Abstract
Abstract. Alluvial and transport-limited bedrock rivers constitute the majority of fluvial systems on Earth. Their long profiles hold clues to their present state and past evolution. We currently possess first-principles-based governing equations for flow, sediment transport, and channel morphodynamics in these systems, which we lack for detachment-limited bedrock rivers. Here we formally couple these equations for transport-limited gravel-bed river long-profile evolution. The result is a new predictive relationship whose functional form and parameters are grounded in theory and defined through experimental data. From this, we produce a power-law analytical solution and a finite-difference numerical solution to long-profile evolution. Steady-state channel concavity and steepness are diagnostic of external drivers: concavity decreases with increasing uplift rate, and steepness increases with an increasing sediment-to-water supply ratio. Constraining free parameters explains common observations of river form: to match observed channel concavities, gravel-sized sediments must weather and fine – typically rapidly – and valleys typically should widen gradually. To match the empirical square-root width–discharge scaling in equilibrium-width gravel-bed rivers, downstream fining must occur. The ability to assign a cause to such observations is the direct result of a deductive approach to developing equations for landscape evolution.
Highlights
Mountain and upland streams worldwide move clasts of gravel (> 2 mm)
Detachment-limited rivers incise at a rate that is set by the mechanics of river incision into bedrock
The key equation of this paper is Eq (20), which captures the dynamics of a gravel-bed river whose bed shear stress is a multiple of the critical shear stress for initiation of motion; such systems are ubiquitous in nature (Phillips and Jerolmack, 2016; Pfeiffer et al, 2017)
Summary
Mountain and upland streams worldwide move clasts of gravel (> 2 mm). they consistently reshape their beds and – unless they are fully bedrock-confined – their bars and banks as well (Parker, 1978; Brasington et al, 2000, 2003; Church, 2006; Eke et al, 2014; Phillips and Jerolmack, 2016; Pfeiffer et al, 2017). Bedrock channels can act as transport-limited systems (Johnson et al, 2009), meaning that an approach to transport-limited conditions may be able to describe the evolution of alluvial rivers, but rivers across much of Earth’s upland surface Based on this past research, we are able to write a simple and consistent set of equations for transport-limited gravel-bed river long-profile evolution that eschews tunable parameters, common in stream-power approaches to river long-profile evolution (Howard and Kerby, 1983; Whipple and Tucker, 1999, 2002) for those based on experimentation, measurements, and theory. We derive that downstream fining and channel concavity must combine to be the mechanistic cause of channel width scaling with the square root of water discharge (b ∝ Q0.5) (Lacey, 1930; Leopold and Maddock, 1953), at least in equilibriumwidth (including near-threshold) transport-limited gravelbed rivers
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