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Hydrologic control of spatial patterns of suspended sediment concentration at a stream confluence
Journal of
Hydrology ELSEVIER
Journal of Hydrology 168 (1995) 251-263
[t]
Hydrologic control of spatial patterns of suspended sediment concentration at a stream confluence Stephen T. Kenworthy 1, Bruce L. Rhoads* Department of Geography, 220 Davenport Hall, 607 S. Matthews Ave., University of Illinois, Urbana, IL 61801, USA
Received 8 March 1994; revision accepted 18 September 1994
Abstract
A conceptual model of the relationship between incoming hydraulic conditions and spatial patterns of suspended sediment at a stream confluence is evaluated using suspended-sediment data collected at a small stream confluence in east-central Illinois, USA. Patterns of normalized sediment concentrations at a cross-section near the exit of the confluence are a function of the ratios of momentum flux and mean sediment concentration in the upstream channels. These patterns reflect a shift in the location of the shear layer toward the outer bank as momentum ratio increases. Appreciable cross-channel mixing occurs within a distance of four channel widths downstream from the confluence. These findings suggest that confluence hydrodynamics may have important effects on the dispersal of dissolved or suspended substances in headwater areas of channel networks.
1. Introduction
A c c u r a t e p r e d i c t i o n o f the dispersal o f solutes o r s u s p e n d e d solids t h r o u g h river n e t w o r k s requires d e t a i l e d k n o w l e d g e o f the h y d r o l o g i c , h y d r a u l i c , a n d g e o m o r p h i c c o n t r o l s o f t r a n s p o r t m e c h a n i s m s in v a r i o u s types o f fluvial e n v i r o n m e n t s . T h e two p r i m a r y t r a n s p o r t m e c h a n i s m s c o n t r o l l i n g d i s p e r s i o n in n a t u r a l rivers are differential a d v e c t i o n , w h i c h is related to cross-sectional v a r i a t i o n s in d o w n s t r e a m velocity, a n d c r o s s - c h a n n e l mixing, which is a f u n c t i o n o f s e c o n d a r y flow a n d transverse t u r b u l e n t diffusion ( Y o u n g a n d Wallis, 1993). B o t h m e c h a n i s m s are s t r o n g l y influenced b y s p a t i a l v a r i a t i o n s in c h a n n e l m o r p h o l o g y a n d p l a n f o r m , b u t c r o s s - c h a n n e l m i x i n g * Corresponding author. J Present address: Department of Geography and Environmental Engineering, The John Hopkins University, Baltimore, MD 21218-2686, USA. 0022-1694/95/$09.50 © 1995 Elsevier Science B.V. All rights reserved SSDI 0022-1694(94)02644-0
252
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specifically is enhanced by geomorphic features that induce transverse fluid motion, such as meander bends (Fischer, 1969). Stream confluences, or locations where water, solutes, and sediment from two or more sources combine, are also important transverse-mixing environments. Previous experimental work and field studies have shown that flow dynamics at stream confluences are characterized by secondary circulation, flow separation, and the development of vertical shear layers, all of which locally should enhance the efficacy of transverse mixing (Best, 1987; Best and Roy, 1991; Rhoads and Kenworthy, 1994). However, few field studies have investigated patterns of transverse mixing in the immediate vicinity of confluences. Roy et al. (1988) observed only minor transverse mixing within the confluence of two small (< 10 m wide), coarse-bed streams in Quebec, but found that rapid mixing of the two flows occurred over transverse boulder 'ribs' located immediately downstream from the confluence. The purpose of this paper is to examine the influence of variations in incoming hydrologic conditions on spatial patterns of suspended sediment concentration at the confluence of two small streams. The results provide insight into the influence of confluences on transverse mixing in headwater portions of drainage networks.
2. Conceptual framework At stream confluences, there is a region where the merging tributary flows must adjust to the planform geometry of the confluence, thereby producing a distinctive set of hydrodynamic features (Fig. 1). This region defines the confluence hydrodynamic
N••.
\ ~..~"'.
•"
Upetroam Junction ".\
0
corner Junction Corner
",%
i
"'\
Rec£raulatlon
Zone
F f
!
....... /'.._ ...... Stagnation
..... _,. Zone ...............
L i m i t of CHZ
.................... F r e e S h e a r L a y e r s
Fig. 1. Flow dynamics at stream confluences(partly after Best, 1987)
S.T. Kenworthy, B.L. Rhoads / Journal of Hydrology 168 (1995) 251-263
253
zone (CHZ). Flow structure within this zone depends primarily on three factors: the junction angle, the planform symmetry of the confluence, and the momentum flux ratio (Mr) of the incoming flows (Mosley, 1976; Best, 1987). The spatial extent of the CHZ corresponds to the distance over which the flow field is influenced by pressure gradients associated with flow convergence and realignment at the confluence or by a free shear layer between the combining flows (Fig. 1). The transitional downstream boundary of the CHZ is marked by the gradual realignment of mean streamlines with the channel margins and the dissipation of vorticity associated with the shear layer. Beyond the CHZ the entire flow field of the receiving stream is adjusted to the gradient and morphology of the downstream channel. At an asymmetrical confluence of a tributary and main stream that have similar widths but different suspended sediment concentrations, spatial patterns of sediment within the CHZ depend on the path of the shear layer and on the efficacy of cross-channel mixing processes (Fig. 2). The path of the shear layer within the CHZ is influenced primarily by M r and the planform geometry of the confluence. Near the upstream junction corner, the orientation of the shear layer can be approximated by assuming that the incoming flows are one-dimensional and merge to form a single one-dimensional flow that is unconstrained by the channel boundaries. Under these assumptions, the orientation of the combined flow, and thus of the shear layer, follows from conservation of linear momentum
A
c,
•
..
&
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ir>l ~
- 4...... ) i ~ri ..........
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~,
A,
~
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af=l
"
A
Mr<1 C ' ~ ~ . A, Sr<1 C i
(a)
********i . . . . . . . . . . .
i A
(b)
Sr=1 Sr>1 IncreasingSr •
Fig. 2. Conceptual model of relationships between hydrologic inputs and spatial patterns of suspended sediment concentration at stream confluences. (a) Variation in the path of the shear layer as m o m e n t u m ratio (Mr) increases. Size of arrows is proportional to m o m e n t u m fluxes o f incoming flows, C l and C2 refer to mean suspended sediment concentrations of these flows. (b) Idealized cross-channel patterns of suspended sediment at a cross-section ( A - A ' ) immediately downstream of a confluence for various combinations of m o m e n t u m ratio and sediment concentration ratio (St). Degree of shading indicates relative sediment concentration.
