Bend theory of river meanders with spatial width variations

Abstract

The present work revisits the classical, uniform-width bend theory with the aim to understand whether and how spatial width oscillations can affect the process of linear bend stability that initiates meander planform evolution. Although longitudinal oscillations of channel width are common along many meandering streams, little investigation of their properties and dynamic effects has been pursued so far. The theory therefore accounts for width variations as a geometrical forcing in a depth-averaged model of meander morphodynamics by assuming the potential interaction with the classical curvature forcing effect. A first quantification of width variations is made by referring to a freely evolving meandering river, which shows that the dimensionless amplitude of width variations is a ‘small’ parameter with comparable magnitude to that of curvature variations, thus suggesting the use of a two-parameter perturbation expansion. Moreover, it is reasonable to assume that channel width oscillates in space with a double frequency relative to curvature, which implies that one nonlinear interaction between the two forcing effects is enough to reproduce the effect of spatial width variations on the process of bend stability. Overall, width variations consistently promote the instability of shorter bends with respect to meanders with uniform width: on average, this predicted tendency is supported by analysis of field data referring to hundreds of natural meander bends. The effect on meander wavelength selection depends on the location of the widest section relative to the bend apex. Under typical formative conditions of gravel-bed rivers, with large-enough channel aspect ratios, two distinct most unstable longitudinal modes develop. Such behaviour is absent when the width is uniform, and suggests a mechanistic interpretation for the reach-scale occurrence of chute cutoffs that can be observed more frequently in wider-at-bends than in equiwidth meandering channels.

Modeling morphodynamic processes in meandering rivers with spatial width variations

“…has been applied to all bends, which have been grouped into classes of similar meander wave number λ. The outcomes, represented in Figure 5 in the form of box plots, are consistent with the findings of Luchi et al [2011] on the Rio Beni. Average δ values are typically slightly lower than 0.1, corresponding to the widest section less than 20% wider than the wavelength‐averaged value.…”

“…investigated the nonlinear interaction between free migrating bars and steady central bars in the same planform configuration. In the case of curved channels, Luchi et al [2010b] have modeled the linear and nonlinear development of midchannel bars in meandering channels, which are typical features of transitional morphologies between meandering and braiding; Frascati and Lanzoni [2011] have extended the theory of Repetto et al [2002] to channels with arbitrarily varying width, and applied this to meandering streams; Luchi et al [2011] have analyzed the dynamic effect of spatial width oscillations on the process of meander bend stability; Luchi et al [2012] have extended the nonlinear model of Bolla Pittaluga et al [2009] to meanders with spatial width oscillations. Linear models for equiwidth meandering channels [ Camporeale et al , 2007] together with these more recent analytical theories for meanders with spatial width variations separately address the key physical processes emerging from the overview of field investigations (section 2.1).…”

“…( τ s , τ n ) and ( Q s , Q n ) are the bottom shear stress and sediment rate vectors. Moreover f α and g α are homogeneous terms accounting for the effect of streamline curvature on the parameterization of secondary flows [see Luchi et al , 2011], which vanish when secondary flows are parameterized using the channel axis curvature.…”

“…This behavior represents a marked difference with respect to equiwidth meanders (continuous lines in Figure 11b), for which bend instability is characterized by the presence of a single unstable range of longitudinal modes. Meanders with intense enough spatial width variations, and at sufficiently large bankfull aspect ratio, might therefore display a long‐term tendency toward almost two different equally unstable planforms characterized by well distinct meander wavelengths Luchi et al [2011] Lagasse et al [2004], based on Brice [1975]).…”

Advances and challenges in meandering channels research

“…Advances in research on river meandering through the '90s and the beginning of the 21th century have focused specifically on several topics: field-based or empirical research on the interactions between flow structure and bed morphology (e.g., Lawler et al, 1997;Frothingham and Rhoads, 2003;Harrison et al, 2011) and on channel planform evolution (e.g., Hooke, 1995;Gilvear et al, 2000;Hooke, 2007;Luchi et al, 2007;Hooke, 2008;Rhoads, 2009b, 2010); experimental-or laboratory-based research on flow and sediment transport in curved channels (e.g., Whiting and Dietrich, 1993a, 1993b, 1993cBlanckaert and de Vriend, 2004;Blanckaert and de Vriend, 2005;Peakall et al, 2007aPeakall et al, , 2007bAbad and García, 2009a, b;Braudrick et al, 2009;Termini, 2009) and theoretical and numerical modeling of meander morphodynamics (e.g., Odgaard, 1989;Tubino and Seminara, 1990;Furbish, 1991;Howard, 1992;Seminara and Tubino, 1992;Sun et al, 1996;Darby et al, 2002;Lancaster and Bras, 2002;Blanckaert and de Vriend, 2003;Bolla Pittaluga et al, 2009;Crosato, 2009;Dulal et al, 2010;Luchi et al, 2010;Güneralp and Rhoads, 2011;Luchi et al, 2011). The same period has also seen the development of research on submarine meandering channels focusing on the detailed characterization of meander geometry, migration rates, and interchannel-sedimentation patterns (e.g., …”