Basic sediment transport Initial motion & bedload Definitions and dimensions Shields stress and initial motion Bedload formulas Shear stress Stress & flow Measurement & estimation Suspension, wash load, total load Rouse number & profile Total-load formulas Links between topography and sediment flux

Sediment characterization Wentworth scale

Grain size distribution Unimodal sand

To the board! analysis of initial motion: forces, force balance dimensional analysis and Shields stress rough analysis of critical Shields

Shields initial motion From Buffington (1999)

Shields initial motion

Initial motion: standard conditions No motion Peter Wilcock, Utah State Univ.

Modifying Shields for slope effects Streamwise slope Lateral slope

What to do about size mixtures? When grain sizes are clearly segregated into patches like this, you can apply Shields to each patch separately.

Within a mixture, all sizes tend to move together up to very large clasts mixture effects diminish for extremely large grain sizes Di / D50 Parker; Wilcock; Proffitt & Sutherland

Initial motion -- summary Brownlie formula for Shields curve: Correction for streamwise slope: Correction for side slope: Correction for mixtures: NB Parker et al. (2003) have suggested reducing this by a factor of 2

Bedload + Suspended load = Total load

Bedload – Meyer-Peter & Müller KMPM = 8 in the original formulation; corrected to 4 by Wong & Parker (2005)

Bedload – more relations threshold Ashida - Michue no threshold Einstein Parker mod. to Einstein

Parker 1990 gravel appropriate for gravel bedload transport rates in gravel-bed streams Fi must be renormalized so that the sand is removed, and the remaining gravel fractions sum to unity, Fi = 1. based on surface geometric size Dsg and surface arithmetic standard deviation s on the  scale, both computed from the renormalized fractions Fi.

Bedload vs suspension suspension Fw ~ w’ (turbulence) bedload Fw ~ bed (collisions, contact)

Bedload vs suspension Turbulent fluctuations w’ ~ u suspension if u ~ settling vel ws Rouse number Ro

Bedload vs suspension

Bedforms

Bedform types: unidirectional flow ripples

Bedform types: unidirectional flow dunes

Bedform types: unidirectional flow dunes

Bedform types: unidirectional flow Kennetcook River, NS Wolfville FM, Red Head, NS dunes

Bedform types: unidirectional flow plane bed

Bedform types: unidirectional flow antidunes

Bedform stability Southard (1991) 0.2 0.4 0.6 0.8 1.0 2.0 0.2 0.4 0.6 0.8 1.0 2.0 0.2 0.4 0.6 0.8 1.0 2.0 Southard (1991)

Bedform stability Southard (1991) 0.2 0.4 0.6 0.8 1.0 2.0 0.2 0.4 0.6 0.8 1.0 2.0 0.2 0.4 0.6 0.8 1.0 2.0 Southard (1991)

Bedform stability Southard (1991) 0.2 0.4 0.6 0.8 1.0 2.0 0.2 0.4 0.6 0.8 1.0 2.0 0.2 0.4 0.6 0.8 1.0 2.0 Southard (1991)

Bedform stability For flow depths: Southard (1991) 0.06 0.1 0.2 0.4 1.0 2.0 4.0 6.0 8.0 Southard (1991)

Bedform stability Southard (1991)

Bedforms - summary Ripples D < 0.5 mm  < 0.3 m /hbf ~15 u ~ uc Upper plane bed D = any u > ws Dunes D > 0.2 mm hbf ~ 0.3 h /hbf >15 ws> u >> uc Antidunes D = any Fr = U/gh ~ 1

Bed forms and form drag Herrmann et al., 2005, Physica A

Can you explain this? Pigeon Roost Creek, Mississippi

Bedload + Suspended load = Total load

Suspension  total load The Rouse theory for suspension is well developed and compares well with data BUT it depends on a lower boundary condition that is set by bedload Since bedload flux is determined empirically, in the end so is suspended flux and hence total load suspended flux per unit width

Total load formulas Engelund-Hansen (1967) Brownlie (1981) K = 1 for lab data = 1.268 for field data r = hydraulic radius (Area/wetted perimeter

Brownlie grand comparison

Van Rijn (1984) An attempt to synthesize the “best of” sediment transport (mainly sand) over many years VR(a): bedload VR(b): suspended load VR(c): bedforms & roughness

Van Rijn (1984) Van Rijn, L. C. (1984a), Sediment transport, part I: bed load transport, Journal of Hydraulic Engineering, 110(10), 1431-1456. Van Rijn, L. C. (1984b), Sediment transport, part II: suspended load transport, Journal of Hydraulic Engineering, 110(11), 1613-1641. Van Rijn, L. C. (1984c), Sediment transport, part III: bed forms and alluvial roughness, Journal of Hydraulic Engineering, 110(12), 1733-1754.