Equilibrium Cross Section of River Channels With Cohesive Erodible Banks

Abstract

Predicting the equilibrium cross section of natural rivers has been widely investigated in Q1 Q2 Q3 fluvial morphology. Several approaches have been developed to meet this aim, starting from regime equations to the empirical formulations of Parker et al. (2007) and Wilkerson and Parker (2011), who Q4 proposed quasi-universal relations for describing bankfull conditions in sand and gravel bed rivers. Nevertheless, a general physics-based framework is still missing, and it remains an open issue to better clarify the basic mechanisms whereby a river selects its width. In this contribution we focus our attention on lowland rivers with cohesive banks, whose resistance to erosion is crucial to control the river width. In particular, we formulate a theoretical model that evaluates the equilibrium width of river cross sections modeling the interaction between the core flow in the central part of the section and the boundary layer that forms in the correspondence of the cohesive banks. The model computes the cross-section equilibrium configuration by which the shear stresses on the banks equal a critical threshold value. These stresses are computed by partitioning the total shear stress into an effective grain roughness component and a form component (Kean and Smith, 2006a). The model is applied to a large data set, concerning both sand and gravel bed rivers, and it is used to determine the relations expressing the channel width and the bankfull flow depth to the bankfull discharge, which appear to provide a unitary description of bankfull hydraulic geometry.

What sets river width?

“…S1) ( 23 ). More refined models for determining C f may improve channel geometry predictions ( 31 ); to first order, however, one may assume C f ∼ 10 1 . Improved knowledge of τ c leads to more accurate predictions of bankfull width and depth, echoing other recent studies that have pointed out the need for site-specific measurements of threshold ( 16 , 17 ).…”

“…We have hypothesized that this deviation results due to a handoff from bed material–controlled hydraulic geometry to bank material–controlled hydraulic geometry ( 23 ), and proposed a generalization of the Parker closure that provides a theoretical explanation for the geometry of both coarse-grained and fine-grained alluvial rivers. Almost concurrently, Francalanci et al ( 31 ) proposed a related model in which τ c of riverbank (rather than bed) material—along with friction effects associated with drag on the banks—determines the hydraulic geometry of sand- and gravel-bedded rivers. We refer to the unification of the Parker closure and the Schumm postulate as the “threshold-limited channel” model.…”

Channel mobility drives a diverse stratigraphic architecture in the dryland Mojave River (California, USA)

“…As most geomorphic work is performed over the yearly time fraction when bankfull discharge is reached (Wolman and Leopold, ; Blom et al ., ; Francalanci et al ., ; Naito and Parker, ; Figure A), the instantaneous migration rate, Mr I ~ Mr / I , is expected to largely exceed the yearly migration rate in ephemeral systems such as the Mojave River. In terminal and moderately sinuous aggradational reaches akin to Soda Lake, physical parameters controlling migration – such as bank erodibility and floodplain roughness (Güneralp and Rhoads, ; Constantine et al ., ; Bogoni et al ., ; Finotello et al ., ; Sylvester et al ., ; Ielpi and Lapôtre, ) – are maintained within relatively narrow bounds, leading us to infer that Mr I should likewise experience limited variability.…”

A Universal Form of Power Law Relationships for River and Stream Channels

“…Researchers have attempted to eliminate these differences by proposing averaged exponents (Cao & Knight, 1996;Finnegan et al, 2005;Huang et al, 2002;Langbein, 1963;Savenije, 2003) or by nondimensionalizing the variables (Francalanci et al, 2020;Millar, 2005;Parker et al, 2007). However, a physical explanation addressing the variability in the exponents for different river systems is still lacking.…”

“…Figure 1a shows a large data set of regime exponents representing the downstream hydraulic geometry, including the fitted values from over 150 natural stream channels (Park, 1977; Rhodes, 1987) and those proposed by previous researchers (Ackers, 1964; Blench, 1957; Cao & Knight, 1996; Chang, 1992; Fahnestock, 1963; Glover & Florey, 1951; Hey & Thorne, 1986; Kellerhals, 1967; Lacey, 1930; Lapturev, 1969; Nixon et al, 1959; Savenije, 2003; Sherwood & Huitger, 2005; Simons et al, 1960; Stevens, 1989; Williams, 1978; Wolman & Brush, 1961; Xu, 2004), which do not show any clear trend in the ternary diagram (see Table 1 for the specific values). Researchers have attempted to eliminate these differences by proposing averaged exponents (Cao & Knight, 1996; Finnegan et al, 2005; Huang et al, 2002; Langbein, 1963; Savenije, 2003) or by nondimensionalizing the variables (Francalanci et al, 2020; Millar, 2005; Parker et al, 2007). However, a physical explanation addressing the variability in the exponents for different river systems is still lacking.…”