Influences of coarse bank roughness on flow within a sharply curved river bend

ELSEVIER

Geomorphology 12 (1995) 241-257

Influences of coarse bank roughness on flow within a sharply curved fiver bend Stephen D. Thorne a, David Jon Furbish b Department of Geology, Florida State University, Tallahassee, FL, USA b Department of Geology and Geophysical Fluid Dynamics Institute, Florida State University, Tallahassee, FL, USA

Received 17 February 1994; revised 26 September 1994;accepted 3 October 1994

Abstract

An experiment was performed to assess the influence of coarse bank roughness on flow within a sharply curved bend of the Ocldawaha Creek, a sand-bedded stream in northern Florida. This involved obtaining systematic measurements of flow velocity and water-surface topography when the outer bank was rough with natural vegetation, and obtaining an identical set of measurements after removing the vegetation and constructing a smooth wall along the outer bank. Results suggest that the roughness from bank vegetation systematically influences the flow field, particularly the secondary current strength and the position of the high-velocity core, because of its effect on the transverse boundary layer. The roughness essentially produces a backwater effect that inhibits outwardly directed surface flow from closely approaching the outer bank. This suppresses superelevation on the outside bank and, therefore, weakens the inwardly directed transverse pressure gradient and secondary current. The flow is steered in a downstream direction, and the core of high velocity is nearly centered in the channel. In absence of roughness from vegetation, outwardly directed surface flows approach the outer bank more directly (and earlier in the bend), superelevation on the outside bank is enhanced, and the transverse pressure gradient and secondary current are strengthened. The core of high velocity is displaced toward the outer bank, and its magnitude is increased. Moreover, the streamwise position where the high-velocity core is closest to the outer bank shifts downstream from its position of closest approach in the presence of roughness. This, in principle, should contribute to asymmetrical bend migration, whereas migration in presence of roughness should be nearly in phase with bend curvature such that bends grow in amplitude, albeit slower, and with less asymmetry.

I. Introduction

A striking feature of many meandering rivers is the self-organized regularity of sinuous shapes, manifest in the tendency for bends composing a meander train to possess similar amplitudes and wavelengths, and by persistence in the spacing of bars. Equally significant is the diversity of bend shapes that can simultaneously occur at any instant along a meander train, manifest in the varying asymmetries of bends, and by occurrences of compound bends and unusually crooked reaches. Although these parallel qualities of meanders have 0169-555x/95/$09.50 © 1995 Elsevier ScienceB.V. All rights reserved SSDIO169-555X(95)O0007-O

interested river scientists for centuries, no theory is yet available that fully clarifies how these qualities-- geometrical regularity and diversity - - mutually evolve over geomorphic time. Recent work suggests that several basic mechanisms underlie meander regularity. In particular, efforts over the past two decades to describe the mechanics of flow and sediment transport in meandering rivers, and interactions among flow and bedforms (e.g., Yen and Yen, 197 l; Engelund, 1974; Ikeda et al., 1981; Dietrich and Smith, 1983, 1984; Smith and McLean, 1984; Odgaard, 1986; Odgaard and Bergs, 1988; Ikeda and Parker,

242

S.D. Thorne. l).J. Furbish / Geomorphoh*gy 12 (I 995) 241 257

1989; Bridge, 1992; Whiting and Dietrich, 1993a, c), suggest that several mechanisms contribute to selforganization during the meandering process. For example, the flow field in a bend at any instant is partly determined by the flow conditions delivered to it from upstream, as characterized by the magnitude and transverse position of the core of high streamwise velocity, and by the secondary current strength (Leopold and Wolman, 1960; Yen and Yen, 1971; Engelund, 1974: Ikeda et al., 1981; Dietrich and Smith, 1983). The evolution of a bend is, therefore, continuously influenced by the geometry of its neighboring bend upstream, which is simultaneously evolving. Likewise, the evolution of an individual bend is not independent of conditions downstream, because backwater effects from a neighboring bend can influence upstream flow conditions (Smith and McLean, 1984). In addition, the possibility exists that meander regularity arises partly from interactions of free and forced bars, including wavelength selection by the phenomenon of resonance (Parker and Johannesson, 1989; Seminara and Tubino, 1989; Whiting and Dietrich, 1993a). These autocatalytic aspects of the meandering process, interestingly. may also contribute to diversity in bendforms (Furbish, 1991 ), possibly including the formation of compound loops that result from mutual interactions between bars and bends (Whiting and Dietrich, 1993b, c). Bend diversity is also enhanced when valley walls interfere with evolving bends, and when variations in the grain sizes and erodibility of alluvium composing the floodplain locally influence bend migration (Howard and Knutson, 1984; Howard and Hemberger, 1991 ). In this regard, bank roughness also is a potentially significant ingredient in meander evolution. Roughness produced by bank vegetation, in particular, may affect patterns of bend migration ( Thorne and Furbish, 1991 : Thorne et al., 1993). Vegetation may in some cases contribute to instability of bank sediments through toppling of trees, or by inhibiting the growth of grasses whose root networks might otherwise stabilize the banks (Murgatroyd and Ternan, 1983). Conversely, roots of the vegetation itself may stabilize channel banks by reinforcing bank sediments, in some cases leading to a narrowing of the channel (e.g., Andrews, 1984), and thereby modulate local migration rates. Equally important, vegetation can provide coarse bank roughness which strongly influences the adjacent flow field. Particularly in the humid, southeastern United

