What controls the disequilibrium state of gravel‐bed rivers?

Abstract

AbstractA river at equilibrium is described by a statistically‐stationary mean bed elevation profile that arises in response to steady supplies of relief, water and sediment. Outside of the profile shape, how is the equilibrium state of a river most reliably identified and rigorously defined? Motivated by a proposed link between equilibrium and physical processes, we use scaling theory to develop the dimensionless channel response number ξ=KUb/Up. ξ is a metric for the local disequilibrium state of gravel‐bed mountain streams, which reflects a balance between the rate of topographic adjustment Ub, and the rate of bed sediment texture adjustment Up. The coefficient K can take one of two forms depending on choice of length scale for topographic adjustment. We hypothesize that equilibrium occurs where and when ξ≈O(1), and consequently, disequilibrium is the more general state captured by conditions of ξ≉O(1). The rates Ub and Up are controlled by the mechanics of sediment deposition and entrainment at the local scale of the channel width. The extent to which either process regulates disequilibrium depends on the bed strength, which is set by the time‐varying grain size distribution and packing. We use flume experiments to understand ξ and find that in the limit ξ>>1, the time‐varying response of an experimental channel depends sensitively on the spatially‐averaged bed shear stress ratio τ/τref. When τ/τref≈1.5, Ub was the dominant control on disequilibrium. However, when τ/τref≈2.0, Up contributed more significantly to disequilibrium. These results suggest that after an upstream supply perturbation, the equilibrium timescale is governed by Up, which we show is consistent with expectations from linear damping theory. Our experimental test of ξ is promising, but inconclusive with respect to our hypothesis. This uncertainty can be readily addressed with numerical or additional physical experiments. © 2019 John Wiley & Sons, Ltd.