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.
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© 2019 John Wiley & Sons, Ltd.
- alluvial fan
- bottom stability
- topographic expansions