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Evolution of Meander Loops

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Evolution of Meander Loops JAMES C. BRICE Department of Earth Sciences, Washington University, St. Louis, Missouri 63130 Evolution of Meander Loops ABSTRACT pound meander loops described in this report. However, attention here is confined to the form and evolution of these and other mean- The evolution of the meanders on reaches of 10 alluvial streams in der types that occur on natural streams, a matter that needs to be the United States is reconstructed, and a scheme for the evolution clarified before further speculations are made on the mechanics of and classification of meander loops, derived from a study of the meandering. meandering pattern of 125 alluvial streams, is proposed. In the main Meander-loop evolution, as described and illustrated here, has evolutionary trend, a low symmetrical arc of approximately con- been interpreted mainly from the sequential development of mean- stant curvature tends to increase in height but decrease in radius as it der scrolls as shown on aerial photographs and from the shift of grows. When its length exceeds its radius, the arc is termed a simple stream position as determined from sequential aerial photographs. symmetrical meander loop. A simple loop becomes asymmetrical by Most old maps have sufficiently great planimetric errors so that they the growth on its perimeter of a second arc of constant curvature, are not useful for this purpose. Aerial photographs and recent U.S. which is commonly tangent to the first and curved toward the same Geological Survey topographic maps have been acquired for about side of the stream. A simple loop becomes compound when a second 125 reaches of meandering streams in the United States, and loop arc on its perimeter has developed into a loop. Four main categories forms on all of these reaches have been studied. However, few river of loops (simple symmetrical, simple asymmetrical, compound flood plains show meander scrolls with sufficient clarity for interpre- symmetrical, and compound asymmetrical) and about 16 form types are proposed. The compound loops are regarded as aberrant forms of indefinite radius and length, but the meandering patterns can be analyzed into simple loops whose properties can be measured and treated statistically. INTRODUCTION It is generally known that the evolution of meander loops on natural streams is likely to include downstream migration, increase in amplitude, and eventual cutoff at the neck; but specific informa- tion as to how the different loop forms evolve seems to be lacking in the literature. This paper presents a scheme for the evolution and classification of meander loops and demonstrates its application to some meandering streams in different geomorphic regions of the United States. The terms "meander" and "meander loop" are some- times used interchangeably, but according to the usage of Leopold and others (1964, p. 295), which is followed here, a meander con- sists of a pair of opposing loops. On natural streams, however, a meander loop is not usually paired with another loop of the same size and form. The hypothetical development of meanders is illustrated and de- scribed in a general way by Davis (1902) and by Lobeck (1939, p. 226). The relevant discussion in Leopold and others (1964) is di- rected mainly toward the mechanics of meandering rather than the evolutionary development of meander forms. Langbein and Leopold (1966) proposed that meanders tend toward the development of a stable form (a "sine-generated" curve) tha t minimizes the sum of the squares of the changes in direction for each successive unit length, but the stages by which such a form may develop are not discussed. An account of migration at certain bends of the lower Mississippi River is given by Carey (1969). Daniel (1971) analyzed the growth of several meanders on streams in Indiana, including the White River, from which he concluded that the process of channel move- ment in a meander system involves rotation and translation of meander loops and an increasing path ler.gth. Handy (1972) plotted the growth of a meander in the Des Moines River for a period of about 90 yr and showed that the rate of growth slowed gradually as the channel approached the edge of the meander belt. Lewin (1972) has described the late-stage growth of meanders on some gravel-bed rivers in Wales. As meander length increases, the meander form increases in complexity which is attributed to the effects of evenly spaced riffles on the stream bed. The late-stage Figure 1. Scheme for evolution and classification of meander loops. Flow direction is meanders illustrated by Lewin are apparently the same as the com- left to right for these and all subsequent illustrations. Geological Society of America Bulletin, v. 85, p. 581-586, 6 figs., April 1974 Downloaded from http://pubs.geoscienceworld.org/gsa/gsabulletin/article-pdf/85/4/581/3443619/i0016-7606-85-4-581.pdf by guest on 29 September 2021 582 J. C. BR [Ci- tation of meander evolution, and meanders on Few rivers grow at a fast enough rate for evolutionary trends to be discerned in the maximum time span (about 30 yr) between photographs. The White River and the East Fork White River in Indiana have both distinct meander scrolls and a rapid rate of meander growth, and several examples are therefore drawn from these rivers. Neither meander loops that are incised in bedrock nor alluvial loops th at are \ * J Y //!