Confluences and Networks

1. Confluences and Networks Outline • Flow and sediment transport characteristics at river confluences • Braid bar development • Network characteristics and organization

2. Sacramento and Feather Rivers Ohio River and Mississippi River Minnesota River (lower branch) entering the Mississippi River

3. Entrance Mixing (Bridge, 2003)

4. Flow Processes (Robert, 2003)

5. Flow and Sediment Transport Processes (Robert, 2003)

6. 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

7. Braid Bar Development Confluence-Diffluence Couplet (Ashmore, 1993)

8. Braid Bar Development (Ashmore, 1993)

9. Significance of Scour Hole Confluence of the Jamuna and Ganges River, Bangladesh 10 X 13 km (Best and Ashworth, 1997) Up to 27 m below msl

10. Networks Driftless Area, SW Wisconsin

11. Networks Turcotte (2007)

12. Network Organization (Bridge, 2003)

13. Network Organization Rb~3 to 5 Rl~1.5 to 3 RA~3 to 6 Hack (1957; e.u.) (Bridge, 2003)

14. 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)

15. Stream length, h = 0.6 Network Organization • Stream length with area is fractal; L is sinuous • Planer projection of river basins is self-affine—basins become elongated Elongation, h’ = 0.52 Stream length vs. diameter, 1.15 (Rignon et al., 1996)

16. 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)

17. 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

18. Network Evolution • Extension Mode • Low-order channels elongate rapidly • 1° streams are longer with smaller angles • Expansion Mode • Network expands slowly • Fully developed in the area

19. Network Evolution: Experimental Watershed Network Evolution: Experimental Watershed 2.4 m 7.1 m Base-level drop Base-level drop

20. Longitudinal Profiles Communication of forcing

21. Headcuts • Drivers of extension and incision

22. 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 • Headcutmorphodynamics in rills and gullies can be “drivers” of channel incision and evolution  potentially analogous to rivers

23. 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)