States and similar densely forested areas, the banks of rivers typically are very rough because of vegetation; only those rivers that are very large relative to the size of the vegetation along the banks exhibit within-bank flows that may be negligibly influenced by this bank roughness. Whereas the influence that bed roughness exerts on flow in bends has been described (e.g., Callender, 1969; Yen, 1970; Smith and McLean, 1984; Nakagawa et al., 1989), the influence that rough channel banks exert on flow and bend evolution has yet to be clarified. This paper examines how bank roughness from vegetation influences the near-bank velocity and the secondary current in particular. Understanding this influence is important because these aspects of flow in a bend have a significant part in governing patterns of sediment transport and bank erosion, and in turn, meander evolution. Herein we provide a qualitative assessment of the influence of vegetation which we are using to constrain related modeling efforts. We describe an experiment that involved measuring flow velocities and water-surface topography in a sharply curved bend in the presence of natural bank vegetation, and then remeasuring these after the vegetation was removed and replaced by a smooth wall. The experiment was designed to minimize effects of variations in discharge and channel dimensions so that changes in the flow field could be attributed to differences in bank roughness. Our results suggest that bank roughness systematically alters the formation and strength of the secondary current, and the magnitude and location of the highest near-bank velocity. This implies that patterns of bend migration may be significantly different from those that would occur in the absence of bank roughness.

2. Flow in a river bend

The following summary is based mainly on the studies of Dietrich and Smith ( 1983, 1984), Smith and McLean (1984), and papers in the monograph edited by Ikeda and Parker (1989), which represent a compact compilation of recent field, laboratory, and theoretical studies of flow and sediment transport in river bends. These studies concern rivers with relatively uniformly erodible floodplain material and minor, or insignificant, bank roughness, and therefore serve to introduce the

S.D. Thorne. D.J. Furbish/ Geomorphology 12 (1995) 241-257

problem in terms of bend flow occurring in absence of bank roughness because of vegetation. River channels flowing through erodible alluvium typically possess approximately symmetrical crosssections at bend crossings, which become asymmetrical at bend apices. The point bar on the inside of a bend leads to shoaling of flow, which induces near-bed flow over the upstream portion of the bar toward the outer bank. Associated with this change in flow direction are convective accelerations that are driven by a crossstream water surface slope directed toward the outside of the bend. This shoaling over the point bar is one mechanism by which flow is topographically steered through the bend (see Nelson and Smith, 1989). The curvature of the bend similarly induces a centrifugal acceleration of flow. The directional change in the flow associated with the curving bend is driven by a cross-stream pressure gradient manifest as a slope in the water surface. Superelevation, produced as nearsurface flow approaches the outer bank, drives a helical flow (the secondary current). With regard to bend erosion, this current tends to pluck sediment from the toe and slope of the outside bank as it flows down the bank and across the channel near the bottom, thereby steepening the bank and decreasing its stability. It also tends to transport this sediment across the bottom of the channel and downstream (Hooke, 1975; Yen, 1975; Dietrich and Smith, 1984; Lapointe and Carson, 1986). Secondary currents thus serve as a mechanism for eroding bank sediments and increasing migration rates. When the curvature is large enough, the transverse water-surface gradient may be greater than that in the streamwise direction resulting in a relatively strong secondary current. In this case, the angle between the outwardly directed surface flow and the inwardly directed bottom flow (helix strength) is large, which contributes to a strong transverse component of sediment transport. The strength of the secondary current therefore can significantly influence the bed morphology and boundary shear stress, and hence the evolution of the bend. The shoaling of flow associated with the point bar, together with the curvature-induced secondary current, combine to shift the core of high streamwise velocity across the channel toward the outside bank, and then back toward the inside as the flow exits the bend. Associated with this high-velocity core is a zone of maximum boundary shear stress, and a zone of maximum

243

bed-load transport; these tend to gradually shift outward through the upstream portion of the bend. Downstream, bend curvature and the slope of the next point bar tend to drive them back across the channel. This shift in the position of the high-velocity core ultimately influences the position and magnitude of bank erosion and bend migration. Considering the simple case where local migration rates are proportional to the near-bank depth-averaged flow velocity (e.g., lkeda et al., 1981; Pizzuto and Meckelnburg, 1989), an understanding of how flow in bends is influenced by rough banks is essential for describing bend migration and meandering processes, and provides the motivation for our field experiment.

