# Experiments on Longitudinal and Transverse Bedload Transport in Sine-Generated Meandering Channels
## 1 Introduction  
Point bars and scouring pools are typical geometric characteristics of meanders, whose formation is strongly related to longitudinal and transverse sediment transport. A deeper understanding of the bed deformation and bedload movement can significantly benefit both river engineers in river restoration, flood control, navigation, etc., and ecologists in protecting aquatic communities, e.g., macrozoobenthic species. Transverse bedload transport refers to the \"crossing-centerline\" sediment movement in consecutive meandering bends. Otherwise, it is longitudinal transport [1]. Observation in both field and laboratories has evidenced that the curved channels often orientate the bedload with significant deviation from the general flow direction [2; 3; 4], and the transport rates are neither homogenous nor isotropic [5]. According to [PERSON] et al. [3], the angle between trajectories of flow and sediment is a function of threshold velocity of sediment, transverse slope of riverbed and sectional averaged velocity. [PERSON] et al. [2] took measurements at a bend of Muddy Creek; they observed that the topography-induced longitudinal and transverse bedload transport prevail at the first two-thirds and at the downstream end of the bend, respectively. [PERSON] [6] emphasized the role of the secondary circulation and argued that the transverse bedload transport could be significant even in straight channels, resulting in alternating bars and in meanders' initiation. In contrast, laboratory experiments by [PERSON] [7], [PERSON] [8], and [PERSON] [9] indicated that most grains eroded near a concave bank are transported longitudinally and deposited at the downstream pointbar on the same side of the riverbed, rather than being transported across the centerline and deposited at the point bar on the opposite side. [PERSON] et al. [10] tested the bedload transport in a sine-generated flume with the deflection angle at the inflection section \(\theta_{0}\) = 60\({}^{\circ}\) and found that longitudinal and transverse transport dominate alternatively along the channel; the bedload \"belt\" tends to cross the channel centerline right after the bend apexes. [PERSON] et al. [11] applied a depth-averaged two-dimensional model to evaluate the influences of flow discharge and particle size on bedload transport trajectories based on the 110\({}^{\circ}\) sine-generated flume experiment with wide-and shallow sections [12]; they found that the shifting of bedload trajectory in the curved channel is not susceptible to particle size, while it considerably varies with flow discharge. Although previous studies on longitudinal and transverse sediment transport offer valuable insights regarding morphological changes in meanders, they could not precisely identify and quantify the \"sources\" and \"sinks\" of bed material during the formation of pools and point bars. Specifically, tracing the movement of bedload grains in a laboratory provides a promising way to measure the accurate rates of bedload grains in any arbitrary directions as well as their destination. Besides, particle tracing technology is able to \"tell\" whether the deposited grains come from the concave banks or their convex counterparts, which is hard to discern in the field. [PERSON] and [PERSON] [13] have dyed bed materials with different colors at different locations in a single 180\({}^{\circ}\) bend in the laboratory. They have also found that most bed material deposited at the point bar came from the same side of the riverbed, and this longitudinal sediment transport is more significant when the flow discharge is higher. The present study builds on [PERSON] and [PERSON]'s [13] particle tracing experiment and goes a step further from a single bend to continuous meander loops. Two sine-generated planforms, i.e., \(\theta_{0}\) = 30\({}^{\circ}\) and 110\({}^{\circ}\), were selected. The small- and large-sinusosity flumes represent the planforms of meander channels in the earlier and later stages, respectively.