency). In fact, when the characteristic time between impacts becomes smaller than the time the bed surface needs to recover from an impact, repeated impacts will increase the fluctuation motion of the bed.…”

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

“…Equation does not account for the influence of particle impacts, which can cause direct sediment entrainment as well as loosen a given grain (e.g., Ancey, ; Lee & Jerolmack, ; Pähtz & Durán, ; Vowinckel et al, ), thereby decreasing its resisting force and making it easier to move. Many studies have also demonstrated that drag and lift force fluctuations are actually responsible for particle entrainment (e.g., Diplas et al, ; Leary & Schmeeckle, ; Schmeeckle et al, ; Valyrakis et al, ) and that these fluctuations in lift and drag forces vary with p (Schmeeckle et al, ).…”