Slide 1

Confluences and NetworksOutlineFlow and sediment transport characteristics at river confluencesBraid bar developmentNetwork 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 ProcessesPrimary Flow CharacteristicsEntrance zonesEquivalent to riffle cross-overInherited helical flow pattern from upstreamConfluence mixing zoneSuper-elevation and two circulation cellsShear layer and zones of flow separationSediment transport becomes spatially variedLocalized erosion in scour hole ~4X average depth of incoming channelsLocalized 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 mslSignificance of Scour Hole

Driftless Area, SW WisconsinNetworksTurcotte (2007)

Networks

Network Organization(Bridge, 2003)Network Organization

(Bridge, 2003)Rb~3 to 5Rl~1.5 to 3RA~3 to 6

Hack (1957; e.u.)

Network OrganizationPlaner projection of river basinsA = sLL where s is a shape factorIf L/L constant for all A & s is constant, self-similarIf L/L decreases as A increases, and s is constant, self-affine (basins elongate)(Rignon et al., 1996)Network OrganizationStream length with area is fractal; L is sinuousPlaner projection of river basins is self-affinebasins become elongated

Stream length, h = 0.6Elongation, h = 0.52Stream 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)1,4,16,64,2561,7,49,343Or 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 principlesMinimum energy expenditure in any linkEqual energy expenditure per unit area of bed anywhere in the networkMinimum 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

Network EvolutionExpansion Mode Network expands slowly Fully developed in the area Extension Mode Low-order channels elongate rapidly 1 streams are longer with smaller anglesNetwork Evolution: Experimental Watershed

Network Evolution: Experimental Watershed7.1 m2.4 mFrame (storm)1234567891011121314151617181920Timespan (min)8515202020202030509012018018020202020305050Total Time (min)8510012014016018020023028037049067085087089091093096010101060Base-level dropBase-level drop

Longitudinal ProfilesCommunication of forcingHeadcuts

Drivers of extension and incisionConfluences, Networks, and River RestorationConfluences have not, as yet, been part of restoration designJunction angles, link lengths, and network organization clearly are part of a dynamically stable fluvial systemHeadcut morphodynamics in rills and gullies can be drivers of channel incision and evolution potentially analogous to riversConfluences and NetworksConclusionsConfluences have generalized flow patterns All flow, bed, and sediment parameters then are modified by this flow patternNetworks display systematic organization (self-similarity, self-affinity) that may represent some internal optimization (energy minimization)