How to make a meandering

Alan D. Howard1 Department of Environmental Sciences, P.O. Box 400123, University of Virginia, Charlottesville, VA 22904-4123

espite the ubiquity of mean- dering in , only recently have appropriate ex- perimental conditions been producedD to replicate a stably - ing in the laboratory, as de- scribed in a recent issue of PNAS (1). Meandering channels occur in a wide variety of sedimentary environments, including on deep sea fans formed by turbidity currents (2), as relict on Mars (3) (Fig. 1), and as channels formed by flowing alkenes on Titan. The mechanics of formation of mean- ders is reasonably well understood (4). When flow enters a bed, a heli- cal secondary is set up that in- creases flow velocity and channel depth along the outer in proportion to bed curvature, which encourages bank . The secondary current has an intrinsic downstream scale related to flow velocity and depth; this results in gradual increase in bend amplitude and propagation of the meandering pattern upstream and downstream. Linear the- ory of flow in bends (5) has permitted construction of simulation models that replicate many aspects of meandering Fig. 1. Fossil highly sinuous meandering channel and floodplain on Mars. Red arrows point to repre- behavior, including meander cutoffs, sentative locations along channel. The channel bed is now a ridge (in inverted relief) because wind erosion creation of oxbow lakes, and patterns of has removed finer from the floodplain and surrounding terrain. The low curvilinear ridges (6, 7). Interac- interior of the main sinuous ridge are remnants of the meander loops as they grew through bank erosion tion of the bend-induced flow and bed along the outside of bends. A cutoff may have occurred shortly before flow ceased above location ‘‘X,’’ resulting in abandonment of the loop lying below. Rough terrain at upper right and lower left is due to topography with superimposed alternate wind scour. Image is a portion of NASA HiRISE image PSP࿝006683࿝1740. complicates the flow and bed topography in wider meandering channels (8, 9). These complications wide, shallow, and braided. Narrow, producing a meandering pattern. The have been incorporated into increasingly deep channels favoring a meandering experiments of Braudrick et al. detailed models of stream meander pattern require appreciable bank (1) described in this issue of PNAS have evolution (10). strength. This typically occurs where identified an ample supply of fine In settings where rivers are not later- carry a high relative quantity of sediment in transport as additional re- ally confined by resistant walls silt and which is easy to transport quirement for stable meandering in either the planform generally displays but is difficult to re-erode once depos- gravel-bed streams. During initial stages sinuous meandering of a single channel ited on stream banks. In terrestrial of meandering as the bends enlarge and or the river splits into multiply intercon- meanders vegetation helps both to en- translate downstream a depressed region nected braided channels. Both empirical courage deposition of silt and clay by of the bed (a chute) is typically left be- studies and theory have helped to define retarding near-bank flows and to add hind between the bed sediment depos- the conditions that control channel pat- additional cohesion by means of root ited on the bend interior (the ) tern (11–15). For a stream of a given and the edge of the adjacent floodplain. strength (16–18). Vegetation also inhib- flow , steep channel gradients In situations where little fine sediment is its bank erosion through flow retarda- and large ratios of channel width to in transport the chute can carry an in- flow depth are associated with braiding, tion. The difficulty of replicating the creasing portion of the flow as the main with the converse for meandering. The effects of vegetation on bank sedimenta- channel meander bend enlarges, eventu- occurrence of braiding has been related tion and stability has been an important ally leading to a cutoff. Such chute cut- to the natural tendency for sediment reason that laboratory meandering has offs have been an important factor transport to produce multiple deposi- been difficult to achieve. Recently, how- tional bars in sufficiently wide channels, ever, the use of seed sprouts has permit- which tends to split the flow as the bars ted scaling the effects of vegetation in Author contributions: A.D.H. wrote the paper. grow (13, 15). If stream banks are com- experimental channels and has encour- The author declares no conflict of interest. posed of loose gravel or sand of the aged channel meandering (1, 19, 20). See companion article on page 16936 in issue 40 of volume same size range that is transported on Past studies have focused on the role 106. the channel bed, channels tend to be of channel width and bank cohesion in 1E-mail: [email protected].

www.pnas.org͞cgi͞doi͞10.1073͞pnas.0910005106 PNAS ͉ October 13, 2009 ͉ vol. 106 ͉ no. 41 ͉ 17245–17246 Downloaded by guest on September 30, 2021 limiting the achievable in labo- ered as a requirement for development rates through greater vegetation density ratory meanders and likewise serve to of cohesive banks and a meandering would allow more complete infilling of limit the amplitude of meanders in natu- pattern. A surprising result of the flume chutes, allowing a more sinuous channel ral gravel channels with meager budgets experiments is that steady high flows to develop. However, the time required of fine sediment. In the flume study re- that only slightly submerge channel mar- to complete the experiment might be- ported here (1) transport of silt and clay gins deposit enough fine sediment to come excessive. in natural channels is scaled to smaller Developing experimental procedures laboratory channels by the use of low- to permit stable, high-sinuosity mean- density, sand-sized plastic particles that The use of seed sprouts dering in scaled laboratory experiment are carried in suspension. The bed sedi- will be a challenge for future work, but ment transported along the bed was has permitted scaling the payoff would be large in terms of coarse sand that scales as gravel in natu- understanding the critical factors re- ral channels. The low-density plastic the effects of vegetation sponsible for meander development and particles accumulated on the inner, up- to address practical issues of meander- stream side of meander bends and in experimental ing river maintenance and restoration. blocked the upstream edge of the Challenges also remain with regard to chutes, preventing appreciable diversion channels. understanding the mechanisms and envi- of flow through the chute, thus allowing ronments creating meandering channels the meanders to enlarge to amplitudes in subsea and extraterrestrial environ- and to an overall sinuosity greater than produce a stable meandering pattern ments. For example, the ancient, highly had been achieved in previous labora- sinuous channels with cutoffs found on with occasional cutoffs. tory studies. Some fine sediment also Mars (Fig. 1) are enigmatic, because Although a stable meandering pattern accumulated on the downstream end of vegetation apparently played no role in with repeated cutoffs was created by the chutes, further blocking them. The dep- Ϸ providing bank cohesion and fine sedi- osition of the fine sediment was en- flume experiments, the 1.2 observed ment deposition. Bank cohesion result- hanced by the flow retardation resulting sinuosity is considerably less than the ing in narrow channels might have been Ϸ from the presence of the alfalfa sprouts value of 3 reached in highly sinuous afforded by a large quantity of silt and that developed on emergent portions of natural channels. Braudrick et al. (1) clay in transport, by ice under perma- the sediment deposited on the inside of attribute the restricted sinuosity to the frost conditions (perhaps analogous to bends. relatively rapid bank erosion in compari- highly sinuous rivers in northern Alaska Deposition of fine sediment by over- son to scaled values in natural channels. and Siberia), or by chemical cementa- bank flows has long been consid- They suggest that reducing bank erosion tion of floodplain deposits (hardpans).

1. Braudrick CA, Dietrich WE, Leverich GT, Sklar LS (2009) 32:2937–2954. 15. Crosato A, Mosselman E (2009) Simple physics-based Experimental evidence for the conditions necessary to 8. Perucca E, Camporeale C, Ridolfi L (2005) Nonlinear predictor for the number of river bars and the transi- sustain meandering in coarse bedded rivers. Proc Natl analysis of the geometry of meandering rivers. Geo- tion between meandering and braiding. Resour Acad Sci USA 106:16936–16941. phys Res Lett 32:L03402, 10.1029/2004GL021966. Res 45:W03424, 10.1029/2008WR007242. 2. Deptuck ME, O’Byrne C, Sylvester Z, Pirmez C (2007) 9. Pittaluga MB, Nobile G, Seminara G (2009) A nonlinear 16. Allmendinger NE, Pizzuto J, Potter N, Johnson T, Hes- Migration- history and 3-D seismic geo- model for river meandering. Water Resour Res sion WC (2005) Influence of riparian vegetation on morphology of submarine channels in the 45:W04432, 10.1029/2008WR007298. stream width, eastern Pennsylvania, USA. Geol Soc Am Benin-major , western Niger Delta slope. Mar 10. Camporeale C, Perucca E, Ridolfi L (2008) Significance Bull 117:229–243. Pet Geol 24:406–433. of cutoff in meandering channel dynamics. J Geophys 17. Eaton BC, Giles TR (2009) Assessing the effect of vege- 3. Burr DM, et al. (2009) Pervasive aqueous paleoflow Res 113:F01001, 10.1029/2006JF000694. tation-related bank strength on channel morphology features in the Aeolis/Zephyria Plana Region, Mars. 11. Dade WB (2000) Grain size, and and stability in gravel-bed streams using a numerical Icarus 200:52–76. alluvial . 35:119–126. model. Earth Surface Processes and 34:712– 4. Seminara G (2006) Meanders. J Fluid Mech 554:271– 12. Leopold LB, Wolman M. G (1957) River Channel Pat- 724. 297. terns; Braided, Meandering, and Straight. (U.S. Geo- 18. Millar RG (2000) Influence of bank vegetation on allu- 5. Johannesson H, Parker G (1989) Linear theory of river logical Survey, Washington, DC) U.S. Geological Survey vial channel patterns. Water Resour J 205:59–75. meanders. Water Resour Monogr 12:181–213. Professional Paper 282-B. 19. Peakall J, Ashworth PJ, Best JL (2007) Meander-bend 6. Howard AD (1996) Modelling channel evolution and 13. Parker G (1976) On the cause and characteristic scales of evolution, alluvial architecture, and the role of cohe- floodplain morphology. Floodplain Processes, eds meandering and braiding in rivers. J Fluid Mech sion in sinuous river channels: A flume study. J Sedi- Anderson MG, Walling DE, Bates PD (Wiley, Chichester, 76:457–480. ment Res 77:197–212, 10.2110/jsr.2007.017. UK), pp 15–62. 14. van den Berg JH (1995) Prediction of alluvial channel 20. Tal M, Paola C (2007) Dynamic single-thread channels 7. Sun T, Jøssang T, Meakin P, Schwarz K (1996) A simu- pattern of perennial rivers. Geomorphology 12:259– maintained by the interaction of flow and vegetation. lation model for meandering rivers. Water Resour Res 279. 35:347–350, 10.1130/G23260A.1.

17246 ͉ www.pnas.org͞cgi͞doi͞10.1073͞pnas.0910005106 Howard Downloaded by guest on September 30, 2021