3. Study area and experiment The Ocklawaha Creek (Fig. 1), located approximately 40 km southwest of Tallahassee, Florida, flows eastward to Lake Talquin, crossing beneath State Highway 267. The Ocklawaha provides a suitable site to assess the influence of bank vegetation on flow. This meandering sand-bedded creek flows through a wide floodplain that is densely vegetated with cyprus (Taxodium ascendens ) and water oak ( Quercus n igra ). The Creek drains a basin whose area is approximately 9 km2; it is entirely underlain by ancient beach terraces (Tanner, 1966). Because of the high permeability of the terrace material, channel flows largely derive as a subsurface component, particularly during low-flow periods. A significant surface-water component, however, is derived from the surrounding floodplain when it is saturated during high-flow periods. Flood hydrographs typically recede slowly. The stream water is virtually clear - - discolored only by tannin - - which allows easy observation of sand transport on the bed. In addition, small organic particles (mostly leaf fragments) that are neutrally buoyant serve effectively as flow tracers for observing local currents. The study reach is approximately 7 m wide, and has an average depth of about 1 m at bankfull flow (Fig. 1 ). It is a sharply curved bend preceded upstream by a long straight reach that delivers a symmetrical flow field and unsorted sediment to the bend. The bend has a well-developed point bar; the bed slopes steeply down into the adjacent pool. The steep outer bank is armored by boles and roots of cyprus. The pool is deep (approx-

244

S.D. Thorne, D.J. F u r b i s h / G e o m o r p h o l o g y 12 (1995) 241-257

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imately 1.4 m) relative to the average channel depth, and some roots project from its bed into the flow. The downstream bend is similar, but is not as sharply curved. The pool of the upstream bend shoals rapidly onto the downstream point bar. A well-defined thalweg exits the upstream pool then crosses over to the opposite bank. Ripples and small dunes migrate over the upstream bar, out of the pool, and along the thalweg. Four section lines were positioned over the crest of the bar and the tail of the pool for flow measurements (Fig. 1). We opted to place the sections normal to the bend centerline, rather than adjust the orientations for discharge which would be necessary for modeling purposes (e.g., Dietrich and Smith, 1983). This choice was based on our priority of obtaining flow measurements at the same sites before and after we modified the hydraulic character of the outside bank, in absence of knowing what changes in the flow field would occur. We selected the four sections anticipating that any changes in the position of the high-velocity core, and

in the strength of the secondary current, would be most pronounced at these locations. Data collected at each section consisted of bed elevations, flow velocities, and water-surface elevations, first obtained in the presence of the natural bank vegetation, and then after the vegetation was removed and replaced by a smooth wall. All measurements were taken from a wooden catwalk spanning the stream. We started our measurements at section 06, then moved to sections upstream. Velocity measurements were made at 0.75 m intervals across the channel, and at depths whose spacing decreased exponentially toward the channel bed. We used a Marsh-McBirney current meter to measure time-averaged flow speeds. Measurement durations were at least 20 s, and normally 30 s or longer. These measurements provided reasonable estimates of average speeds allowing for moderate-to-low-frequency turbulent fluctuations, but they probably do not fully represent low-frequency variations in flow associated

S.D. Thorne, D.J. Furbish/Geomorphology 12 (1995) 241-257

with passage of dunes. Flow directions were determined by first tying ribbons to the current-meter rod. The ribbons were swept downstream parallel to local flow directions, and could easily be seen. We then aligned the meter with them, and used a compass to measure the azimuth direction of the flow. In addition, we attached a swivel to the base of the current rod. This consisted of a closed aluminum cylinder into which the flat base of the current-meter rod was placed, with a layer of ball bearings above and beneath it. We also constructed a tail vane whose vertical breadth was 4 cm. The vane and swivel allowed the meter to align itself with the local flow, and allowed us to take measurements close to the channel bed (although at a few sites, roots protruding from the bed interfered with the measurements). In addition, the vane provided a measure of flow direction that was integrated over a short vertical distance. We recorded flow directions relative to the orientations of the section lines to obtain the streamwise and transverse components of velocity described below. Water-surface elevations were measured using a transit and stadia rod according to the procedure described by Dietrich and Smith (1983). These were taken at 1 m intervals across the channel, before and after velocity measurements at each section. After obtaining velocity and water-surface measurements under natural conditions, we removed the vegetation, mostly roots, that protruded into the flow from the outside bank and from the channel bed, and then constructed a smooth wall along the outside bank. Note that the large tree bole extending from the right bank at the upstream part of the bend (Fig. 1) is mostly above the channel, and does not significantly obstruct the flow. The wall spanned the distance from this bole to section 06, and from the top of the bank to the channel bed. The natural, outer bank upstream from the tree bole is smooth (without vegetation roughness), so we did not extend the wall upstream from the bole. Care was taken in maintaining the original channel width. The wall consisted of a series of wooden posts (5 cm × 5 cm) anchored to the bank and bed; these supported a wire mesh (chicken wire) that was covered with several layers of plastic and secured with wooden slats (Fig. 2). The wall was probably as hydraulically smooth (or smoother) than an alluvial bank without vegetation. We felt that placement of the wall was necessary for our purposes because it was impossible to

245

/

Fig. 2. Schematic diagram of wall constructed of chicken wire and plastic sheeting anchored with wooden slats to 5 cm × 5 cm posts.

completely remove the bank vegetation and the roughness it produced. We made the first set of measurements with the natural bank on 29 July 1991, then constructed the wall and made the second set on 5 August 1991. The discharge was about 1.83 m 3 s - l with the natural bank, and steadily decreased to about 1.72 m 3 s - 1 when the wall was in place. These values are slightly less than bankfull flow. The decrease in discharge of about 6% is considered below. Although we do not have supporting data, we suspect that the bed had ample time to adjust to the new flow and bank conditions during the interval between measurement surveys, because sediment transport in the Creek at bankfull is rapid, as visibly evidenced by ripple and dune migration. As described below, the bed changed little between surveys.

4. Results The figures referred to below in some cases contain redundant information. We have selected them to reveal specific features of the flow field that might not otherwise be as apparent from another perspective. Original data are provided elsewhere (Thorne, 1993). 4.1. Flow velocities Flow velocities at section 4.5 (Fig. 3) were weak near the right (outer) bank and increased in magnitude away from the bank; flow was slowed near the bank and the channel bed. Surface flows were directed toward the outer bank in both surveys at angles up to 27 ° and 25 ° from the local streamwise direction, before

246

S.D. Thorne, D.J. Furbish/Geomotphology 12 (1995)241-257

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At section 5.5 (Fig. 4), the highest velocities (reaching a maximum of 0.48 m s - 1) occurred in the center of the channel where the influence of the bank was minimal. Surface flow near the outer bank was directed more downstream than at sections 4.5 and 05. When bank vegetation was removed, the magnitudes of flow velocities near the right bank increased substantially. Removal of the bank roughness led to a total average increase in velocity of 155% within 1 m of the right bank, with an 85% increase in velocities at the surface. The secondary current strength was enhanced by a maximum of 110% in the channel center (3.5 m from the right bank), and 1,150% at the left bank. Moreover, near-bed flows as far as 5 m from the outer bank were significantly affected. These near-bed velocities had

S.D. Thorne, D.J. Furbish/ Geomorphology 12 (1995) 241-257

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Fig. 4. Vector diagramsof velocity (m s - ~) at sections 5.5 and 06 with natural bank (A) and smoothwall ( B ); numbers indicate relative depth, increasing toward the channel bed; stations begin at right bank. higher magnitudes, and were directed more inward than when the bank vegetation was present. Similar conditions existed at section 06 (Fig. 4). The most striking changes at this section, with removal of the bank roughness, included a large increase in the magnitude of the surface velocity near the outer bank (from 0.08 m s - 1 to 0.51 m s - l ) , a strengthening of the deeper flows over the left half of the channel (as illustrated by an average increase of 53% over the left three measurement sites) and an overall strengthening of the secondary current. 4.2. Streamwise velocity components Vertical and cross-channel velocity profiles The streamwise component of velocity at section 4.5, with the natural bank, varied significantly throughout the fluid column and over the width of the channel (Fig.

5a). The lowest velocities occurred near the bank (0.25 m s - 1 at a depth of 0.6 m compared to a maximum of 0.41 m s - ~2.25 m from the right bank). With the wall, streamwise components noticeably increased near the bed ( Fig. 5b) and across most of the channel ( Fig. 6a). At section 05 (Fig. 5c), vertical profiles were irregular, reflecting how vegetation along the outer bank influenced flow over much of the channel width. With the wall (Fig. 5d), the flow field adjusted such that the velocity profiles were more orderly, and more closely resembled a logarithmic form typically observed with unidirectional flow (e.g., Schlichting, 1979, fig. 18.5, p. 567). The depth-averaged velocity values at section 05 with the smooth wall increased to a nearly uniform value across the channel (Fig. 6b). Vertical profiles at section 5.5 (Figs. 5e and 5f) also reflected an increase in order, stemming in part from

S.D. Thorne, D.J. Furbish/ Geomorphology 12 (1995) 241 257

248

depth-averaged velocity occurred near the bank (Fig. 6c), a reduction in this velocity was observed in the center of the channel. Flow at section 06 was affected in a similar manner: with the wall, less resistance to

the enhanced velocities at the measurement site nearest the bank. However, little change occurred at distances of 3.5 m, 4.25 m, and 5 m from the outer bank (Figs. 5g and h). In addition, although an increase in the

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flow near the bank occurred, and differences among flow velocities across the channel were reduced. This

is reflected by flow velocities nearest the right bank (at 0.03 m and 0.2 m depth) that increased 127% and