S.T. Kenworthy,B.L. Rhoads / Journal of Hydrology 168 (1995) 251 263
254
(e.g. Mosley, 1976) tan ~ =
--
pzQ2 v2 sin a pl Ql VI + p2Q2 v2 cos ce Mr sin a 1 + Mr cosc~
(1)
where 4~ is the angle between the shear layer and a plane parallel to the main stream above the confluence (Fig. 2(a)), a is the junction angle, Q is discharge, V is mean velocity, p is fluid density, subscripts 1 and 2 refer to the main stream upstream of the confluence and the tributary, and Mr = (p2Q2 V2/plQ1 Vl) is the m o m e n t u m flux ratio of the incoming flows. Thus, as Mr increases, greater deflection of the main stream flow by the tributary causes 0 to increase. Because planform geometry constrains the pattern of flow within the confluence, Eq. (1) does not provide a complete description of the path of the shear layer through the CHZ. This constraint produces a curving pattern of streamlines within the C H Z and thus the path of the shear layer remains linear for only a limited distance from the upstream junction corner (Figs. 1 and 2(a)). At or near the downstream junction corner, the cross-channel distribution of depth-averaged sediment concentrations is a function of the location of the shear layer, the ratio of the incoming sediment loads (Sr = C2/CI), and the degree of cross-channel mixing that has occurred upstream. I f only minor mixing has taken place, a discontinuity in the transverse distribution of suspended sediment concentrations will occur where the shear layer intersects a cross-section (Fig. 2(b)). As m o m e n t u m ratio increases, the shear layer and sediment discontinuity will shift toward the outer bank. For low values of M r , flow from the main stream will occupy most of the crosssection and tributary sediments will be confined to a small area near the inner bank. Main stream sediments will extend over progressively smaller portions of the crosssection as Mr increases. For high values of Mr, the shear layer will be located near the outer bank and most of the cross-section will be dominated by the sediment concentration of the tributary. In this case, the path of the shear layer curves abruptly as it approaches the outer bank to allow passage of the main channel flow into the receiving channel. The degree of curvature increases and the location of m a x i m u m curvature shifts upstream as m o m e n t u m ratio increases (Fig. 2(a)). Thus, for high values of Mr, the location of the shear layer within the cross-section will be less sensitive to changes in m o m e n t u m ratio than for moderate and low values of M r. At extremely high m o m e n t u m ratios, tributary flow may penetrate across the junction and impinge on the outer bank, in which case the shear layer will intersect the outer channel wall. Farther downstream, variation in the cross-stream distribution of sediment concentration at successive cross-sections depends on the path of the shear layer within the downstream channel and on the spatial progression of cross-channel mixing below the confluence. Cross-channel mixing occurs through transverse turbulent diffusion and transverse advective transport by secondary currents (Fischer, 1967,
S. T. Kenworthy, B.L. Rhoads / Journal of Hydrology 168 (1995) 251-263
255
Fig. 3. Site map depicting upper Kaskaskia basin, the confluence of the Kaskaskia River and Copper Slough, and cross-sections referred to in the text.
1969; Young and Wallis, 1993). Both of these mechanisms may be enhanced at stream confluences. Strong vertical vorticity generated along a shear layer (or mixing layer) between confluent streams (e.g. Biron et al., 1993) may accelerate transverse turbulent diffusion considerably. Mixing layer distortion at confluences of unequal depth channels may also affect transverse mixing in some cases (Best and Roy, 1991). In
256
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addition, mixing may be enhanced by secondary currents associated with flow curvature at confluences (Weerakoon et al., 1991; Ashmore et al., 1992; Rhoads and Kenworthy, 1994). Assuming steady state conditions, the net effect of these various transverse mixing mechanisms will be to produce an increasingly uniform cross-channel distribution of suspended sediment concentration as distance from the confluence increases.
3. Study site The study site is the confluence of the Kaskaskia River and the Copper Slough in Champaign county, Illinois (Fig. 3). The confluence has an asymmetrical planform and a junction angle of 60 °. The Kaskaskia River upstream of this confluence drains 54 km 2 of agricultural land and has sandy bed material (ds0 = 0.65 mm). The Copper Slough has a mixed sand and gravel bed (ds0 -- 3.5 mm), a basin area of 41 km 2, and receives urban runoff from the western portion of the city of Champaign. Each stream has been channelized and consists of a shallow low-flow channel (mean depth 0.3-0.8 m) set within a deep (3-5 m) trapezoidal ditch with steep, thickly vegetated banks. The low-flow channels upstream of the confluence are straight and have similar widths (7-8 m). Immediately downstream of the confluence, the Kaskaskia River is 8-10 m wide and exhibits mild curvature (Fig. 3). The two streams differ considerably in their hydrologic response to precipitation events. The largely urbanized basin of the Copper Slough generates 'flashy' discharge hydrographs typical of urban streams. The hydrologic response of the Kaskaskia River is generally more subdued than that of the Copper Slough, but depends strongly on antecedent soil moisture conditions, seasonal variations in potential evapotranspiration, and precipitation intensity. This difference in hydrologic response produces considerable variation in momentum ratio at the confluence. Large differences in the suspended sediment concentrations of the two streams are common, reflecting differences in basin hydrology and land use.
4. Data collection and analysis Sediment sampling was conducted at one cross-section on each channel upstream of the confluence (Fig. 3) and at three cross-sections immediately downstream of the confluence (A, C and E) for several flows with varying hydrologic conditions and sediment loads (Table 1). Mean sediment concentrations in the Kaskaskia River (CK) and Copper Slough (Cs) were computed from several individual samples collected at the two upstream cross-sections. Samples were also collected at six to ten positions along cross-sections A, C, and E to document cross-stream and longitudinal variations in sediment concentration downstream of the confluence. All samples were collected with a USDH-48 depth-integrating suspended sediment sampler, and therefore represent discharge-weighted mean concentrations at a vertical. Estimates of discharge at the two upstream cross-sections were obtained by the
S.T. Kenworthy, B.L. Rhoads / Journal of Hydrology 168 (1995) 251-263
257
Table 1 Summary of hydraulic parameters and sediment concentrations Date
Discharge (m 3 s-l)
11-20-91 04-17-92 07-16-92 07 23 92
Momentum flux (kg ms -2)
Sediment cone. (mg l-l)
QK
Qs
QK q- Os
MK
Ms
Mr
CK
Cs
Cm
0.25 0.59 1.37 0.41
1.66 0.90 0.87 0.70
1.92 1.48 2.24 1.11
22.6 128.8 633.8 85.8
951.0 292.1 289.7 299.8
42 2.3 0.46 3.5
2.6 8.7 119.7 76.6
59.1 22.3 17.7 19.4
51.6 16.9 80.1 40.5
Subscripts K and S denote the Kaskaskia River and Copper Slough, respectively.
velocity-area method (Buchanan and Somers, 1969). These measurements were used to compute M r . The effect of variations in temperature or suspended sediment concentration on fluid density were assumed to be negligible for purposes of calculating Mr. This assumption is justified because: (1) differences in the densities of the Kaskaskia River and Copper Slough arising from differences in water temperature were always much less than 1%, (2) the maximum sediment concentration measured in this study was less than 200 mg 1-1, far below concentrations at which the density of a water-sediment mixture differs appreciably from that of clear water (Guy, 1969). The relative magnitudes of the incoming sediment loads were characterized by a simple sediment concentration ratio Cs
(2)
Sr - - CK
Measured suspended sediment concentrations downstream of the confluence were normalized by a theoretically derived concentration representing complete mixing of the flows. In the absence of temporal trends in sediment load, and assuming no net deposition or resuspension of sediment within the confluence, the average suspended sediment concentration once the streams mix completely is given by Cm =
QKCK qOK +
QsCs Qs
(3)
Thus, under steady state conditions, measured concentrations normalized by Cm should tend toward unity downstream of the confluence as mixing progresses.
5. Results
Spatial patterns of normalized sediment concentrations at the confluence on four separate dates reflect differences in M r and Sr (Fig. 4, Table 1). The suspended sediment on these dates consisted predominantly of silt and clay (< 63 #m); however, small but measurable amounts of fine sand were also present. Because sand concentrations are partially controlled by local hydrodynamics (e.g. shear layer turbulence), the data include only the fine fraction (< 63 #m) of material in suspension, which more accurately reflects spatial patterns of mixing.
258
S. T. K e n w o r t h y , B . L . R h o a d s
/
Journal o f H y d r o l o g y 168 (1995) 2 5 1 - 2 6 3
97.10
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.......................................................................................
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I
; ..... 0
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8
i=!:6 9 10
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8
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tion E 11-20~1 Mr =42-3 Sr=22 7
30
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....................................
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9696
95 85
Cross Sec',on C 11-20-91 Mr=42 3 8r=22 7 O
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0
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(m)
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q r7l r P E6
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3
4
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Distance
6 ? (m)
8
9
10
(b)
Fig. 4. Cross-channel distributions of suspended sediment at the three downstream cross-sections. Concentrations are normalized by Cm for each date. D a s h e d lines indicate normalized values of CK and Cs. Perspective is looking upstream, with west bank on the left. (a) 20 November 1991, (b) 17 April 1992, (c)
16 July 1992, (d) 23 July 1992.
At cross-section A, an abrupt change in sediment concentration marks the location of the shear layer, which is defined as the midpoint between the pair of adjacent sampling locations having the greatest difference in sediment concentration. This shear layer is located within a zone of mixing near the thalweg where sediment concentrations lie between the normalized values of Cs and CK (Fig.4). Sediment concentrations outside of this zone are relatively uniform and similar to the normal-
S.T. Kenworthy, B.L. Rhoads / Journal of Hydrology 168 (1995) 251 263 97.3~
27.ao
Z.0 1.8
J
27,10
259
| I
.Iz` 2.2
~ m
2.0
.............................................................
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.7o !11,,,,,
1,8 ).8 ).4
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1.8
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.,o
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A
95.50 25.30
Distance (m)
Distlnce (m)
97.35 97.15
~
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
96.75
95.75 ~.55 ~5.35b
.............. 0 1 2
.,.o,t..~..--
..........
II,
:1.6 :1.4
Z1.2 :1.0
:0.8 O~
C r ~ s Section C 07-16-02 Mr=0.46 =0,61 ~". . . . . . . . . . . . . . . . . . . . . . . . . . 3 4 5 6 7 0 9 10 Distance (m)
0
2.0 1.8
97.20
1.6
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~.20
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1
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7
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iil illl,,,, o
~c~ ~llan E 07-16412 Mr=O,~
95.8O~
95.4O I
| ................................................
o,.4 i | i'
~ 0.4 ~ 0.2 .~ o.o ~ ~
:2.0 ;1.8
).8 ).B
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2.4
2.0 1,8 1,6 1.4
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
0
1
2
3
4
5
6
7
8
9
10
Distance (m)
Distance (m)
(c)
(d)
Fig. 4. (Continued). ized values of Cs and CK. The tendency for concentrations to decrease towards the banks may reflect a non-uniform transverse distribution of suspended sediment (e.g. Horowitz, 1991, pp. 108-109) in the channels upstream of the confluence. However, the magnitude of transverse variations in sediment concentration inherited from the upstream channels is much less than that resulting from differences between Cs and CK. Moreover, the sharp discontinuity in sediment concentrations at cross-
260
S.T. Kenworthy, B.L. Rhoads / Journal of Hydrology 168 (1995) 251-263
section A suggests that only limited mixing of the flows occurs upstream of this crosssection. In general, variation in the spatial pattern of sediment concentrations at crosssection A is consistent with the relationships depicted in Fig. 2. Concentrations are low on the west (Kaskaskia) side of the channel when Sr > 1, whereas low concentrations occur on the east (Copper Slough) side when Sr < 1. On three of the dates, normalized concentrations vary systematically from values less than one on one side of the channel to values greater than one on the opposite side. Systematic cross-channel variation is also evident on 20 N o v e m b e r 1991, but all normalized concentrations are less than one because of a temporal trend in Cs (Fig. 4(a)). Spatial patterns of sediment concentrations also reflect changes in M r. As M r increases, flow from the Kaskaskia River is more strongly deflected by the Copper Slough and the distance (d) from the west bank to the shear layer decreases (Fig. 4). The location of the shear layer at cross-section A ranges from d = 2.5 m on 20 N o v e m b e r 1991 (Fig. 4(a) M r = 42.3) to d = 4.6 m on 16 July 1992 (Fig. 4(c), Mr = 0.46). As the location of the shear layer shifts toward the west bank, the portion of the channel area occupied by flow from the Copper Slough grows at the expense of the portion occupied by water and sediment from the Kaskaskia River. Although Mr is higher on 23 July 1992 than on 17 April 1992, the location of the shear layer is the same (d = 3.5 m) on both dates (Figs. 4(b) and (d)). Difficulties in accurately defining the location of the shear layer may be partially responsible for this inconsistency, but it is probably also related to differences in bed morphology for the two dates. On 20 N o v e m b e r 1991 and 17 April 1992 a large bar was present at the downstream junction corner, as is apparent from the asymmetry of cross-section A. At low stage, this bar deflects flow from the Copper Slough toward the west bank (Rhoads and Kenworthy, 1994). High flows in the Kaskaskia River in early July 1992 eroded the bar, producing a nearly symmetrical cross-section on 16 July 1992 and 23 July 1992. Outward deflection of the shear layer by the junction corner bar on 17 April 1992 m a y explain why the location of the shear layer on this date is the same as on 23 July 1992, even though the m o m e n t u m ratio is lower on the former date than on the later. At cross-section C, spatial distributions of suspended sediment reflect transverse mixing between cross-sections A and C as well as differences in M r and Sr a m o n g the four dates. The transition in sediment concentrations at cross-section C is less pronounced than at cross-section A, but it is still possible to distinguish the Kaskaskia River flow from that of the Copper Slough, particularly on 17 April 1992 and 16 July 1992. In contrast, on 23 July 1992, the cross-channel transition in concentration is less abrupt, suggesting more effective mixing between cross-sections A and C on this date than on 17 April 1992 or 16 July 1992. The recirculation zone at cross-section C on 17 April 1992 is the result of flow separation at the downstream junction corner (Fig. 4(b)). Sediment concentrations in this region are relatively high. On 20 N o v e m b e r 1991 the distribution of sediment at cross-section C is nearly uniform (Fig. 4(a)). The high m o m e n t u m ratio on this date allowed flow from the Copper Slough to penetrate across the entire width of the downstream channel and impinge upon the west bank between cross-sections A and C. Thus the shear layer
S.T. Kenworthy, B.L. Rhoads / Journal of Hydrology 168 (1995) 251-263
261
does not intersect cross-section C and no area of low sediment concentration (~ CK) is present within the main flow near the west bank. Sediment concentrations are much higher than the normalized value of CK over the entire channel width, but are somewhat lower on the west side of the channel than on the east. The lower concentrations near the west bank probably reflect entrainment and mixing of Kaskaskia water along the shear layer upstream of cross-section C. The small region of recirculation adjacent to the west bank developed in the lee of a detached block of bank material (Fig. 4(a)). At cross-section E, the range in sediment concentration is much lower and the transverse variation more gradual than at cross-section A for each date. These patterns clearly indicate that appreciable cross-channel mixing has occurred upstream of cross-section E and that in each case the mixing process has affected sediment concentrations over most or all of the flow width. However, for all four dates a systematic transverse variation in sediment concentration is still evident at cross-section E, i.e. the flows have not yet mixed completely.
6. Discussion and conclusion
In general, the relationship between momentum ratio and the spatial pattern of suspended sediment described by the conceptual model (Fig. 2) is supported by the field data. These results suggest that the fundamental concepts underlying the conceptual model are applicable to this particular confluence and sufficient to explain most of the observed variation in patterns of suspended sediment concentration. Thus, although the model is quite simple, it can serve as a first step toward understanding the relationship between channel network hydrology and the spatial patterns of suspended sediment in the vicinity of stream confluences. Because the data consist of only depth-integrated sediment samples and measures of bulk upstream hydraulic variables, a rigorous analysis of the mixing process in terms of flow mechanics is not possible. However, the data clearly show that appreciable cross channel mixing, affecting nearly the entire width of flow, occurs within a distance of less than four channel widths downstream of the junction. Measurements of flow structure at this site suggest that this rapid mixing may be related to strong secondary currents immediately downstream of the confluence (Rhoads and Kenworthy, 1994). The measurements also indicate that these secondary currents are weak at cross-section E, suggesting that the substantial mixing of suspended sediment documented in this study occurs within the CHZ. The results of this research may also have implications for dispersal of sediment at the network scale. As a suspended sediment plume travels through a channel network, transverse mixing of this material with a conjoining stream is reinitiated at each confluence. In general, the distance required for complete mixing of tributary inputs to a stream is directly proportional to the square of the channel width and inversely proportional to the rate of transverse mixing (Young and Wallis, 1993). In large, wide rivers, the downstream length scale for mixing can be on the order of tens to hundreds of channel widths (Coldwell, 1947; Mackay, 1970; Meade et al., 1983; Stallard, 1987). In these cases the mixing process extends far beyond the zone of complex hydro-
262
S.T. Kenworthy, B.L. Rhoads / Journal of Hydrology 168 (1995) 251 263
dynamics associated with a confluence. In contrast, substantial mixing occurs over a d i s t a n c e o f f o u r c h a n n e l w i d t h s at t h e K a s k a s k i a - C o p p e r Slough confluence. This d i f f e r e n c e in l e n g t h scale m a y s i m p l y reflect d i f f e r e n c e s in c h a n n e l w i d t h , b u t c o u l d a l s o be r e l a t e d to d i f f e r e n c e s in the r e l a t i v e efficacy o f m i x i n g w i t h i n the C H Z o f large v e r s u s s m a l l c o n f l u e n c e s . F u r t h e r e x p e r i m e n t a l a n d field r e s e a r c h is r e q u i r e d to fully u n d e r s t a n d the r e l a t i o n s h i p b e t w e e n c o n f l u e n c e f l o w s t r u c t u r e a n d t r a n s v e r s e m i x i n g a n d to assess the r o l e o f c h a n n e l j u n c t i o n s in t h e d i s p e r s i o n o f d i s s o l v e d a n d s u s p e n d e d s u b s t a n c e s in v a r i o u s p o r t i o n s o f r i v e r n e t w o r k s .
Acknowledgments D a n M a y e r assisted w i t h the c o l l e c t i o n o f field d a t a . T w o a n o n y m o u s r e v i e w e r s p r o v i d e d h e l p f u l c o m m e n t s . T h i s r e s e a r c h w a s p e r f o r m e d as p a r t o f 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 g r a n t S E S 90-24225.
