V.R. Voller+, J. B. Swenson*, W. Kim+ and C. Paola+
description
Transcript of V.R. Voller+, J. B. Swenson*, W. Kim+ and C. Paola+
National Center for Earth-surface Dynamicsan NSF Science and Technology Center
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V.R. Voller+, J. B. Swenson*, W. Kim+ and C. Paola+
+ National Center for Earth-surface Dynamics University of Minnesota, Minneapolis*Dept. Geological Sciences and Large Lake Observatory, University of Minnesota-Duluth
National Center for Earth-surface Dynamicsan NSF Science and Technology Center
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Ganges-Brahmaputra Delta “growth” of sediment delta into oceanGrain Growth in Metal Solidification
From W.J. Boettinger
m
10km
Commonality between solidification and ocean basin formation
Geometry and Heat transfer Models of Shoreline movements
1As always “-- the material presented should be approached with an open mind, studied carefully, and critically considered.”
Cobb County Geogia
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Fans Toes Shoreline
Two Problems of Interest
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1km
Examples of Sediment FansMoving Boundary
How does sediment-basement interfaceevolve
Badwater Deathvalley
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sediment
h(x,t)
x = u(t)
0q
bed-rock
ocean
x
shoreline
x = s(t)
land surface
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An Ocean Basin
Melting vs. Shoreline movement
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pressurizedwater reservoir
to water supply
solenoidvalve
stainless steelcone
to gravel recycling
transport surface
gravel basement
rubber membrane
experimental deposit
Experimental validation of shoreline boundary condition
~3m
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Experimental validation of shoreline boundary condition
dtdS)su(2
1dx)x(dtdZ)su()t,s(qdt
dsS)su( f2u
s
blsff
eXperimental EarthScape facility (XES)
Flux balance at shoreline
Flux base subsidence slope
Calculated frontvelocity from
exp. measurment of RHS
measured
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Base level
Measured and Numerical results ( calculated from 1st principles)
1-D finite difference deforming grid vs. experiment
xxt+Shoreline balance
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Limit Conditions: A Fixed Slope Oceanq=1
s(t)
similarity solution
q2
)(erfe
)(erf1,t2s2
2/1
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Time
shor
elin
e
0if),x(LH
2
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xtH
Enthalpy Sol.
A Melting Problem driven by a fixed flux with SPACE DEPENDENT
Latent Heat L = s
dtdss
x)t(sx0,
xt s2
2
s Depth at toe
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h(x,y,t)
q
bed-rock
ocean
y
shoreline
x = s(t)
land surface
(x,y,t)
A 2-D Front -Limit of Cliff face Shorefront But Account of Subsidence and relative ocean level
0hif),t,y,x(LhH
)h(tH
Enthalpy Sol.
xy]/H,1[MINfrac
Solve on fixed gridin plan view
Track Boundary by calculating in each cell
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0
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time
shor
elie
n po
sitio
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time
shor
elin
e po
sitio
nnumericalsteady state
s(t)
s(t)
Hinged subsidenceq2
)(erfe
)(erf1,t2s2
2/1
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A 2-D problem Sediment input into an oceanwith an evolving trench driven By hinged subsidence
First look at case whereOcean is at constant depthNO TRENCH
Then Look at case with Trench
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National Center for Earth-surface Dynamicsan NSF Science and Technology Center
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National Center for Earth-surface Dynamicsan NSF Science and Technology Center
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National Center for Earth-surface Dynamicsan NSF Science and Technology Center
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National Center for Earth-surface Dynamicsan NSF Science and Technology Center
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National Center for Earth-surface Dynamicsan NSF Science and Technology Center
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With Trench
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National Center for Earth-surface Dynamicsan NSF Science and Technology Center
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National Center for Earth-surface Dynamicsan NSF Science and Technology Center
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National Center for Earth-surface Dynamicsan NSF Science and Technology Center
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National Center for Earth-surface Dynamicsan NSF Science and Technology Center
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No Trench Trench
Plan view movement of fronts
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s(t) s(t)
R
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shoreline
sea-level
geometric – modelof shoreline movementwith changing sea level
q=1
Assumption of rapid fluvial transport allow for a geometric balance
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2
22
RBQ2RRu
0RQ
Ruu2
2)uR(
2uRuQ
NOTE: REVERSE of shoreline! u(t)
t
0
t
0
dtqQ
dtrR
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sediment
Movement of sediment plug behind a dam Dam reservoir profileWith sediment plug downstream of dam
At time t = 0 water levelin reservoir dropped at a Constant rate
assume cliff faceno flow in or out
Describe movement ofSediment by
2
2
xtH
)t(LH
Water depth
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Experiments by Chris Bromley, University of Nottingham
Ekwha dam Oregon
National Center for Earth-surface Dynamicsan NSF Science and Technology Center
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National Center for Earth-surface Dynamicsan NSF Science and Technology Center
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National Center for Earth-surface Dynamicsan NSF Science and Technology Center
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National Center for Earth-surface Dynamicsan NSF Science and Technology Center
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National Center for Earth-surface Dynamicsan NSF Science and Technology Center
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National Center for Earth-surface Dynamicsan NSF Science and Technology Center
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Movement of toeGoes as t2
Movement of sediment plug behind a dam drawdown rate
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WHY Build a model
Stratigraphy and Shoreline
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Models can predict stratigraphy“sand pockets” = OIL
The Po
Shoreline position is signature of channels
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Shoreline Tracking Model has beenValidated (Experiments)
And a numerical method based on HeatTransfer concepts has been Verified. 0hif),t,y,x(LhH
)h(tH
Enthalpy Sol.
Will allow for a first cut simulationof how sea-level and subsidence Could effect the motion of shorelines
Can be used to model short time systemsRelated to dam removal
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Space and time dependent latent heat
Other Systems of interest
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e.g. the Dessert Sediment Fan
1km
How does sediment-basement interfaceevolve
Badwater Deathvalley
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An experiment
• Water tight basin -First layer: gravel to allow easy drainage-Second layer: F110 sand with a slope ~4º.
• Water and sand poured in corner plate
• Sand type: Sil-Co-Sil at ~45 mm• Water feed rate:
~460 cm3/min• Sediment feed rate: ~37cm3/min
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The Desert Fan Problem
xxt )t,s(,0x s
A Stefan problem with zero Latent Heat
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The Numerical Method-Explicit, Fixed Grid, Up wind Finite Difference VOF like scheme
Flux out of toe elements =0Until Sediment height >Downstream basement
fill point
P
)qq(tout2P
newP in
E
The Toe Treatment EPq
Square grid placed onbasement
At end of each time stepRedistribution scheme is requiredTo ensure that no “downstream” covered areas are higher
r
Determine height at fill : Position of toe
.05 grid size
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y – (x,t) = 0
0y)t,x(,0xW
),y,x(Qxxxxt
),x(,0 s n
On toe0
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00.511.5
x-location (m)
y-location (m)
rk
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time (min)
feed
hig
ht (m
) height at input
fan with time