Confluences and Networks

Outline• Flow and sediment transport

characteristics at river confluences• Braid bar development• Network characteristics and organization

Ohio River and Mississippi River

Minnesota River (lower branch) entering the Mississippi River

Sacramento and Feather Rivers

(Bridge, 2003)

Entrance Mixing

(Robert, 2003)

Flow Processes

(Robert, 2003)

Flow and Sediment Transport Processes

Primary Flow Characteristics• Entrance zones

– Equivalent to riffle cross-over– Inherited helical flow pattern from upstream

• Confluence mixing zone– Super-elevation and two circulation cells– Shear layer and zones of flow separation– Sediment transport becomes spatially varied

• Localized erosion in scour hole ~4X average depth of incoming channels

• Localized deposition as side bars and downstream

Braid Bar Development

(Ashmore, 1993)

Confluence-Diffluence Couplet

Braid Bar Development

(Ashmore, 1993)

Confluence of the Jamuna and Ganges River, Bangladesh10 X 13 km(Best and Ashworth, 1997)

Up to 27 m below msl

Significance of Scour Hole

Driftless Area, SW Wisconsin

Networks

Turcotte (2007)

Networks

Network Organization

(Bridge, 2003)

Network Organization

(Bridge, 2003)

Rb~3 to 5 Rl~1.5 to 3 RA~3 to 6

6.04.1 DAL

Hack (1957; e.u.)

Network Organization

• Planer projection of river basins

• A = sLL where s is a shape factor

• If L/L constant for all A & s is constant, self-similar

• If L/L decreases as A increases, and s is constant, self-affine (basins elongate)

(Rignon et al., 1996)

Network Organization

• Stream length with area is fractal; L is sinuous

• Planer projection of river basins is self-affine—basins become elongated

Stream length, h = 0.6

Elongation, h’ = 0.52

Stream length vs. diameter, 1.15

(Rignon et al., 1996)

Network Organization (1)• Woldenberg (1969, 1971)

– Drainage basins develop as mixed hexagonal hierarchies of basin area (orders 3, 4, and 7)• 1,3,9,27,81… (n = n-1 x 3)• 1,4,16,64,256…• 1,7,49,343…

– Or Fibonaci series (1,3,4,7,11…; 1,4,5,9,14…)– A balance of least work and maximum entropy

(both economies of energy loss by overland flow and through channels is minimized)

Network Organization (2)• Rodriguez-Iturbe et al. (1992)—tree-like

structure of drainage networks is a combination of three energy principles– Minimum energy expenditure in any link– Equal energy expenditure per unit area of bed

anywhere in the network– Minimum energy expenditure in the network as a

whole

where Q0.5 and L are mean annual discharge and length of ith link and X is a constant

min5.0ii LQ

Network Evolution

Expansion Mode• Network expands slowly• Fully developed in the area

Extension Mode• Low-order channels

elongate rapidly• 1° streams are

longer with smaller angles

Network Evolution: Experimental WatershedNetwork Evolution: Experimental Watershed

7.1 m

2.4 m

Frame (storm) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Timespan (min) 85 15 20 20 20 20 20 30 50 90 120 180 180 20 20 20 20 30 50 50

Total Time (min) 85 100 120 140 160 180 200 230 280 370 490 670 850 870 890 910 930 960 1010 1060

Base-level drop Base-level drop

Longitudinal Profiles

Communication of forcing

Headcuts

• Drivers of extension and incision

Confluences, Networks, and River Restoration

• Confluences have not, as yet, been part of restoration design

• Junction angles, link lengths, and network organization clearly are part of a dynamically stable fluvial system

• Headcut morphodynamics in rills and gullies can be “drivers” of channel incision and evolution potentially analogous to rivers

Confluences and Networks

Conclusions• Confluences have generalized flow

patterns • All flow, bed, and sediment parameters

then are modified by this flow pattern• Networks display systematic organization

(self-similarity, self-affinity) that may represent some internal optimization (energy minimization)