Skip to main content

Numerical Solution to Horizontal Zero-inertia, Viscous Dam-Break Problem

  • Conference paper

Abstract

Debris flows such as avalanches and lahars differ from the classical dam-break problem of hydraulics due to the relative importance of viscous versus inertial forces in the momentum balance. An equation of motion describing debris flow in the limit of zero inertia is developed and solved using a converged finite difference numerical, in two limits: short time and long time. These solutions are then combined into a single, universal model.

Keywords

  • Debris Flow
  • Free Surface Profile
  • Flow Height
  • Shallow Water Approximation
  • Short Time Solution

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   129.00
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   169.99
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   169.99
Price excludes VAT (Canada)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. A. Ritter ,,Die fortpflanzung der wesser wellen.“ Ver Deutsch Ingenieure Zeitschrift, vol. 36(33), pp. 947-954, 1892 (in German)

    Google Scholar 

  2. M. A. Gill, “Dam-break problem.” Encyclopedia of fluid mechanics, 6, N.P. Cheremisinoff, eds., Gulf, Houston (Texas), 1429-1473, 1987

    Google Scholar 

  3. B. Zanuttigh and A. Lamberti, “Dam-Break Waves in Power-Law Channel Section.” J. Hydr. Eng. (ASCE), vol. 127(4), pp. 322-326, 2001

    CrossRef  Google Scholar 

  4. Frazao, S.S. and Zech, “Dam-Break in Channels with 90r Bend.” J. Hydr. Eng. (ASCE), vol. 128(11), pp. 956-968, 2002

    CrossRef  Google Scholar 

  5. B. De Saint-Venant, “Théorie du mouvement non permanent des eaux”, C. R. Acad. Sci., vol. 73(3), pp. 147-154, 1871 (in French)

    Google Scholar 

  6. Faure, J. And Nahas, N., “Etude numérique et expérimentale d’intumescences á forte courbure du front.”, La Houille Blanche, vol. 16(5), pp. 576-587, 1961 (in French)

    Google Scholar 

  7. B. Hunt, “Newtonian fluid mechanics treatment of debris flows and avalanches”, J. Hydr. Div. (ASCE), vol. 120(12), 1350-1363, 1994

    Google Scholar 

  8. B. Nsom, K. Debiane, and J. M. Piau, “Bed slope effect in the dam-break problem”, J. Hydr. Res. (IAHR), vol. 38(6), pp. 459-464, 2000

    Google Scholar 

  9. B. Nsom, “Horizontal Viscous Dam-Break Flood: Experiments and Theory.” J. Hydr. Eng. (ASCE), vol. 128(5), pp. 543-546, 2002

    CrossRef  Google Scholar 

  10. L. W. Schwarz, ,,Viscous flows down an inclined plane: Instability and finger formation.”, Phys. Fluids A, vol. 1(3), pp. 443-445, 1989

    CrossRef  Google Scholar 

  11. C. Zoppou, and S. Roberts, “Explicit Schemes for Dam-Break Simulations” J. Hydr. Eng.(ASCE), vol. 129(1), pp. 11-34, 2003

    CrossRef  Google Scholar 

  12. T. Shigematsu, P.L.F. Liu, and K. Oda, “Numerical modeling of the initial stages of dam-break waves.” J. Hydr. Res. (IAHR), vol. 42(2), pp. 183-195, 2004

    Google Scholar 

  13. D. Barthes-Biesel, “ Rectification d’un film liquide sous l’effet de la gravité et de la tension superficielle ” http://www.enseignement.polytechnique.fr/profs/informatique/Georges.Gonthier/pi98/film.html}>, June 1, 1998 (in French)

    Google Scholar 

  14. G.D. Smith, Numerical Solution of Partial Differential Equations, Oxford University Press, New York, 1969.

    Google Scholar 

  15. G.E. Forsythe and W.R. Wasow, Finite-Difference Methods for Partial Differential Equations, John Wiley and Sons, New York, 1967

    Google Scholar 

  16. R.D. Richtmyer, and K.W. Morton, Difference Methods for Initial Value Problems, John Wiley and Sons, New York, 1967

    MATH  Google Scholar 

  17. R.C. Weast, M.J. Astle and W.H. Beyer, eds., Handbook of chemistry and physics, CRC, Boca Raton (Fla), 1987

    Google Scholar 

  18. H.E. Huppert, “The propagation of two-dimensional and axisymmetric viscous gravity currents over a rigid horizontal surface”, J. Fluid Mech., vol. 121, pp. 43-58, 1982

    CrossRef  Google Scholar 

  19. J.C. Martin, and W.J. Moyce, “An experimental study of the collapse of liquid columns on a rigid horizontal plane”, Phil. Trans. Roy. Soc. Lond. A, vol. 244(882), pp. 312-324, 1952

    CrossRef  Google Scholar 

  20. P.K. Stanby, A. Chegni and T.C.D. Barnes. “The initial stages of dam-break flow”, J. Fluid Mech., vol. 374, pp. 407-424, 1998.

    CrossRef  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 2007 Springer

About this paper

Cite this paper

NSOM, B., JENNY, M., ASKOURA, Y., PERON, F. (2007). Numerical Solution to Horizontal Zero-inertia, Viscous Dam-Break Problem. In: Sobh, T. (eds) Innovations and Advanced Techniques in Computer and Information Sciences and Engineering. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-6268-1_23

Download citation

  • DOI: https://doi.org/10.1007/978-1-4020-6268-1_23

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-1-4020-6267-4

  • Online ISBN: 978-1-4020-6268-1

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics