1B Clastic SedimentsLecture 28

BEDFORMS IN COHESIONLESS SUBSTRATE

Structure of bedformsFormative conditions

Unidirectional and Oscillating flows

NH 01-2007

BURSTS AND SWEEPS

Flow streaks in wall region.

Spacing of streaks, depends on flow properties:

Re* = u*/ = 100

Re* is boundary Reynolds no.u* = √0/ is shear velocity.

Burst-sweep process ismain creator of turbulence.

Inrush of high-velocity sweepsmay locally exceed thresholdof sediment motion.

RIPPLE INITIATION

Ripples form when random points of high boundary shear stress (sweeps) cause formation of a pile of grains. Pile of height v causes flow disturbance ~100 v long downstream, similar to the separation zone behind a ripple.

D > 0.7 mm: grains disrupt viscous sublayer and discrete flow disturbancesno longer occur. Ripples do not form, bed is plane.

Bedform wavelength

~100 v

FLOW OVER BEDFORM

Ripples and dunes formed under uni-directional flow have shallow upstreamor stoss faces, dominated by rolling grains,and steep downstream or lee slopes, dominated by grain avalanching.

BEDFORM MIGRATION AND SEDIMENT FLUX

Downstream flux of sedimentdue to bedform migration:

where UB is speed of bedform,H is height of bedform, is porosity of bed material.

12HUQ Bs

SEDIMENT FALLOUT

Climbing ripples

Angle of climb and preservationof stoss and lee side are determinedby balance of downstream translation and vertical build up.

BEDFORMS PLANFORM AND INTERNAL STRUCTURE

Planar cross stratification

Trough cross stratification

Basic bedform: crescent

FLOW OVER BEDFORM

Ripples and dunes formed under uni-directional flow have shallow upstreamor stoss faces, dominated by rolling grains,and steep downstream or lee slopes, dominated by grain avalanching.

Dunes: ~ 2h dune height = h/3 to h/D where h is flow depth, and D is grain size.Ripples: height < 4 cm

BEDFORMS UNDER SHEAR FLOW

On flat bed, resistance to flow isdue to boundary roughness (~ grainsize): skin friction

0 ~ Ua

Developing bedforms become main roughness element: form drag

With increasing flow velocity : 1) bedforms grow, shear stress up.2) dunes wash out, replaced by flat bed: shear stress down.3) standing waves and antidunes form: shear stress up.

Shear stress bad indicator ofstate of bed; use flow velocity.

Flatbed

Ant

idun

es

CONTROLS ON BEDFORM:

Assumptions: steady and uniform flow, equilibrium bedforms, mean grain size describes bed material.

Variables:Grain size D [L]Density of grains s [ML-3]Density of fluid f [ML-3]Viscosity of fluid [ML-1T-1]Gravitational acceleration g [LT-2]Flow depth h [L]Flow velocity U [LT-1]

BEDFORMS STABILITY FIELDS

Flow depth: 0.25 – 0.40 m

BEDFORMS STABILITY FIELDS

Absence of ripples in course sand:Lack of viscous sublayer overhydraulically rough boundary.

Upper plane bed in fine grains:Due to high sediment concentrationdamping turbulence.

FLOW REGIMES

Lower flowregime

Upper flowregimeH

ydraulic jump

gh

UFr

Gravity works to flatten a rough flow:Froude number is dimensionless productexpressing balance of inertial and gravitational forces

Fr < 1: subcritical flow Fr > 1: supercritical flow

BEDFORMS STABILITY FIELDS; FLOW REGIMES

Super criticalUpper

Sub criticalLower flowregime

CONTROLS ON BEDFORM: DIMENSIONAL ANALYSIS

Assumptions: steady and uniform flow, equilibrium bedforms, mean grain size describes bed material.

Variables:Grain size D [L]Density of grains s [ML-3] excludeDensity of fluid f [ML-3] repeatViscosity of fluid [ML-1T-1] repeatGravitational acceleration g [LT-2] repeatFlow depth h [L]Flow velocity U [LT-1]

Dimensionless Products:

Experimental set up:Water, quartz sand, variable temperature.

3/1

0

gUU f

3/1

2

20

g

hh f

3/1

2

20

g

DD f

3/1

210

2

10

3/1

2

2

g

hg

h f

p

fp

3/2

10010

p

hh

constant in temp

BEDFORMS STABILITY FIELDS

Bedform stability can be representedin 3D plot of standardized flowvelocity, flow depth and grain size.

Sections through this cube can be viewed.

h 10

BEDFORMS UNDER OSCILATORY WAVES

Controls on bedform: Flow velocitySediment grain sizeWave period

Form Index: L/H

BEDFORMS UNDER OSCILATORY WAVES