Geomorphology 163–164 (2012) 10–25 Contents lists available at SciVerse ScienceDirect Geomorphology journal homepage: www.elsevier.com/locate/geomorph A simplified 2D model for meander migration with physically-based bank evolution Davide Motta a,⁎, Jorge D. Abad b, Eddy J. Langendoen c, Marcelo H. Garcia a a Dept. of Civil and Environmental Engineering, University of Illinois at Urbana-Champaign, Urbana, IL, 61801, United States b Dept. of Civil and Environmental Engineering, University of Pittsburgh, Pittsburgh, PA, 15261, United States c US Department of Agriculture, Agricultural Research Service, National Sedimentation Laboratory, Oxford, MS, 38655, United States article info abstract Article history: The rate of migration, calculated by numerical models of river meandering, is commonly based on a method Received 1 July 2010 that relates the rate of migration to near-bank excess velocity multiplied by a dimensionless coefficient. Received in revised form 18 January 2011 Notwithstanding its simplicity, since the early 1980s this method has provided important insight into the Accepted 1 June 2011 long-term evolution of meander planforms through theoretical exercises. Its use in practice has not been as Available online 16 August 2011 successful, because the complexity of the physical processes responsible for bank retreat, the heterogeneity in floodplain soils, and the presence of vegetation, make the calibration of the dimensionless coefficient rather Keywords: Meander migration challenging. This paper presents a new approach that calculates rates of meander migration using physically- Migration coefficient based streambank erosion formulations. The University of Illinois RVR Meander model, which simulates Bank erosion meandering-river flow and bed morphodynamics, is integrated with algorithms for streambank erosion of the Planform shape US Department of Agriculture channel evolution computer model CONCEPTS. The performance of the Computer model proposed approach is compared to that of the more simple classic method through the application to several test cases for idealized and natural planform geometry. The advantages and limitations of the approach are discussed, focusing on simulated planform pattern, the impact of soil spatial heterogeneity, the relative importance of the different processes controlling bank erosion (hydraulic erosion, cantilever, and planar failure), the requirements for obtaining stable migration patterns (centerline filtering and interpolation of bank physical properties), and the capability of predicting the planform evolution of natural rivers over engineering time scales (i.e., 50 to 100 years). The applications show that the improved physically-based method of bank retreat is required to capture the complex long-term migration patterns of natural channels, which cannot be merely predicted from hydrodynamics only. © 2011 Elsevier B.V. All rights reserved. 1. Introduction difference between bed and bank material particle sizes. Bed load is quantified using empirical formulations (Garcia, 2008), and its The modeling of meandering-river migration requires the simu- direction is determined by the near-bed flow direction corrected by lation of the following processes: hydrodynamics, sediment transport, the effect of bed slopes (Seminara and Tubino, 1989; Kovacs and bed morphodynamics, and bank erosion. The hydrodynamic modeling Parker, 1994; Talmon et al., 1995; Mosselman, 2005; Abad et al., resolves the mean and turbulent flow fields: e.g., primary and 2008). The suspended load is calculated using an advection–diffusion secondary flows, Reynolds stresses, and turbulent kinetic energy equation, where the diffusion coefficient is related to the turbulence among other hydrodynamic parameters. In bends, curvature-driven characteristics of the flow (Lyn, 2008). Abad et al. (2008) show the (Prandtl's first kind) and turbulence-driven (Prandtl's second kind) application of this methodology for the case of laboratory meandering secondary flow can be present and alter the morphology of the bed channels. and banks, which then affects the anisotropy of the flow (Akahori and Modeling of the bed morphodynamics provides the bed morphol- Schmeeckle, 2002; Blanckaert and de Vriend, 2005). Because the shear ogy at different spatial scales, which allows for reproducing the stresses exerted by the flow on the bed and banks control the erosion feedback between bed structures and flow field (Best, 2005), like the and transport of the boundary materials, their modeling is critical. disruption of secondary flows because of migrating bedforms (Abad Modeling of the sediment transport in meandering streams et al., 2010) and the interactions between suspended sediment simulates the transport of sediments as a combination of bed and particles and bed morphology (Schmeeckle et al., 1999). suspended load, because of the complex flow and the possible large Modeling bank erosion allows for simulating the migration of the meandering channel, which in turn affects hydrodynamics, sediment transport and bed morphodynamics. In a bend, faster and deeper flow ⁎ Corresponding author. E-mail addresses: [email protected] (D. Motta), [email protected] (J.D. Abad), develops near the outer bank, which causes bank erosion (Thomson, [email protected] (E.J. Langendoen), [email protected] (M.H. Garcia). 