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) EntranceMixing

(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, Bangladesh 10 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) R b ~3 to 5R l ~1.5 to 3R A ~3 to 6 Hack (1957; e.u.)

Network Organization Planer projection of river basins A = sL  L  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 Q 0.5 and L are mean annual discharge and length of ith link and X is a constant

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 Watershed 7.1 m 2.4 m Frame (storm) Timespan (min) Total Time (min) 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)