S.D. Thorne. D.J. Furbistt / Gemnoq~hology 12 (1995) 241-257

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Contour maps of streamwise velocity' Streamwise components of velocity at section 4.5 gradually increased away from the bed and bank ( Fig. 7a). A small core of high velocity of approximately 0.42 m s - ~occurred on the left side of the channel. This is expected; as water enters a sharply curved bend, an irrotational influence tends to keep the high velocity core near the inside of the channel (Parker and Andrews, 1986; also see Fig. 9 of Smith and McLean, 1984, p. 1312). As the flow shoals onto the point bar farther downstream, the high velocity core shifts toward the outer bank (e.g., Dietrich and Smith, 1983: Smith and McLean, 1984). Velocities near the vegetated bank were low: 0.13 m s ~ as far as 1.5 m away from the outer bank. With the wall (Fig. 7b), surface

velocities near the outer bank increased by 55% 1.5 m from the right bank (0.18 m s ~ to 0.28 m s - ~ ) , but the overall configuration of the flow field remained relatively unchanged, with the core of high velocity remaining in the same location. Velocities near the center of the pool, approximately 2.0 m from the outer bank, however, increased by 100% (at a depth of 1.4 m). At section 05 (Fig. 7c) streamwise components of velocity near the bank were significantly higher than at section 4.5. This is particularly true of those at the surface, which increased from less than 0.14 m s with the natural bank to 0.30 m s - ] with the smooth wall at a position 1 m from the right bank. The effect of bank and bed vegetation at this section was particularly noticeable, as reflected by low velocities associated with roughness elements extending into the channel (Fig. 7c). Relative to section 4.5, the position of the high-velocity core shifted toward the center of

S.D. Thorne, D.J. Furbish / Geomorphology 12 (1995) 241-257

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252

S.D. Thorne, D.J. Furbish / Geomorphology 12 (1995)241-257

the channel, which is expected as shoaling over the point bar becomes more significant. With the wall, the streamwise flow field was altered such that several locations of high velocity existed (Fig. 7d). These corresponded to the position of highest velocity when the vegetation was in place; however, the magnitude increased by about 5% (from 0.38 m s J to 0.40 m s - z). A well-defined high velocity core was observed in the center of the channel and, following the same pattern as the upstream sections, velocities in the vicinity of the outer bank increased noticeably (from 0.30 m s - 1 to 0.36 m s - ~ at the surface I m from the right bank). The position of the core of high velocity at section 5.5, with bank vegetation, was essentially the same as at section 05 (2.5 to 3.0 m from the right bank) (Fig. 7e). Streamwise velocities in this core exceeded 0.48 m s ~, then rapidly decreased toward the outer bank. With the wall, however, the high-velocity core shifted all the way to the right bank (Fig. 7f), with velocities exceeding 0.50 m s - 1 (the highest measured). A similar core, but of lower magnitude (approximately 0.42 m s i), occurred in the same position that was occupied by the high velocity core in the presence of the vegetation, but the overall flow field was significantly altered, as characterized by the dramatic increase in near-bank velocities (greater than 100% in some places). At section 06 (Fig. 7g), the influence of bed and bank roughness on the flow was reflected by compression of velocity contours in the vicinity of the roughness elements. Vegetation on the bed (at 1.5 m to 1.75 m from the outer bank) influenced flow as far as 20 cm from the water surface. Roughness along the right bank produced a similar effect. A well-defined core of high velocity (0.50 m s - l ) at approximately 2.5 m from the outer bank remained stationary after the bank was altered (Fig. 7h). The most striking change was an increase in velocities near the outer bank throughout most of the fluid column.

4.3. Transverse velocity components At section 4.5 (Figs. 8a and 8b), outwardly directed near-surface flow and inwardly directed near-bed flow were apparent, as is typical of bend flow. Transverse components of velocity varied little between the two surveys. Likewise, at section 05, transverse compo-

nents varied little, with the possible exception of a less positive transverse component near the right bank and at the center of the channel (Figs. 8c and 8d). At section 5.5 (Figs. 8e and 8f), in contrast, nearbed transverse flow increased noticeably over the left half of the channel (by an average of 79% over three measurement sites), and the bottom current, in general, was better developed over the entire width. Although the directions of the cross-stream components of the surface flow remained the same, the flow velocities increased, for example, by 57% and 48% at positions 2.0 m and 2.75 m from the right bank. At section 06 (Figs. 8g and 8h), a similar increase in the strength of the transverse near-bed flow occurred; as described below, this reflects an adjustment in the secondary current to enhanced superelevation of the water surface.

4.4. Bed and water-surface elevations Bed elevations changed negligibly between surveys (at least within expected variations because of local dune migration and survey error). With the wall, the transverse water-surface slope remained essentially the same at section 4.5, remained the same or possibly decreased slightly at section 05, noticeably increased at section 5.5, and possibly increased slightly at section 06 (Fig. 9, Table 1 ). The significance of this increase in superelevation at the outside bank is discussed below. The transverse slope also decreased from a maximum near the bend apex to essentially zero at the inflection point (section 06) (Table 1 ). The computed negative slope at section 06 with the natural bank may merely reflect surveying error given that the slope is nearly zero.

