Bedforms in Unidirectional Flow

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

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

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

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

Low velocity in eddy on lee side leads to deposition Ripples are the smallest bedform, typically a few cm tall and 10-20 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

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

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

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

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

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

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

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