References Ashmore, P.E., Ferguson, R.I., Prestegaard, K.L., Ashworth, P.J.and Paola, C., 1992. Secondary flow in anabranch confluences of a braided, gravel-bed stream. Earth Surf. Process. Landforms, 17:299-311. Best, J.L., 1987. Flow dynamics at river channel confluences: Implications for sediment transport and bed morphology. In: F.G. Ethridge, R.M. Flores and M.D. Harvey (Editors), Recent Developments in Fluvial Sedimentology. Spec. Publ. 39, Society of Economic Paleontologists and Mineralogists, Tulsa, pp. 27-35. Best, J.L. and Roy, A.G., 1991. Mixing layer distortion at the confluence of channels of different depth. Nature, 350:411-413. Biron, P., De Serres, B., Roy, A.G. and Best, J.L., 1993. Shear layer turbulence at an unequal depth channel confluence. In: N.J. Clifford, J.R. French and J. Hardisty (Editors), Turbulence: Perspectives on Flow and Sediment Transport. John Wiley & Sons Ltd, New York, pp. 197-214. Buchanan, J.J. and Somers, W.P., 1969. Discharge measurements at gaging stations. U.S. Geol. Surv. Tech. Water-Resour. Invest. 3-A8. Coldwell, A.E., 1947. Transverse distribution of suspended sediment below river confluences. Trans. Am. Geophys. Union, 28(5): 747-751. Fischer, H.B., 1967. The mechanics of dispersion in natural streams. J. Hydraul. Div., Proc. ASCE, 93(HY6): 187-216. Fischer, H.B., 1969. The effect of bends on dispersion in streams. Water Resour. Res., 5(2): 496 506. Guy, H.P., 1969. Laboratory theory and methods for sediment analysis. U.S. Geol. Surv. Tech. WaterResour. Invest. 5-C1. Horowitz, A.J., 1991. A Primer on Sediment-Trace Element Chemistry, 2nd edn. Lewis, Chelsea. Mackay, J.R., 1970. Lateral mixing of the Laird and Mackenzie Rivers downstream from their confluence. Can. J. Earth Sci., 7(1): 111 124. Meade, R.H., Nordin, C.F., Perez Hernandez, D., Mejia, B.A. and Perez Godoy, J.M., 1983. Sediment and water discharge in Rio Orinoco, Venezuela and Colombia. In: Proc. Second Int. Symp. on River Sedimentation, Nanjing. pp. 1134-1143. Mosley, M.P., 1976. An experimental study of channel confluences. J. Geol., 84(5): 535-562. Rhoads, B.L. and Kenworthy, S.T., 1994. Flow structure at an asymmetrical stream confluence. Geomorphology, in press. Roy, A.G., Roy, R. and Bergeron, N., 1988. Hydraulic geometry and changes in flow velocity at a river confluence with coarse bed material. Earth Surf. Process. Landforms, 13(7): 583-598.
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263
Stallard, R.F., 1987. Cross-channel mixing and its effect on sedimentation in the Orinoco River. Water Resour. Res., 23(10): 1977-1986. Weerakoon, S.B., Kawahara, Y. and Tamai, N., 1991. Three-dimensional flow structure in channel confluences of rectangular section. In: Proc. XXIV Congress, Madrid. International Association for Hydraulic Research, Vol. A, pp. 373 380. Young, P.C. and Wallis, S.G., 1993. Solute transport and dispersion in channels. In: K. Beven and M.J. Kirkby (Editors), Channel Network Hydrology. John Wiley & Sons Ltd, New York, pp. 129-173.
Hydrology ELSEVIER
Journal of Hydrology 168 (1995) 251-263
[t]
Hydrologic control of spatial patterns of suspended sediment concentration at a stream confluence Stephen T. Kenworthy 1, Bruce L. Rhoads* Department of Geography, 220 Davenport Hall, 607 S. Matthews Ave., University of Illinois, Urbana, IL 61801, USA
Received 8 March 1994; revision accepted 18 September 1994
Abstract
A conceptual model of the relationship between incoming hydraulic conditions and spatial patterns of suspended sediment at a stream confluence is evaluated using suspended-sediment data collected at a small stream confluence in east-central Illinois, USA. Patterns of normalized sediment concentrations at a cross-section near the exit of the confluence are a function of the ratios of momentum flux and mean sediment concentration in the upstream channels. These patterns reflect a shift in the location of the shear layer toward the outer bank as momentum ratio increases. Appreciable cross-channel mixing occurs within a distance of four channel widths downstream from the confluence. These findings suggest that confluence hydrodynamics may have important effects on the dispersal of dissolved or suspended substances in headwater areas of channel networks.
1. Introduction
A c c u r a t e p r e d i c t i o n o f the dispersal o f solutes o r s u s p e n d e d solids t h r o u g h river n e t w o r k s requires d e t a i l e d k n o w l e d g e o f the h y d r o l o g i c , h y d r a u l i c , a n d g e o m o r p h i c c o n t r o l s o f t r a n s p o r t m e c h a n i s m s in v a r i o u s types o f fluvial e n v i r o n m e n t s . T h e two p r i m a r y t r a n s p o r t m e c h a n i s m s c o n t r o l l i n g d i s p e r s i o n in n a t u r a l rivers are differential a d v e c t i o n , w h i c h is related to cross-sectional v a r i a t i o n s in d o w n s t r e a m velocity, a n d c r o s s - c h a n n e l mixing, which is a f u n c t i o n o f s e c o n d a r y flow a n d transverse t u r b u l e n t diffusion ( Y o u n g a n d Wallis, 1993). B o t h m e c h a n i s m s are s t r o n g l y influenced b y s p a t i a l v a r i a t i o n s in c h a n n e l m o r p h o l o g y a n d p l a n f o r m , b u t c r o s s - c h a n n e l m i x i n g * Corresponding author. J Present address: Department of Geography and Environmental Engineering, The John Hopkins University, Baltimore, MD 21218-2686, USA. 0022-1694/95/$09.50 © 1995 Elsevier Science B.V. All rights reserved SSDI 0022-1694(94)02644-0
252
S.T. Kenworthy, B.L. Rhoads / Journal of Hydrology 168 (1995) 251 263
specifically is enhanced by geomorphic features that induce transverse fluid motion, such as meander bends (Fischer, 1969). Stream confluences, or locations where water, solutes, and sediment from two or more sources combine, are also important transverse-mixing environments. Previous experimental work and field studies have shown that flow dynamics at stream confluences are characterized by secondary circulation, flow separation, and the development of vertical shear layers, all of which locally should enhance the efficacy of transverse mixing (Best, 1987; Best and Roy, 1991; Rhoads and Kenworthy, 1994). However, few field studies have investigated patterns of transverse mixing in the immediate vicinity of confluences. Roy et al. (1988) observed only minor transverse mixing within the confluence of two small (< 10 m wide), coarse-bed streams in Quebec, but found that rapid mixing of the two flows occurred over transverse boulder 'ribs' located immediately downstream from the confluence. The purpose of this paper is to examine the influence of variations in incoming hydrologic conditions on spatial patterns of suspended sediment concentration at the confluence of two small streams. The results provide insight into the influence of confluences on transverse mixing in headwater portions of drainage networks.
2. Conceptual framework At stream confluences, there is a region where the merging tributary flows must adjust to the planform geometry of the confluence, thereby producing a distinctive set of hydrodynamic features (Fig. 1). This region defines the confluence hydrodynamic
N••.
\ ~..~"'.