5. Discussion The data indicate that the flow field changed significantly when vegetation along the outer bank was removed and replaced by a smooth wall. The small difference in discharge, and channel dimensions that changed little with the addition of the wall, suggest that adjustments in the flow field resulted primarily from the absence of bank roughness. The increase in depthaveraged velocity throughout the reach, even though the discharge decreased by 6% between surveys, under-

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S.D. Thorne, D.J. Furbish/Geomorphology 12 (1995) 241-257

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was steered in a downstream direction, and the core of high velocity was nearly centered in the channel. In contrast, superelevation was better developed with the smooth wall and occurred earlier in the bend. The associated transverse pressure gradient was large enough to drive a strong secondary flow toward the inner bank such that the helix strength - - the angle between the near-surface and near-bed flows - - increased over much of the channel bed (Fig. 10). The overall friction through the smooth bend presumably was less although our data are insufficient to compute an effective friction coefficient). In addition, surface velocities increased throughout the reach when the wall was in place. Without the drag associated with bank roughness. near-bank velocities remained high along the entire length of the wall. The clearest consequence of this was that the high velocity core shifted toward the outer bank in the downstream part of the pool (sections 5.5 and 06). The significance of this with regard to bank erosion is discussed below. In absence of the vegetation, because superelevation occurred earlier in the bend, was of greater magnitude, and extended farther downstream, several observations regarding channel evolution can be made. First, because the secondary current develops early in the bend (in a spatial sense), removal of sediment from the outer bank (and hence, lateral migration) may begin farther upstream than in the presence of the vegetation. Second, because the strength of the secondary A

B

o

scores the importance of the influence of bank vegetation on bend flow. With the smooth outer bank, surface flows closely approached the bank early in the bend, and with relatively high velocities. Flow drag previously associated with bank roughness was reduced, and the cross-channel extent of the lateral boundary layer decreased relative to its extent with the vegetated bank. In effect, the flow resistance provided by bank roughness produced a backwater effect that inhibited outwardly directed surface flow from closely approaching the outer bank. This suppressed superelevation on the outside bank and, therefore, weakened the inwardly directed transverse pressure gradient and secondary current. The flow

r ~

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S.D. Thorne, D.J. Furbish / Geomorphology 12 (1995) 241-257

Fig. 11. Paths of high velocityfilamentfor the natural bank (short dashed line) and for the smoothwall (heavy line); phase shifts are defined by positions of maximumdisplacement of filament from centerline relativeto bend apex,for the naturalbank and the smooth wall; dashed arrow is expected path in absenceof flow obstruction near section06. current increases, a relatively strong transverse component of sediment transport should develop. This could enhance the growth of the point bar through convergence of sediment at the tall of the bar, which would strengthen the convective accelerations that help shift the filament of high velocity toward the outer bank. If sustained, this could enhance lateral migration as the core is shifted closer to the outside bank. The filament of high velocity, defined here in terms of the position of the core of highest velocity, impinges on the outer bank at section 5.5 in the presence of the smooth bank (Fig. 11). The likelihood for lateral migration at this location is high. In principle, the filament of high velocity should remain near the bank until it exits the bend, and then enter the downstream bend near its inside bank. (The data at section 06, however, indicate a path away from the outer bank, which results from the local influence of a large obstruction immediately upstream. If the position of the filament is defined in terms of depth-averaged velocities, this position would remain close to the right bank.) In contrast, backwater effects induced by bank roughness deflect the surface currents away from the bank and downstream. Because this delays development of superele-

255

vation and the secondary current, erosion of bank sediment would not begin as far upstream as with a smoother outer bank. The extent to which bank roughness affected flow throughout much of the channel width is further illustrated by the streamwise reduction of helix strength when bank vegetation was present (Fig. 10a). With the removal of the bank roughness, wall effects did not extend as far into the channel, and helix strength along the channel centedine remained high over the full distance spanned by the study sections (Fig. 10b). Moreover, because the core of high velocity did not impinge on the outer bank when the vegetation was present, lateral migration would be further subdued relative to migration associated with the smooth wall. A comparison of the high velocity filaments (Fig. 11) reveals that, with bank roughness, the filament is displaced toward the center of the channel. In a river with large vegetation roughness along its banks, this influence over time should tend to reduce the lateral migration of the channel banks, and should produce an upstream phase shift in sites of maximum migration assuming that the rate of local migration is proportional to the near-bank velocity. This phase shift (Fig. 1 l) is determined by the location of the highest near-bank velocity relative to the bend apex. As a point of reference, an increasing phase shift with decreasing bed roughness is implicitly contained in the relative roughness parameter of the linear model of bend flow from Ikeda et al. ( 1981 ) ( see also Parker and Andrews, 1986 and Furbish, 1991 ), and in the linear model of Johannesson and Parker (1989). A phase shift associated with bed roughness is explicitly contained in the linear model of bend flow from Odgaard (1986), apparent as a shift in the position of the onset of bank erosion in bends of the Nishnabotna River, Iowa (Odgaard, 1987). A similar displacement of highest near-bank velocities to a position downstream of the curvature maximum is mildly apparent in surface velocity vectors plotted in fig. 8 of Smith and McLean (1984, p. 1312), although this result is only indirectly related to roughness via variations in turbulent coupling. Thus, although the sources of flow resistance differ between these models and our experiment, the effects of this resistance are qualitatively similar. The position where the high-velocity filament reaches its maximum displacement from the centerline (and is closest to the outer bank) is well downstream from the bend apex in the case of the smooth bank (Fig.

