For flow of 1 m/s in round-bottom channel of radius 1 m, what is the Reynold’s number? Is the flow laminar or turbulent? Re < 500 laminar Re > 2000 turbulent 500 to 2000 elements of both density of water = 1000 kgm -3 Viscosity water = Pas = Nsm -2 ; N= kgms -2 Re = ρuR h / η, and R h = A/P Answer: R h = 0.5 m ? 15 m ? 50 m ? Re = 50 ? 5,000 ? 500,000 ?

Rivers are complicated… u u Laminar sublayer transition Turbulent So use empirical Shields equation for shear stress on a channel bed. τ c = critical shear stress to initiate particle mobilization Basal shear stress in a flow is: τ s = ρgy sin(θ) We need Shields equation to tell us if shear stress is enough to mobilize grains on the bed θ y

Rivers are complicated… u u Laminar sublayer transition Turbulent Shields equation τ c = τ* (ρ s – ρ w ) g D θ y Critical shear Stress to initiate mobilization ≈ 0.6 for sand-size grains, but f(D) (determined from flume experiments & natural observations) grainsize (diameter)

Shields equation τ c = τ* (ρ s – ρ w ) g D Critical shear Stress to initiate mobilization ≈ 0.6 for sand-size grains, but f(D) (determined from flume experiments & natural observations) grainsize (diameter) log velocity log grainsize 0.1 mm silt 1 mm coarse sand EROSION DEPOSITION TRANSITION ZONE OF TRANSPORT cohesive non cohesive (for 1 m deep flow over flat bed with uniform grainsize)

Bedload – coarse material/larger particles move by rolling in a shearing fluid. Sedimentary particles supported by the bed. Also saltation – “saltare = jump.” skipping where an impacted grain bounces high enough to pass through laminar sublayer Suspended load – suspended particles are kept aloft by turbulent eddies which transfer momentum from fluid to particle, moving it upward at a rate that is faster than its settling velocity - typically 90-95% of sed moved by rivers - clay, silt, sometimes fine sand settling velocity: Stoke’s Law - viscosity, denisty of fluid (uniform in a river) - size, shape, density of particles (not uniform in a river) (dissolved load – ions from chemical weathering reactions)

Depositional, transporting, erosional and entrainment regimes in a channel are determined by the flow regime (laminar, turbulent), flow velocity, and particle sizes making up the bed. Net result of particle motion by flow is… Beds acquire ripples from particles moving by rolling in a shearing fluid. Grains transported up upstream side (erosion), cascade down the slip face of downstream side (deposition). Not just vertical velocity structure, but 3-D velocity field in rivers affects sediment transport and gives rivers the morphologies and behaviors we observe.

Bedrock channel

Alluvial channel

Scroll bars – raised ridges that mark successive positions of inside of migrating meander bend Oxbow lake – occupy abandoned meander loops

Meandering river carves out floodplain at the level of the highest overbank flows. Floodplains are efficient traps for fine-grained silt and clay carried by rivers.

Results of these processes on the sedimentary record… Flow velocities in channel also determine grains size distribution of sediment on the bed, which grades from fine mud and silt on the lip of the point bar to gravel in the channel axis. Point bar axis NET EROSION DEPOSITIONAL SURFACE

Braided rivers – have less sinuous channels, which branch, diverge and converge around ephemeral sand and gravel bars -High river gradients, high sediment loads, intermittent flow favors braided channels -Low gradients, low sediment loads, and COHESIVE BANKS (vegetation…) favor formation of meandering channels.

End here for midterm