What controls the disequilibrium state of gravel‐bed rivers?. Issue 15 (4th December 2019)

• Record Type: Journal Article
• Authors: Chartrand, Shawn M.; Jellinek, A. Mark; Hassan, Marwan A.; Ferrer‐Boix, Carles
• Is Part Of: Earth surface processes and landforms. Volume 44:Issue 15(2019)
• Page Start: 3020
• Page End: 3041
• Publication Date: 2019-12-04
• Subjects: statistically steady‐state -- equilibrium -- fluvial geomorphology -- scaling theory -- experimentation; Geomorphology -- Periodicals; 551.4
• DOI: 10.1002/esp.4695
• Languages: English
• ISSNs: 0197-9337

Abstract

Abstract: A 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= K U b / U p . ξ is a metric for the local disequilibrium state of gravel‐bed mountain streams, which reflects a balance between the rate of topographic adjustment U b, and the rate of bed sediment texture adjustment U p . 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 U b and U p 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 / τ r e f . When τ / τ r e f ≈1.5, U b was the dominant control on disequilibrium. However, when τ / τ r e f ≈2.0, U p contributed more significantly to disequilibrium. These results suggest that after an upstream supply perturbation, the equilibrium timescale is governed by U p, 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. Abstract : We introduce a new metric which quantifies the disequilibrium condition of mountain gravel‐bed streams. The disequilibrium condition is set by how the rates of bed topography and grain size texture adjustment compare. Our work provides a link between local processes and watershed scale conditions, and may prove useful for landscape evolution studies.