S.D. Thorne, D.J. Furbish/Geomorphology 12 (1995) 241-257

256

A

thereby "delaying" adjustment to a fully developed bend-flow state compatible with the local bend curvature. Thus, large bank roughness influences flow within individual bends in a way that suppresses bend interactions, inasmuch as the local flow field and bend migration are only weakly influenced by upstream bend conditions. This mechanism probably is manifest as a tendency for recurrence of symmetrical bend forms.

6. Conclusions

.....

EARLY STATE LATE STATE

Fig. 12. Schematicdiagramof three instancesduringbend migration (short dashed lines are early state, solid lines are latest state) for large phase shift (A) and small phase shift (B) in high-velocity filament: flow is frombottomto top; note predominantdownvalley migration (A) versustransversegrowth (B) of bends. 11 ). Conversely, the position where the high-velocity filament reaches its maximum displacement from the centerline is closer to the bend apex with the rough bank. This in principle should contribute to asymmetrical bend migration in the case of the smooth bank, whereas migration in presence of roughness should be nearly in phase with bend curvature such that bends grow in amplitude, albeit slower, and with less asymmetry (Fig. 12) (Thorne et al., 1993). In effect, increasing roughness suppresses the interaction between neighboring bends. The velocity structure delivered to a rough bend from upstream is quickly modified by turbulence generated within the lateral boundary layer, such that the flow field adjusts to a fully developed state after a short distance into the bend in response to the local bend geometry and roughness. With smooth bends, the flow structure that develops within one bend persists for a greater distance downstream into the next bend before being fully dissipated,

Our experiment on the Ocklawaha Creek suggests that flow resistance from bank vegetation can exert a sufficiently strong influence on the adjacent flow field to systematically affect locations and rates of lateral bend migration. In the absence of bank vegetation, flow approaching the outer bank encounters less resistance; the extent of the transverse boundary layer is reduced and the filament of high velocity is displaced toward the outer bank. Helix strength is high, particularly along the channel centerline, increasing the potential for transverse sediment transport throughout the bend. In the presence of bank vegetation, depth-averaged velocities are lower, and flow resistance from the roughness along the bank leads to a well-developed transverse boundary layer. Lower velocity flows in effect are deflected downstream, and the associated cross-stream pressure gradient is weak. Helix strength is high near the entrance to the bend, but rapidly decreases downstream as bank vegetation increasingly influences the flow structure across much of the channel width. The filament of high velocity remains closer to the channel centerline, and the location where it most closely approaches the outer bank is farther upstream than in the absence of the vegetation. In absence of bank roughness, the location of the high-velocity filament in principle should contribute to asymmetrical bend migration, whereas migration in the presence of roughness should be nearly in phase with bend curvature such that bends grow in amplitude, albeit slower because of the armoring effect of the vegetation, and with less asymmetry.

Acknowledgements This work was partly supported by the Geological Society of America (Grant 4821-91 to SDT) and the

S.D. Thorne, D.J. Furbish / Geomorphology 12 (1995) 241-257 N a t i o n a l S c i e n c e F o u n d a t i o n ( E A R - 9 0 0 4 6 4 6 to D J F ) . W e are grateful to the l a n d o w n e r s for a l l o w i n g a c c e s s to the O c k l a w a h a study site. J a m e s P i z z u t o a n d P e t e r W h i t i n g p r o v i d e d t h o u g h t f u l r e v i e w s o f an earlier version o f this paper.