•"
Upetroam Junction ".\
0
corner Junction Corner
",%
i
"'\
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Zone
F f
!
....... /'.._ ...... Stagnation
..... _,. Zone ...............
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.................... F r e e S h e a r L a y e r s
Fig. 1. Flow dynamics at stream confluences(partly after Best, 1987)
S.T. Kenworthy, B.L. Rhoads / Journal of Hydrology 168 (1995) 251-263
253
zone (CHZ). Flow structure within this zone depends primarily on three factors: the junction angle, the planform symmetry of the confluence, and the momentum flux ratio (Mr) of the incoming flows (Mosley, 1976; Best, 1987). The spatial extent of the CHZ corresponds to the distance over which the flow field is influenced by pressure gradients associated with flow convergence and realignment at the confluence or by a free shear layer between the combining flows (Fig. 1). The transitional downstream boundary of the CHZ is marked by the gradual realignment of mean streamlines with the channel margins and the dissipation of vorticity associated with the shear layer. Beyond the CHZ the entire flow field of the receiving stream is adjusted to the gradient and morphology of the downstream channel. At an asymmetrical confluence of a tributary and main stream that have similar widths but different suspended sediment concentrations, spatial patterns of sediment within the CHZ depend on the path of the shear layer and on the efficacy of cross-channel mixing processes (Fig. 2). The path of the shear layer within the CHZ is influenced primarily by M r and the planform geometry of the confluence. Near the upstream junction corner, the orientation of the shear layer can be approximated by assuming that the incoming flows are one-dimensional and merge to form a single one-dimensional flow that is unconstrained by the channel boundaries. Under these assumptions, the orientation of the combined flow, and thus of the shear layer, follows from conservation of linear momentum
A
c,
•
..
&
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A,
ir>l ~
- 4...... ) i ~ri ..........
A
A,
~,
A,
~
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A
Mr<1 C ' ~ ~ . A, Sr<1 C i
(a)
********i . . . . . . . . . . .
i A
(b)
Sr=1 Sr>1 IncreasingSr •
Fig. 2. Conceptual model of relationships between hydrologic inputs and spatial patterns of suspended sediment concentration at stream confluences. (a) Variation in the path of the shear layer as m o m e n t u m ratio (Mr) increases. Size of arrows is proportional to m o m e n t u m fluxes o f incoming flows, C l and C2 refer to mean suspended sediment concentrations of these flows. (b) Idealized cross-channel patterns of suspended sediment at a cross-section ( A - A ' ) immediately downstream of a confluence for various combinations of m o m e n t u m ratio and sediment concentration ratio (St). Degree of shading indicates relative sediment concentration.
S.T. Kenworthy,B.L. Rhoads / Journal of Hydrology 168 (1995) 251 263
254
(e.g. Mosley, 1976) tan ~ =
--
pzQ2 v2 sin a pl Ql VI + p2Q2 v2 cos ce Mr sin a 1 + Mr cosc~
(1)
where 4~ is the angle between the shear layer and a plane parallel to the main stream above the confluence (Fig. 2(a)), a is the junction angle, Q is discharge, V is mean velocity, p is fluid density, subscripts 1 and 2 refer to the main stream upstream of the confluence and the tributary, and Mr = (p2Q2 V2/plQ1 Vl) is the m o m e n t u m flux ratio of the incoming flows. Thus, as Mr increases, greater deflection of the main stream flow by the tributary causes 0 to increase. Because planform geometry constrains the pattern of flow within the confluence, Eq. (1) does not provide a complete description of the path of the shear layer through the CHZ. This constraint produces a curving pattern of streamlines within the C H Z and thus the path of the shear layer remains linear for only a limited distance from the upstream junction corner (Figs. 1 and 2(a)). At or near the downstream junction corner, the cross-channel distribution of depth-averaged sediment concentrations is a function of the location of the shear layer, the ratio of the incoming sediment loads (Sr = C2/CI), and the degree of cross-channel mixing that has occurred upstream. I f only minor mixing has taken place, a discontinuity in the transverse distribution of suspended sediment concentrations will occur where the shear layer intersects a cross-section (Fig. 2(b)). As m o m e n t u m ratio increases, the shear layer and sediment discontinuity will shift toward the outer bank. For low values of M r , flow from the main stream will occupy most of the crosssection and tributary sediments will be confined to a small area near the inner bank. Main stream sediments will extend over progressively smaller portions of the crosssection as Mr increases. For high values of Mr, the shear layer will be located near the outer bank and most of the cross-section will be dominated by the sediment concentration of the tributary. In this case, the path of the shear layer curves abruptly as it approaches the outer bank to allow passage of the main channel flow into the receiving channel. The degree of curvature increases and the location of m a x i m u m curvature shifts upstream as m o m e n t u m ratio increases (Fig. 2(a)). Thus, for high values of Mr, the location of the shear layer within the cross-section will be less sensitive to changes in m o m e n t u m ratio than for moderate and low values of M r. At extremely high m o m e n t u m ratios, tributary flow may penetrate across the junction and impinge on the outer bank, in which case the shear layer will intersect the outer channel wall. Farther downstream, variation in the cross-stream distribution of sediment concentration at successive cross-sections depends on the path of the shear layer within the downstream channel and on the spatial progression of cross-channel mixing below the confluence. Cross-channel mixing occurs through transverse turbulent diffusion and transverse advective transport by secondary currents (Fischer, 1967,
S. T. Kenworthy, B.L. Rhoads / Journal of Hydrology 168 (1995) 251-263
255
Fig. 3. Site map depicting upper Kaskaskia basin, the confluence of the Kaskaskia River and Copper Slough, and cross-sections referred to in the text.
1969; Young and Wallis, 1993). Both of these mechanisms may be enhanced at stream confluences. Strong vertical vorticity generated along a shear layer (or mixing layer) between confluent streams (e.g. Biron et al., 1993) may accelerate transverse turbulent diffusion considerably. Mixing layer distortion at confluences of unequal depth channels may also affect transverse mixing in some cases (Best and Roy, 1991). In
256
S.T. Kenworthy, B.L. Rhoads / Journal of Hydrology 168 (1995) 251-263
addition, mixing may be enhanced by secondary currents associated with flow curvature at confluences (Weerakoon et al., 1991; Ashmore et al., 1992; Rhoads and Kenworthy, 1994). Assuming steady state conditions, the net effect of these various transverse mixing mechanisms will be to produce an increasingly uniform cross-channel distribution of suspended sediment concentration as distance from the confluence increases.