1879). At the inner bank, a point bar commonly forms and promotes 0169-555X/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.geomorph.2011.06.036 D. Motta et al. / Geomorphology 163–164 (2012) 10–25 11 bank accretion. Widening in meandering channels may happen when assessment studies, using the classic migration method, will accu- outer bank retreat exceeds the rate of accretion of the opposite bank rately simulate the response of meandering streams to in-stream and (Nanson and Hickin, 1983). riparian management practices over engineering time scales (that is, a Models of different degrees of sophistication have been used to few years to decades or, in general, periods before cutoff occurrence). simulate freely meandering channels. For example, Ruether and Olsen A new physically-based approach is, therefore, needed, which (2007) performed three-dimensional (3D) numerical modeling using explicitly relates meander migration to the processes controlling Reynolds Averaged Navier–Stokes (RANS) equations, a k−ε model for streambank erosion. turbulence, an advection–diffusion equation for suspended sediment, This paper presents a new modeling approach that merges the and van Rijn's (1984) formulation for bed load. Bolla Pittaluga et al. functionalities of the RVR Meander toolbox (Abad and Garcia, 2006), (2009) developed a 3D analytical model for low-sinuosity meanders which is a 2D long-term meander migration model based on Ikeda et and steady bed morphology. These models need coupling with bank al.'s (1981) model, with the physically-based streambank erosion erosion and meander evolution submodels, however, to simulate algorithms of the CONCEPTS (CONservational Channel Evolution and planform changes for engineering and geological time scales. Pollutant Transport System) channel evolution model (Langendoen Two-dimensional (2D) analytical models for long-term river and Alonso, 2008; Langendoen and Simon, 2008; Langendoen et al., migration, again valid for low-sinuosity meanders and steady bed 2009). Darby et al. (2002) and Rinaldi et al. (2008) carried out similar morphology, were developed, among others, by Ikeda et al. (1981), efforts, however, only for short reaches and simulation periods. The Blondeaux and Seminara (1985), Johannesson and Parker (1989b), paper describes the new physically-based methodology for comput- Howard (1992, 1996), Sun et al. (1996, 2001), Zolezzi and Seminara ing river migration and presents model tests for idealized (sine- (2001), and Lancaster and Bras (2002). These models calculate the generated and Kinoshita curve) and observed planforms. The rate of migration based on a method independently introduced by computed planform evolution is compared to that obtained with the Hasegawa (1977) and Ikeda et al. (1981). This method relates the rate classic method based on a migration coefficient. of migration to the near-bank excess velocity multiplied by a dimensionless coefficient, and is referred to as the classic or MC 2. Model description (Migration Coefficient) approach hereafter. The dimensionless coef- ficient is obtained by means of calibration against field data and is The modeling platform is composed of two main components. The typically a very small number (10− 7–10− 8). From a theoretical first component simulates the hydrodynamics and bed morphody- perspective, this method has provided fundamental insight into the namics. The second component simulates the channel migration. planform evolution of meandering channels, but it has not been as Because the main goal of this paper is to evaluate the performance of successful in practical applications, where the calibration of the the new approach for bank retreat as compared to the classic method, dimensionless coefficient can be challenging and unable to capture it is coupled with a simple physically-based analytical model for the observed migration patterns. Constantine et al. (2009) sought to hydrodynamics and bed morphodynamics of meandering streams, establish a relation between the migration coefficient and measurable which is based on the model of Ikeda et al. (1981). physical characteristics of the materials of the channel boundary using data from