Moving boundary problems in earth-surface dynamics
1 / 27

Moving boundary problems in earth-surface dynamics , Vaughan R. Voller - PowerPoint PPT Presentation

  • Uploaded on

Moving boundary problems in earth-surface dynamics , Vaughan R. Voller NSF, National Center for Earth-surface Dynamics, University of Minnesota, USA. Input From Chris Paola, Gary Parker, John Swenson, Jeff Marr, Wonsuck Kim, Damien Kawakami. What is NCED?. A National Science Foundation

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
Download Presentation

PowerPoint Slideshow about ' Moving boundary problems in earth-surface dynamics , Vaughan R. Voller' - dore

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

Moving boundary problems in earth-surface dynamics

, Vaughan R. Voller

NSF, National Center for Earth-surface Dynamics,

University of Minnesota, USA.

Input From

Chris Paola, Gary Parker, John Swenson, Jeff Marr,

Wonsuck Kim, Damien Kawakami

What is NCED?

A National Science Foundation

Science and Technology Center

NCED develops integrated models of the physical and ecological dynamics of the channel systems that shape Earth’s surface through time, in support of river management, environmental forecasting, and resource development

Examples of Sediment Fans

Badwater Deathvalley


How does sediment-

basement interface


Two Problems of Interest


Fans Toes

Sediment Transport on a Fluvial Fan

Sediment transported and

deposited over fan surface

From a momentum balance and

drag law it can be shown that

the diffusion coefficient n

is a function of a drag coefficient

and the bed shear stress t

Sediment mass balance gives

when flow is channelized n= constant

when flow is “sheet flow”

A first order approx. analysis indicates n  1/r

(r radial distance from source)

An Ocean Basin


Limit Conditions: Constant Depth Ocean


Enthalpy solution

angle of repose





A “Melting Problem” driven by a fixed flux with Latent Heat L

Track of Shore Line


Limit Conditions: A Fixed Slope Ocean

A Melting Problem driven by a

fixed flux with SPACE DEPENDENT

Latent Heat L = gs





similarity solution


g = 0.5

Enthalpy Sol.

Limit Conditions: Sea-Level Change Very Steep Angle of Repose



Reaches Steady State Position

s = 1/(dL/dt)




Enthalpy Sol.

dL/dt = 0.1

a Repose




Limit Conditions: Sea-Level Change Finite Angle of Repose



An enthalpy like fixed grid

Solution can be constructed

The concept of an “Auto-Retreat” Repose

To stay in one place the flux to the shore front

Needs to increase to account for the increase in the

accommodation increment with each time step

NOT possible

For flux to increase

So shoreline moves landward


a Repose




“Jurassic Tank” A Large Scale Exp. Repose


Computer controlled subsidence

How does shore line move in response to sea-level changes Repose

Swenson et al can be posed as a generalized Stefan Problem

Numerical Solution Repose

1-D finite difference deforming grid

Base level

(n calculated from 1st principles)

Measured and Numerical results

The Desert Fan Problem -- A 2D Problem Repose

A Stefan problem with

zero Latent Heat

A two-dimensional version (experiment) Repose

  • 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

The Numerical Method Repose

-Explicit, Fixed Grid, Up wind Finite Difference VOF like scheme

fill point

The Toe Treatment




Square grid

placed on


.05 grid size

Flux out of toe elements =0

Until Sediment height >

Downstream basement

At end of each time step

Redistribution scheme is required

To ensure that no

“downstream” covered areas are higher

Determine height at fill : Position of toe

Experimental Measurements Repose

  • Pictures taken every half hour

    • Toe front recorded

  • Peak height measure every half hour

  • Grid of squares

  • 10cm x 10cm

Observations (1) Repose

  • Topography

    • Conic rather than convex

    • Slope nearly linear across position and time

    • bell-curve shaped toe

Observations (2) Repose

  • Three regions of flow

    • Sheet flow

    • Large channel flow

    • Small channel flow

  • Continual bifurcation governed by shear stress

y – Reposey(x,t) = 0

On toe

height at input

fan with time

Front Perturbations: An Initial Model Repose

Example shows a “numerical experiment”

of sediment filling of a deep constant depth


with persistent (preferred) channelization

Solution of Exner with

Simplified Swenson-Stefan condition and

Spatially changing diffusion coefficient

Next change

Diffusion field with time

Moving Boundaries on Earth’s surface Repose

A number of moving boundary problems

in sedimentary geology have been


It has been shown that these problems

can be posed as Generalized Stefan


Fixed grid and deforming grid schemes have been shown to produce results in

Reasonable agreement with experiments

Improvements in model are needed

Utilize full range of moving boundary numerical technologies to arrive at

a suite of methods with geological application

Full sim sol Repose