On the incipient formation of bars and channels on alluvial fans

Abstract

The morphodynamics of topographic expansion has been recently investigated both experimentally, by Sittoni et al., (2014) Shaw et al., (2018), and numerically Sittoni et al., 2014. Here, we study the basic mechanism that governs the evolution of topographic and expansions and explore the instability of the bottom topography under conditions of steady but spatially expanding flow. We model the expanding flow via a by configuration where water and sediments are supplied from a central hole and flow on a cone shaped surface confined by lateral walls. The governing equations are the shallow‐water equations coupled with the Exner equation, written in cylindrical coordinates. We initially approach the problem analytically by considering the conditions required for the basic state, consisting of a pure radial flow and bottom profile, to lose stability to small amplitude perturbations. This analysis suggests that more than one mode may be unstable, encouraging us to extend the analysis to the nonlinear regime. We do this through numerical modeling of the full governing equations, which allows us to predict the establishment of a bar pattern whose features are similar to those experimentally observed. Two prominent features of the finite‐amplitude bar pattern are (1) bar apices are distributed at a radial distance from the inflow consistent with work of Shaw et al. (2018); and (2) that the flow aspect ratio of the interbar areas remain high without provoking further instability. Both features imply that in general expansion acts to reduce bar development relative to an equivalent rectilinear flow. © 2019 John Wiley & Sons, Ltd.

River, Coastal and Estuarine Morphodynamics Selected papers from the 10th anniversary of the RCEM Symposium

“…Tambroni et al . () use analytical and numerical tools to investigate the basic mechanism that governs the evolution of topographic expansions and explore the instability of the bottom topography under conditions of steady, spatially expanding flow. The bar pattern emerging from numerical simulations is found to have consistent features with those observed in the field, suggesting that, in general, expansion acts to reduce bar development relative to an equivalent rectilinear flow.…”

“…The 17 collected contributions include four state-of-science papers concerning the most recent advances in computational morphodynamic modelling of coupled flow-bed-sediment systems (Shimizu et al, 2019), a critical analysis of existing data on vegetation-flow-sediment interactions obtained through both laboratory experiments and field campaigns (Tinoco et al, 2020), a review of existing moving-boundary theories of shorelines with two extensions to allow inclusion of firstorder effects of waves and tides (Voller et al, 2020), and an overall assessment of the role played by wave forcing on the hydro-morphodynamics in shallow nearshore areas and at river mouths (Brocchini, 2019). The other 13 papers cover different topics about morphodynamics, spanning multiple environments, tackling concepts and processes with the aid of refined theoretical and numerical tools (Redolfi et al, 2019;Tambroni et al, 2019), grounding the results on laboratory data (Finotello et al, 2019;Geng et al, 2019;Matoušek et al, 2019, Porcile et al, 2020 and field observations (Fogarin et al, 2019;Tommasini et al, 2019), and making use of interdisciplinary approaches (Calvani et al, 2019;Chen et al, 2019;Pivato et al, 2019;van de Vijsel et al, 2020) also to develop new conceptualizations (Schlömer et al, 2020).…”

“…Analytical modelling has been at the core of theoretical morphodynamics well before the beginning of the RCEM symposia, especially when computational tools did not allow powerful numerical simulations of the governing differential equations of fluid flow over movable boundaries. Despite massive improvements in computational power, analytical approaches are still essential to capture the key physical processes and controlling parameters of several morphodynamic problems, as exemplified in the papers by Redolfi et al (2019) and Tambroni et al (2019). Redolfi et al (2019) present a theoretical analytical framework that clarifies the intrinsic 'free' instability and the role of external forcings that control the dynamics of river bifurcations, based on morphodynamic influence.…”

“…bed effects, slope advantage), which instead control the bifurcation stability under sub-resonant conditions. Tambroni et al (2019) use analytical and numerical tools to investigate the basic mechanism that governs the evolution of topographic expansions and explore the instability of the bottom topography under conditions of steady, spatially expanding flow. The bar pattern emerging from numerical simulations is found to have consistent features with those observed in the field, suggesting 2020) show how laboratory experiments can be used to unravel physical processes at quite different spatial and temporal scales and in different environments.…”

When and Where do Free Bars in Estuaries and Tidal Channels Form?

“…shallow streams, in several rows (multiple row bars) (Seminara, 2010). Due to the autogenic character of their development, they are said to be "free," in opposition to the so-called "forced" bars, which are steady features that do not arise spontaneously but as a response to some physical constraint such as a geometrical variation (e.g., curvature, channel widening) or a local disturbance (e.g., the presence of an in-stream obstacle) (Bittner, 1995;Duró et al, 2016;Redolfi et al, 2016Redolfi et al, , 2021Repetto et al, 2002;Seminara & Tubino, 1989;Struiksma & Crosato, 1989;Wu et al, 2011;Tambroni et al, 2019;Zolezzi et al, 2005).…”