/ in contact with valley sides have been used as examples; nor have I used meanders that might have evolved with the "underfit" condi- / Xl/ 0 5 KM tions postulated by Dury (1964). With the exception of the Maamee River meanders, all meanders used as examples have probably evolved within the past 500 yr, as indicated either by historical records or by extrapolation of measured migration rates. " Jillw Meander loops and meandering reaches are represented on the illustrations herein by a single line that represents the stream center- m '••Nfcfji ^^ line. Where a stream centerline is traced from maps or aerial photo- graphs, it applies to the stream at a stage near the median point on Mx.7^ V/ i^^tAo M the flow duration curve, which is an approximation to the modal stage and to the "normal" stage used by the Topographic Division of the U.S. Geological Survey for representation of streams on maps. The centerline at beads is drawn halfway between the shoreline of the point bar and the cut bank on the outside of bends. Reconstruction of former stream centerlines from meander scrolls has been based on the assumptions that a stream centerline is parallel I . • • • f to a contemporaneous meander scroll and that contemporaneous 0 500 M scrolls of adjoining loops can be correlated on the basis of trend and position. All map references, given in the captions of illustra:ions and elsewhere, apply to U.S. Geological Survey topographic maps. Figure 3. Evolution of simple asymmetrical meander loops. A, Mississippi River On all illustrations, the flow direction is from left to right and the betveen New Madrid, Missjuri, and Dyersburg, Tennessee (Dyersburg 1:250,000); metric scale is used. cent :rlines prior to 1944 intei preted from chronological sequence of alluvial deposits as Circular arcs are inscribed on the loops of Figure 1 for compara- illus rated by Fisk (1944, PI. j 2, Sheet 3). B, White River near Petersburg, Indiana (Iona 7%'I; centerline of 1937 (heiviest line) from aerial photograph and prior centerlines tive purposes to indicate the general geometry and symmetry ol the intei preted from meander sciolls. C, Elkhorn Fiver, Scribner, Nebraska (Scribner 7Vi' idealized forms. For the evolutionary scheme, an approximate ft of and Uehling 7 V;':. Redrawn from Bentall and others (1971, p. 20). circular arcs to segments of the meandering pattern is suffic ent. Such approximation can be quickly ascertained by fitting one of a successive small segments of the stream centerline against distance as series of concentric circles, inscribed on transparent film, to the measured along the stream, according to the useful method devised pattern. Curvature can also be studied by plotting the angular devia- by Langbein and Leopold (1966). Segments of the resulting plot, tion from mean downstream direction (or simply the azimuth) of which have a uniform slope, represent arcs of uniform curvature. Langbein and Leopold |p. H4) reported that the radius of curvature is nearly constant for £ full third of the length of a meander loop. Plots made in the cou-se of this study indicate that segments of constant curvature are much more prominent in the geometry of most meanders, which apparently have not attained the ultimate equilibrium form propesed by Langbein and Leopold. A quantitative analysis of the whole meandering pattern on natural streams must be preceded by a careful consideration of what forms are to be measure d. This paper is intended to provide a basis for such analysis by def ning and classifying meander loops and by demonstrating the genstic relations between loops of different conf guration. The fit of circular arcs to a meandering reach and the technique proposed for quantitative analysis of the pattern are de- monstrated by an example at the end of this paper. SCHEME FOR EVOLUTION AND CLASSIFICATION The scheme of Figure 1 applies to about 125 reaches of meander- ing rivers in the United States, from which examples corresponding to the different loop forns will be cited. The sequence of forms A through C in Figure 1 tepresents an evolutionary trend in which meander ioops originate as stream segments of approximately con- stant curvature, or low circular arcs, that increase in height with time. Length of an arc i:; measured along a chord drawn between point; of tangency with adjoining arcs.
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