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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