Modelling mid‐channel bars in meandering channels

Abstract

An analytical modelling framework is proposed to reproduce the frequently observed but poorly studied occurrence of mid-channel bars in meandering channels. Mid-channel bars occur in meanders and may characterize transitional morphologies between pure meandering and braided rivers. Based on existing fi eld and experimental observations, we propose that two different mechanisms can generate central topographical patterns in meanders. A former mechanism ('width-forced') is related to spatial width oscillations which determine a laterally symmetrical bed shear stress pattern that promotes mid-channel bars. A second mechanism ('curvature-forced') can take place also in curvilinear equiwidth streams since also longitudinal variations of channel curvature can produce laterally symmetrical alterations of the sediment transport capacity. A perturbation approach is employed to model both mechanisms within a common framework, allowing reproduction, at least qualitatively, of several observed features. While width-forced mid-channel bars are a symmetric linear altimetric response, to reproduce curvature-forced mid-channel bars requires modelling nonlinear fl ow-bed topography interactions at the second order of the perturbation expansion. Hypotheses on how these mechanisms operate are further discussed through an application to fi eld cases. The amplitude of the nonlinear response can be relevant compared to that of the point bar in equiwidth meanders and the location of midchannel bars seldom coincides with bend apexes, mainly depending upon the intrinsic meander wavelength. Central bars tend to symmetrically divert the fl ow against the two banks, a process which is proposed as a possible cause of cross-sectional overwidening, along with the asymmetry between the rates of bank erosion and of the opposite bank accretion. The outcomes of this fi rst modelling step on the subject allow discussion of the mutual feedback processes that characterize interactions between midchannel bars and width variations in river meanders.

A simplified 2D model for meander migration with physically-based bank evolution

“…We, therefore, suggest to use Option 1 for relatively short-term simulations, which are associated with small longitudinal changes in channel width resulting from net erosional processes. A more accurate description of the hydrodynamics and morphodynamics of varyingwidth channels requires either a fully non-linear 2D depth-averaged numerical model or, as previously mentioned, an analytical solution which also considers width variations, such as that developed by Luchi et al (2010). The cross-section geometry obtained with Option 1 is not that corresponding to morphologic equilibrium, because only the flow in the central region of the channel is actually computed.…”

“…A more robust description of channel migration, however, requires a hydrodynamic model, which considers, besides the interactions between channel curvature and flow-bed topography, also the interactions associated with width variations and the mutual width-curvature interactions (Luchi et al, 2010).…”

Diffusive evolution of experimental braided rivers

“…Despite the complex appearance and erratic dynamics of braided rivers, decades of laboratory experiments and field observations have documented order in the structure of the channel network [3,[5][6][7][8][9][10][11][12]. The processes at the scale of individual channels that drive their formation and movement have also been identified [5,[13][14][15][16][17][18] and were used to inform a cellular numerical model of water routing and sediment transport that qualitatively reproduced braided river morphology and dynamics [2]. Yet some of the most basic questions about these systems remain unanswered: Do the individual channels exhibit equilibrium geometry, and if so what sets this equilibrium?…”

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., …”