3. Study site The study site is the confluence of the Kaskaskia River and the Copper Slough in Champaign county, Illinois (Fig. 3). The confluence has an asymmetrical planform and a junction angle of 60 °. The Kaskaskia River upstream of this confluence drains 54 km 2 of agricultural land and has sandy bed material (ds0 = 0.65 mm). The Copper Slough has a mixed sand and gravel bed (ds0 -- 3.5 mm), a basin area of 41 km 2, and receives urban runoff from the western portion of the city of Champaign. Each stream has been channelized and consists of a shallow low-flow channel (mean depth 0.3-0.8 m) set within a deep (3-5 m) trapezoidal ditch with steep, thickly vegetated banks. The low-flow channels upstream of the confluence are straight and have similar widths (7-8 m). Immediately downstream of the confluence, the Kaskaskia River is 8-10 m wide and exhibits mild curvature (Fig. 3). The two streams differ considerably in their hydrologic response to precipitation events. The largely urbanized basin of the Copper Slough generates 'flashy' discharge hydrographs typical of urban streams. The hydrologic response of the Kaskaskia River is generally more subdued than that of the Copper Slough, but depends strongly on antecedent soil moisture conditions, seasonal variations in potential evapotranspiration, and precipitation intensity. This difference in hydrologic response produces considerable variation in momentum ratio at the confluence. Large differences in the suspended sediment concentrations of the two streams are common, reflecting differences in basin hydrology and land use.
4. Data collection and analysis Sediment sampling was conducted at one cross-section on each channel upstream of the confluence (Fig. 3) and at three cross-sections immediately downstream of the confluence (A, C and E) for several flows with varying hydrologic conditions and sediment loads (Table 1). Mean sediment concentrations in the Kaskaskia River (CK) and Copper Slough (Cs) were computed from several individual samples collected at the two upstream cross-sections. Samples were also collected at six to ten positions along cross-sections A, C, and E to document cross-stream and longitudinal variations in sediment concentration downstream of the confluence. All samples were collected with a USDH-48 depth-integrating suspended sediment sampler, and therefore represent discharge-weighted mean concentrations at a vertical. Estimates of discharge at the two upstream cross-sections were obtained by the
S.T. Kenworthy, B.L. Rhoads / Journal of Hydrology 168 (1995) 251-263
257
Table 1 Summary of hydraulic parameters and sediment concentrations Date
Discharge (m 3 s-l)
11-20-91 04-17-92 07-16-92 07 23 92
Momentum flux (kg ms -2)
Sediment cone. (mg l-l)
QK
Qs
QK q- Os
MK
Ms
Mr
CK
Cs
Cm
0.25 0.59 1.37 0.41
1.66 0.90 0.87 0.70
1.92 1.48 2.24 1.11
22.6 128.8 633.8 85.8
951.0 292.1 289.7 299.8
42 2.3 0.46 3.5
2.6 8.7 119.7 76.6
59.1 22.3 17.7 19.4
51.6 16.9 80.1 40.5
Subscripts K and S denote the Kaskaskia River and Copper Slough, respectively.
velocity-area method (Buchanan and Somers, 1969). These measurements were used to compute M r . The effect of variations in temperature or suspended sediment concentration on fluid density were assumed to be negligible for purposes of calculating Mr. This assumption is justified because: (1) differences in the densities of the Kaskaskia River and Copper Slough arising from differences in water temperature were always much less than 1%, (2) the maximum sediment concentration measured in this study was less than 200 mg 1-1, far below concentrations at which the density of a water-sediment mixture differs appreciably from that of clear water (Guy, 1969). The relative magnitudes of the incoming sediment loads were characterized by a simple sediment concentration ratio Cs
(2)
Sr - - CK
Measured suspended sediment concentrations downstream of the confluence were normalized by a theoretically derived concentration representing complete mixing of the flows. In the absence of temporal trends in sediment load, and assuming no net deposition or resuspension of sediment within the confluence, the average suspended sediment concentration once the streams mix completely is given by Cm =
QKCK qOK +
QsCs Qs
(3)
Thus, under steady state conditions, measured concentrations normalized by Cm should tend toward unity downstream of the confluence as mixing progresses.
5. Results
Spatial patterns of normalized sediment concentrations at the confluence on four separate dates reflect differences in M r and Sr (Fig. 4, Table 1). The suspended sediment on these dates consisted predominantly of silt and clay (< 63 #m); however, small but measurable amounts of fine sand were also present. Because sand concentrations are partially controlled by local hydrodynamics (e.g. shear layer turbulence), the data include only the fine fraction (< 63 #m) of material in suspension, which more accurately reflects spatial patterns of mixing.
258
S. T. K e n w o r t h y , B . L . R h o a d s
/
Journal o f H y d r o l o g y 168 (1995) 2 5 1 - 2 6 3
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; ..... 0
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30
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Fig. 4. Cross-channel distributions of suspended sediment at the three downstream cross-sections. Concentrations are normalized by Cm for each date. D a s h e d lines indicate normalized values of CK and Cs. Perspective is looking upstream, with west bank on the left. (a) 20 November 1991, (b) 17 April 1992, (c)