References Andrews, E.D., 1984. Bed-material entrainment and hydraulic geometry of gravel-bed rivers in Colorado. Geol. Soc. Am. Bull., 95: 371-378. Bridge, J.S., 1992. A revised model for water flow, sediment transport, bed topography and grain size sorting in natural river bends. Water Resour. Res., 28:999-1013. Callender, R.A., 1969. Instability and river channels. J. Fluid Mech., 10: 129-158. Dietrich, W.E. and Smith, J.D., 1983. Influence of the point bar on flow through curved channels. Water Resour. Res., 19:11731192. Dietrich, W.E. and Smith, J.D., 1984. Bed load transport in a river bend. Water Resour. Res., 20: 1355-1380. Engelund, F., 1974. Flow and bed topography in channel bends. J. Hydraul. Div. Am. Soc. Civ. Eng., 100: 1631-1648. Furbish, D.J., 1991. Spatial autoregressive structure in meander evolution. Geol. Soc. Am. Bull., 103: 1576-1589. Howard, A.D. and Hemberger, A.T., 1991. Multivariate characterization of meandering. Geomorphology, 4: 161-186. Howard, A.D. and Knutson, T.R., 1984. Sufficient conditions for river meandering: a simulation approach. Water Resour. Res., 20: 1659-1667. Hooke, R.L., 1975. Distribution of sediment transport and shear stress in a meander bend. J. Geol., 83: 543-565. Ikeda, S. and Parker, G. (Editors), 1989. River Meandering. Am. Geophys. Union, Washington, DC, 485 pp. Ikeda, S., Parker, G. and Sawai, K., 1981. Bend theory of river meanders, Part 1: Linear development. J. Fluid Mech., 112: 363377. Johannesson, H. and Parker, G., 1989. Linear theory of river meanders. In: S. Ikeda and G. Parker (Editors), River Meandering. Am. Geophys. Union, Washington, DC, pp. 181-213. Lapointe, M.F. and Carson, M.A., 1986. Migration patterns of an asymmetric meandering fiver: The Rouge River, Quebec. Water Resour. Res., 22:731-743. Leopold, L.B. and Wolman, M.G., 1960. River meanders. Geol. Soc. Am. Bull., 71: 769-793. Murgatroyd, A.L. and Teman, J.L., 1983. The impact of afforestation on stream bank erosion and channel form. Earth Surf. Process. Landforms, 8: 357-369. Nakagawa, H., Tsujimoto, T. and Shimizu, Y., 1989. Turbulent flow with small relative submergence. Int. Workshop on Fluvial Hydraulics of Mountain Regions, pp. A 19-A30.

257

Nelson, J.M. and Smith, J.D., 1989. Evolution and stability of erodible channel beds. In: S. Ikeda and G. Parker (Editors), River Meandering. Am. Geophys. Union, Washington, DC, pp. 321377. Odgaard, A.J., 1986. Meander-flow model I: development. J. Hydraul. Eng., 112:1117-1136. Odgaard, A.J., 1987. Streambank erosion along two rivers in Iowa. Water Resour. Res., 23: 1225-1236. Odgaard, A.J. and Bergs, M.A., 1988. Flow processes in a curved alluvial channel. Water Resour. Res., 24: 45-56. Parker, G. and Andrews, E.D., 1986. On the time development of meander bends. J. Fluid Mech., 162: 1361-1373. Parker, G. and Johannesson, H., 1989. Observations on several recent theories of resonance and overdeepening in meandering channels. In: S. Ikeda and G. Parker (Editors), River Meandering. Am. Geophys. Union, Washington, DC, pp. 379-415. Pizzuto, J.E. and Meckelnburg, T.S., 1989. Evaluation of a linear bank erosion equation. Water Resour. Res., 25: 1005-1013. Schlichting, H., 1979. Boundary Layer Theory. McGraw-Hill, New York, 817 pp. Seminara, G. and Tubino, M., 1989. Alternate bars and meandering: free, forced and mixed interactions. In: S. Ikeda and G. Parker (Editors), River Meandering. Am. Geophys. Union, Washington, DC, pp. 267-320. Smith, J.D. and McLean, S.R., 1984. A model for flow in meandering streams. Water Resour. Res., 20: 1301-1315. Tanner, W.F., 1966. Late Cenozoic history and coastal morphology of the Apalachicola river region, western Florida. Deltas in Their Geologic Framework. Houston Geological Society. Thorne, S.D., 1993. Influences of coarse bank roughness on flow within a sharply curved fiver bend (M.Sc. thesis). Florida State University, Tallahassee, 126 pp. Thorne, S.D. and Furbish, D.J., 1991. Influences of coarse bank roughness on flow within a sharply curved river bend. EOS Trans. Am. Geophys. Union, 72(44): 219 (abstract). Thorne, S.D., Croup, V.N. and Furbish, D.J., 1993. Modem fluvial processes in a sand-bedded meandering stream: flow structure, sediment transport, bed forms and bend migration. In: S. Kish (Editor), Geologic Field Studies of the Coastal Plain in Alabama, Georgia, and Florida. Southeastern Geological Society, Guidebook 33, pp. 75-89. Whiting, P.J. and Dietrich, W.E., 1993a. Experimental constraints on bar migration through bends: implications for meander wavelength selection. Water Resour. Res., 29:1091-1102. Whiting, P.J. and Dietrich, W.E., 1993b. Experimental studies of bed topography and flow patterns in large-amplitude meanders 1: observations. Water Resour. Res., 29: 3605-3614. Whiting, P.J. and Dietrich, W.E., 1993c. Experimental studies of bed topography and flow patterns in large-amplitude meanders 2: mechanisms. Water Resour. Res., 29: 3615-3622. Yen, C.L., 1970. Bed topography effect on flow in a meander. J. Hydraul. Div. Am. Soc. Civ. Eng., 96: 57-73. Yen, B.C., 1975. Spiral motion and erosion in meanders. In: 16th Congr. Int. Assoc. Hydraul. Res. Proc., pp. 338-346. Yen, C. and Yen, B., 1971. Water surface configuration in channel bends. J. Hydraul. Div. Am. Soc. Civ. Eng., 97: 303-321.