Upload
gus
View
45
Download
0
Embed Size (px)
DESCRIPTION
~10m m. Grain Growth in Metal Solidification From W.J. Boettinger. National Center for Earth-surface Dynamics an NSF Science and Technology Center. MOVING BOUNDARY PROBLEMS ON THE EARTHS SURFACE V.R. Voller+, J. B. Swenson*, W. Kim+ and C. Paola+ - PowerPoint PPT Presentation
Citation preview
National Center for Earth-surface Dynamicsan NSF Science and Technology Center
www.nced.umn.edu
MOVING BOUNDARY PROBLEMS ON THE EARTHS SURFACEV.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
www.nced.umn.edu
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
National Center for Earth-surface Dynamicsan NSF Science and Technology Center
www.nced.umn.edu
An Ocean Basin
Melting vs. Shoreline movement
National Center for Earth-surface Dynamicsan NSF Science and Technology Center
www.nced.umn.edu
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
National Center for Earth-surface Dynamicsan NSF Science and Technology Center
www.nced.umn.edu
Experimental validation of shoreline boundary condition
dt
dS)su(
21
dx)x(dt
dZ)su()t,s(q
dtds
S)su( f2u
s
blsff
eXperimental EarthScape facility (XES)
Flux balance at shoreline
Flux base subsidence slope
Calculated frontvelocity from
exp. measurment of RHS
measured
National Center for Earth-surface Dynamicsan NSF Science and Technology Center
www.nced.umn.edu
Limit Conditions: A Fixed Slope Ocean
q=1
s(t)
similarity solution
q
2
)(erfe
)(erf1,t2s
22/1
21
21
2
21
21
0
5
10
15
20
25
0 100 200 300
Time
sh
ore
line
0if),x(LH
2
2
xt
H
Enthalpy Sol.
A Melting Problem driven by a fixed flux with SPACE DEPENDENT
Latent Heat L = s
dt
dss
x)t(sx0,
xt s2
2
National Center for Earth-surface Dynamicsan NSF Science and Technology Center
www.nced.umn.edu
A Further Limit Solution—No sediment storage in the fluvial domain
s(t)
Let diffusivity LARGE in analyticalsolution
qt2s
From previous analytical or
Simple Geometry
s(t)
A even more simple versionAssume a “cliff” face at shoreline
Can model 2-D problem like polymer filling
National Center for Earth-surface Dynamicsan NSF Science and Technology Center
www.nced.umn.edu
A Monte-Carlo (lattice-Boltzmann) Polymer Filling Algorithm
“Dump” total flux in “gate” cell and redistribute excess over amount requiredfor filling to neighboring cells in ratios proportional tocoefficients of the discretization of
0)k( Iteration can be written in the form of Lattice Boltzmann iterations
Voller: To be published in JCP 2005
0)k( Note:
Can be used to accountfor effects of channels
PW E
]0,1F[MAX]0,1F[MAX]1,F[MINF E21
W21
PNEWP
In One-D iterations could look like
National Center for Earth-surface Dynamicsan NSF Science and Technology Center
www.nced.umn.edu
High K(1) chanalized surface
Low K(0.05) few channels
Simulation of shoreline motion into a variable depth ocean with variable channelization
t=50
National Center for Earth-surface Dynamicsan NSF Science and Technology Center
www.nced.umn.edu
t=100
National Center for Earth-surface Dynamicsan NSF Science and Technology Center
www.nced.umn.edu
t=150
National Center for Earth-surface Dynamicsan NSF Science and Technology Center
www.nced.umn.edu
t=200
National Center for Earth-surface Dynamicsan NSF Science and Technology Center
www.nced.umn.edu
t=250
National Center for Earth-surface Dynamicsan NSF Science and Technology Center
www.nced.umn.edu
t=300
National Center for Earth-surface Dynamicsan NSF Science and Technology Center
www.nced.umn.edu
WHY Build a model
Stratigraphy and Shoreline
-30-20-10
0102030405060
0 10 20 30
Models can predict stratigraphy“sand pockets” = OIL
The Poe
Shoreline position is signature of channels
National Center for Earth-surface Dynamicsan NSF Science and Technology Center
www.nced.umn.edu
s(t) s(t)
z(t)
Further Work:--Include Ocean Level Rise
0
5
10
15
20
25
30
35
40
45
50
0 20 40 60 80 100
shoreline
sea-level
geometric – modelof shoreline movementwith changing sea level
NOTE: REVERSE ofshoreline!
q=1