16 July 1992, (d) 23 July 1992.
At cross-section A, an abrupt change in sediment concentration marks the location of the shear layer, which is defined as the midpoint between the pair of adjacent sampling locations having the greatest difference in sediment concentration. This shear layer is located within a zone of mixing near the thalweg where sediment concentrations lie between the normalized values of Cs and CK (Fig.4). Sediment concentrations outside of this zone are relatively uniform and similar to the normal-
S.T. Kenworthy, B.L. Rhoads / Journal of Hydrology 168 (1995) 251 263 97.3~
27.ao
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~
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0
1
2
3
4
5
6
7
8
9
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Distance (m)
Distance (m)
(c)
(d)
Fig. 4. (Continued). ized values of Cs and CK. The tendency for concentrations to decrease towards the banks may reflect a non-uniform transverse distribution of suspended sediment (e.g. Horowitz, 1991, pp. 108-109) in the channels upstream of the confluence. However, the magnitude of transverse variations in sediment concentration inherited from the upstream channels is much less than that resulting from differences between Cs and CK. Moreover, the sharp discontinuity in sediment concentrations at cross-
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section A suggests that only limited mixing of the flows occurs upstream of this crosssection. In general, variation in the spatial pattern of sediment concentrations at crosssection A is consistent with the relationships depicted in Fig. 2. Concentrations are low on the west (Kaskaskia) side of the channel when Sr > 1, whereas low concentrations occur on the east (Copper Slough) side when Sr < 1. On three of the dates, normalized concentrations vary systematically from values less than one on one side of the channel to values greater than one on the opposite side. Systematic cross-channel variation is also evident on 20 N o v e m b e r 1991, but all normalized concentrations are less than one because of a temporal trend in Cs (Fig. 4(a)). Spatial patterns of sediment concentrations also reflect changes in M r. As M r increases, flow from the Kaskaskia River is more strongly deflected by the Copper Slough and the distance (d) from the west bank to the shear layer decreases (Fig. 4). The location of the shear layer at cross-section A ranges from d = 2.5 m on 20 N o v e m b e r 1991 (Fig. 4(a) M r = 42.3) to d = 4.6 m on 16 July 1992 (Fig. 4(c), Mr = 0.46). As the location of the shear layer shifts toward the west bank, the portion of the channel area occupied by flow from the Copper Slough grows at the expense of the portion occupied by water and sediment from the Kaskaskia River. Although Mr is higher on 23 July 1992 than on 17 April 1992, the location of the shear layer is the same (d = 3.5 m) on both dates (Figs. 4(b) and (d)). Difficulties in accurately defining the location of the shear layer may be partially responsible for this inconsistency, but it is probably also related to differences in bed morphology for the two dates. On 20 N o v e m b e r 1991 and 17 April 1992 a large bar was present at the downstream junction corner, as is apparent from the asymmetry of cross-section A. At low stage, this bar deflects flow from the Copper Slough toward the west bank (Rhoads and Kenworthy, 1994). High flows in the Kaskaskia River in early July 1992 eroded the bar, producing a nearly symmetrical cross-section on 16 July 1992 and 23 July 1992. Outward deflection of the shear layer by the junction corner bar on 17 April 1992 m a y explain why the location of the shear layer on this date is the same as on 23 July 1992, even though the m o m e n t u m ratio is lower on the former date than on the later. At cross-section C, spatial distributions of suspended sediment reflect transverse mixing between cross-sections A and C as well as differences in M r and Sr a m o n g the four dates. The transition in sediment concentrations at cross-section C is less pronounced than at cross-section A, but it is still possible to distinguish the Kaskaskia River flow from that of the Copper Slough, particularly on 17 April 1992 and 16 July 1992. In contrast, on 23 July 1992, the cross-channel transition in concentration is less abrupt, suggesting more effective mixing between cross-sections A and C on this date than on 17 April 1992 or 16 July 1992. The recirculation zone at cross-section C on 17 April 1992 is the result of flow separation at the downstream junction corner (Fig. 4(b)). Sediment concentrations in this region are relatively high. On 20 N o v e m b e r 1991 the distribution of sediment at cross-section C is nearly uniform (Fig. 4(a)). The high m o m e n t u m ratio on this date allowed flow from the Copper Slough to penetrate across the entire width of the downstream channel and impinge upon the west bank between cross-sections A and C. Thus the shear layer
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does not intersect cross-section C and no area of low sediment concentration (~ CK) is present within the main flow near the west bank. Sediment concentrations are much higher than the normalized value of CK over the entire channel width, but are somewhat lower on the west side of the channel than on the east. The lower concentrations near the west bank probably reflect entrainment and mixing of Kaskaskia water along the shear layer upstream of cross-section C. The small region of recirculation adjacent to the west bank developed in the lee of a detached block of bank material (Fig. 4(a)). At cross-section E, the range in sediment concentration is much lower and the transverse variation more gradual than at cross-section A for each date. These patterns clearly indicate that appreciable cross-channel mixing has occurred upstream of cross-section E and that in each case the mixing process has affected sediment concentrations over most or all of the flow width. However, for all four dates a systematic transverse variation in sediment concentration is still evident at cross-section E, i.e. the flows have not yet mixed completely.
6. Discussion and conclusion
In general, the relationship between momentum ratio and the spatial pattern of suspended sediment described by the conceptual model (Fig. 2) is supported by the field data. These results suggest that the fundamental concepts underlying the conceptual model are applicable to this particular confluence and sufficient to explain most of the observed variation in patterns of suspended sediment concentration. Thus, although the model is quite simple, it can serve as a first step toward understanding the relationship between channel network hydrology and the spatial patterns of suspended sediment in the vicinity of stream confluences. Because the data consist of only depth-integrated sediment samples and measures of bulk upstream hydraulic variables, a rigorous analysis of the mixing process in terms of flow mechanics is not possible. However, the data clearly show that appreciable cross channel mixing, affecting nearly the entire width of flow, occurs within a distance of less than four channel widths downstream of the junction. Measurements of flow structure at this site suggest that this rapid mixing may be related to strong secondary currents immediately downstream of the confluence (Rhoads and Kenworthy, 1994). The measurements also indicate that these secondary currents are weak at cross-section E, suggesting that the substantial mixing of suspended sediment documented in this study occurs within the CHZ. The results of this research may also have implications for dispersal of sediment at the network scale. As a suspended sediment plume travels through a channel network, transverse mixing of this material with a conjoining stream is reinitiated at each confluence. In general, the distance required for complete mixing of tributary inputs to a stream is directly proportional to the square of the channel width and inversely proportional to the rate of transverse mixing (Young and Wallis, 1993). In large, wide rivers, the downstream length scale for mixing can be on the order of tens to hundreds of channel widths (Coldwell, 1947; Mackay, 1970; Meade et al., 1983; Stallard, 1987). In these cases the mixing process extends far beyond the zone of complex hydro-
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dynamics associated with a confluence. In contrast, substantial mixing occurs over a d i s t a n c e o f f o u r c h a n n e l w i d t h s at t h e K a s k a s k i a - C o p p e r Slough confluence. This d i f f e r e n c e in l e n g t h scale m a y s i m p l y reflect d i f f e r e n c e s in c h a n n e l w i d t h , b u t c o u l d a l s o be r e l a t e d to d i f f e r e n c e s in the r e l a t i v e efficacy o f m i x i n g w i t h i n the C H Z o f large v e r s u s s m a l l c o n f l u e n c e s . F u r t h e r e x p e r i m e n t a l a n d field r e s e a r c h is r e q u i r e d to fully u n d e r s t a n d the r e l a t i o n s h i p b e t w e e n c o n f l u e n c e f l o w s t r u c t u r e a n d t r a n s v e r s e m i x i n g a n d to assess the r o l e o f c h a n n e l j u n c t i o n s in t h e d i s p e r s i o n o f d i s s o l v e d a n d s u s p e n d e d s u b s t a n c e s in v a r i o u s p o r t i o n s o f r i v e r n e t w o r k s .
Acknowledgments D a n M a y e r assisted w i t h the c o l l e c t i o n o f field d a t a . T w o a n o n y m o u s r e v i e w e r s p r o v i d e d h e l p f u l c o m m e n t s . T h i s r e s e a r c h w a s p e r f o r m e d as p a r t o f 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 g r a n t S E S 90-24225.
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