THE ORIGINS OF MORPHODYNAMICS:DUNE ASYMMETRY

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THE ORIGINS OF MORPHODYNAMICSDUNE ASYMMETRY
Why do river dunes have gentle stoss (upstream)
faces and steep lee (downstream) faces?
Dunes in a flume water turned off, looking
upstream, SAFL
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MORE DUNES NOTE THAT ASYMMETRY!
Looking upstream Lab (H. Ikeda)
Looking downstream Field (Amazon basin)
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FELIX EXNER, 1920 THE FIRST MORPHODYNAMICIST

• THE ACTORS
• x streamwise distance L
• t time T
• bed elevation L
• qsed volume sediment transport rate per unit
  stream width L2/T
• ?p bed porosity 1
• g acceleration of gravity L/T2
• H flow depth
• U depth-averaged flow velocity L/T
• Cf bed friction coefficient 1

Talk with me, baby! Clapton, 197? The flow
changes the bed The bed changes the flow
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FELIX EXNER, THE FIRST MORPHODYNAMICIST
THE STAGE
Enxer equation of bed sediment continuity
Sediment transport relation
St. Venant shallow water eqns.
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SO WHAT DID HE FIND?

• Dunes like subcritical flow.
• Dunes migrate downstream as mass waves.
• Dunes are nonlinear waves migration speed
  changes with elev, c c(?)
• In particular, wave speed increases with
  elevation
• Voilà, the asymmetry evolves on its own!

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We will not consider dunes further in this
course. This course will be devoted to the
morphodynamics of fans and fan-deltas. To
accomplish this we must first review open-channel
hydraulics and sediment transport.
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RELATIONS FOR CONSERVATION OF BED SEDIMENT

• PARAMETERS
• x streamwise coordinate (boundary-attached) L
• bed elevation L
• H flow depth L
• In most but not all applications x is nearly
  horizontal and z is nearly vertical.

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ALLUVIAL TRANSPORT Modes of sediment
transport wash load or bed material load 62.5
?m?   Modes of bed material transport bedload or
suspended load bedload sliding, rolling or
saltating just above bed role of turbulence is
indirect   suspended load feels direct
dispersive effect of eddies may be wafted high
into the water column
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MORE PARAMETERS

• ?s sediment density M/L3
• water density M/L3
• R (?s/? - 1) submerged specific gravity of
  sediment ( 1.65) 1
• qb volume bedload transport rate per unit width
  L2/T
• gb mass bedload transport rate per unit width
  ?sqb M/L/T

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1D CONSERVATION OF BED SEDIMENT BEDLOAD ONLY
Rio Cordon, Italy
1
x
?x
x?x
Or
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CONSERVATION OF BED SEDIMENT ADD SUSPENDED
LOAD Es volume rate of entrainment of bed
material into suspension per unit bed area per
unit time L/T Ds volume rate of deposition
of bed material into suspension per unit bed area
per unit time L/T
Fly River, PNG
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CONSERVATION OF BED SEDIMENT ADD TECTONISM ?s
vertical subsidence rate L/T ?s - ?s
vertical uplift rate L/T
Grand Canyon, USA
Or
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CONSERVATION OF BED SEDIMENT ADD TRANSVERSE AS
WELL AS STREAMWISE BEDLOAD TRANSPORT (2D) y
transverse coordinate L qb ? qbx qby
transverse volume bedload transport rate per
unit normal distance L2/T
Jamuna River, Bangladesh
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WHAT COMES NEXT? We need to specify forms
for qb, Es, Ds as functions of the flow. Key
parameter boundary shear stress ?b at bed ?b
?CfU2