In search of a unifying criterion for meandering systems: examples from natural and built environments

Meandering of river systems has been attributed to erosion and deposition of sediments along river banks, yet a universal cause of the instability has not been identified that can be applied to other meandering systems. Here, we address the conditions that lead to the meander instability, in effect "upstream" of the many previous and thorough analyses of hydraulics and morphological patterns that ensue when such conditions exist. Rivers are only one of many fluid systems that exhibit meandering behavior, and no other involves sediment. Meandering is observed in the Gulf Stream, free-falling streams of viscous fluid, derailed trains, jackknifed trucks, and other systems in one, two or three dimensions. As such, a universal criterion is needed to explain meandering in general. We propose that meandering in all systems is driven by development of an adverse pressure gradient that results from an imbalance between driving and resistive forces. A universal framework will make it possible to determine under what conditions the meandering instability will manifest in altered flow and channel morphology. Toward that end, we conducted laboratory experiments in 2- and 3-dimensions and analyzed systems with either reduction in driving forces or increase in resistive forces. We also examine the ubiquitous example of natural rivers to identify the conditions under which rivers meander or ply a more direct course to base level. Further, we define a dimensionless "Meander Number" as (driving-resistive)/resistive forces. The observations presented here support a common cause that leads to instability of a wide range of meandering systems and with further exploration, may ultimately lead to a universal theory of meandering systems.