Getting to the Root of River Meanders

Abstract:

Historically, river meandering has been attributed to erodible banks and sediment transport. Previous formulations have characterized meandering as a response of a straight river to an imposed perturbation and comprehensively addressed meander development and morphology as well as the hydraulics internal to the various parts of meandering rivers, but not attempted to identify a universal cause of meandering itself. It was recognized in the mid-20^th century that "no general theory of meanders is as yet satisfactory” and this remained the case to the present time. Rivers are only one of many fluid systems that exhibit meandering behavior, and no other involves sediment. Meandering is observed in glacial meltwater, the Gulf Stream, Jet Stream, submarine channels, free-falling streams of viscous fluid, and other systems in one, two and three dimensions, including derailed trains and jackknifed tractor trailer trucks. Yet, a universal criterion is lacking to explain meandering of rivers and other systems. We thus explore the common cause of the instability behind all meandering systems, including rivers, the poster child of meandering.

We suggest that meandering in a broad range of systems is triggered by fundamental processes stemming from the dynamics of fluid flow that lead to local deceleration and development of an adverse pressure gradient within the flow. As such, our analysis conceptually precedes meandering behavior, and does not conflict with the detailed sedimentological and hydraulic studies available in the literature. As such, we are not concerned with the timescale of sedimentary response of rivers, but strictly the existence of an adverse pressure gradient that leads to the instability itself. The subsequent evolution and morphology of meanders has been extensively investigated. Even Albert Einstein explored the “cause” of river meanders in 1926 (translated to English in 1954, a year before his death) and did not investigate the fundamental instability, but rather, in refuting “Baer’s Law,” focused on the response of sediments to river internal velocity structure.

In its simplest, yet most fundamental form, the meandering instability can be easily observed in an ordinary kitchen/bath sink, with a slow and steady flow from the faucet (no aeration). The flow released from the faucet accelerates downward, causing the stream to become thinned, but maintaining its integrity for some distance due to surface tension. The driving forces (gravity) exceed resistive forces, so the flow accelerates and does not meander. However, when the flow encounters an obstruction, it must decelerate, and an adverse pressure gradient is imposed. The information regarding the existence of an obstruction in the flow (such as your finger) is transmitted upstream (in this case straight UP!), triggering meandering (called “coiling” in 3-D) immediately upstream of (above) the obstruction. This is an extreme case of vertical flow (φ = 90 ̊), and a sudden break in slope to 0 ̊. We suggest that the phenomena of meandering (e.g. rivers) and coiling (e.g. free-falling streams) both involve the same meander instability, but river (and many other) meandering systems are constrained to two dimensions (quasi-planar), while coiling occurs in three dimensions.

Rivers may be considered the most widely encountered meandering systems, but the instability is applicable for any system involving flow of a deformable medium. In the practical case of a sudden deceleration of a locomotive, the rate of deceleration of the cars behind it is reduced by derailing in response to the same instability type. Likewise, a tractor-trailer truck, when suddenly applying brakes to wheels of the cab, would force a greater deceleration to the trailer if it were to remain directly behind, than if it jackknifed. We utilize laboratory experiments and a rod-chain model to test and characterize the instability in various systems, grading to inviscid and finally viscous fluids. As such, this simple formulation for the balance of forces in rivers can be applied to the broad spectrum of meandering systems, subject to the same fundamental instability.