1. Bedforms in Unidirectional Flow

2. Sedimentary layer thicknesses span several orders of magnitude, from mm to more than a meter
That continuum is arbitrarily subdivided: anything <1 cm is called a lamina, >1 cm is a bed

3. Although beds can be planar or contain parallel laminae, turbulent flow in the boundary layer combined with sediment deposited from traction often produce bedforms (three-dimensional features on the bed)
Kennetcook River, Nova Scotia

4. Flow velocity decreases close to the bed surface, due to frictional interaction between the water and the sediment
This interval of reduced flow is called the boundary layer

5. Boundary layer divided into turbulent sublayer (10s of cm to m thick) and laminar sublayer (basal mm or less of the boundary layer)
Constant average velocity
Laminar Sublayer
Turbulence controlled by relative importance of inertial vs. viscous forces (Reynolds number Re)
Density, velocity, depth
Re= ruD m
Viscosity
Re > 2000
Re < 500

6. Low velocity in eddy on lee side leads to deposition
Ripples are the smallest bedform, typically a few cm tall and cm wavelength
Erosion
Deposition
Current ripple video linked
Due to flow reattachment on stoss side of ripple, laminar sublayer of boundary layer is compressed and flow velocity is higher – leads to erosion
Low velocity in eddy on lee side leads to deposition

7. Dunes have a similar appearance to ripples (gentle stoss slope, steep lee side), but are larger
Height: 10 cm to 10 m, spacing: 60 cm to 100s of m

8. Are dunes just big ripples?
Dunes form from large-scale turbulence; ripples related to laminar sublayer
Dune size scales with flow depth; ripples scale with grain size instead
Height and wavelength distribution of dunes and ripples are separate

9. Upper plane bed produces parallel laminations with low-relief ridges and grooves (called “parting lineations”) parallel to flow on the bed surface
Parallel laminations
Parting lineations

10. Parting lineations form because turbulent boundary layer develops longitudinal regions of higher and lower velocity flow
High-velocity bursts disrupt laminar sublayer and erode sediment

11. Antidunes are unusual in typical river flows, but are broad, slightly asymmetrical bedforms that migrate upstream (!) in most cases
Form where supercritical flow produces standing waves

12. What is supercritical flow?
Subcritical and supercritical flows are defined by a Froude number, the ratio of flow velocity to the speed of wave propagation (wave celerity)
Fr= u gD
Fr < 1: subcritical – velocity less than wave celerity
Supercritical
Waves cannot propagate into supercritical smooth region because celerity < outward velocity. Hydraulic jump also associated with change in depth.
Fr > 1: supercritical – velocity is greater than wave celerity
Hydraulic Jump
Subcritical

13. Low velocity
When Fr < 1, the water surface perturbation is out of phase with the bed perturbation
High velocity
Forms regular dunes
High shear stress
Erosion
Low shear stress
Deposition
Low velocity
When Fr > 1, the water surface perturbation is in phase with the bed perturbation
High velocity
Based on complicated calculations (linear inviscid shallow-water formulation for 1D bedforms)
Forms antidunes
Low shear stress
Deposition
High shear stress
Erosion