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Methods of similitude in granular avalanche flows

  • Snow Thermo-Mechanics, Avalanches
  • Conference paper
  • First Online:
Advances in Cold-Region Thermal Engineering and Sciences

Part of the book series: Lecture Notes in Physics ((LNP,volume 533))

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Abstract

Snow avalanches are relatively dry and dense granular flows for which the Savage-Hutter (SH) equations have been demonstrated to be an adequate mathematical model. We review these equations and point out for which cases the equations have been tested against laboratory experiments. Since the equations are scale invariant and because agreement with experiments is good, laboratory experiments can be used to test realistic flows. This is detailed in this paper. We demonstrate how shocks are formed when dilatational flow states merge into compacting states and show that shock formation is an essential mechanism in flows against obstructions. We finally apply the theory of similitude to the design of a projected avalanche protection structure of the Schneefernerhaus at the Zugspitze.

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References

  1. Gray, J. M. N. T. and Hutter, K., Pattern formation in granular avalanches, Continuum Mechanics and Thermodynamics, 9 (1997), 341–345

    Article  ADS  Google Scholar 

  2. Gray, J. M. N. T. and Hutter, K., Physik granularer Lawinen, Physikalische Blätter, 54 (1998), 37–44

    Google Scholar 

  3. Gray, J. M. N. T., Wieland, M. and Hutter, K., Gravity driven free surface flow of granular avalanches over complex basal topography, Proc. R. Soc. London (in press)

    Google Scholar 

  4. Greve, R. and Hutter, K., Motion of a granular avalanche in a convex and concave curved chute: experiments and theoretical predictions, Phil. Trans. R. Soc. London, A342 (1993), 573–600)

    Article  ADS  Google Scholar 

  5. Greve, R., Koch, T. and Hutter, K., Unconfined flow of granular avalanches along a partly curved surface — Part I: Theory, Proc. Royal Soc. London, 445A (1994), 399–413

    Article  ADS  MATH  Google Scholar 

  6. Hutter, K., Avalanche Dynamics, A Review, In: Hydrology of Disasters (V. P. Singh, ed.), Kluwer Academic, Amsterdam, 1996, pp. 313–390

    Google Scholar 

  7. Hutter, K. and Greve, R., Two-dimensional similarity solutions for finite mass granular avalanches with Coulomb and viscous-type frictional resistance, J. Glaciology 39, 357–372 (1993)

    ADS  Google Scholar 

  8. Hutter, K. and Koch, T., Motion of a granular avalanche in an exponentially curved chute: Experiments and theoretical predictions, Phil. Trans. Royal Soc. London, A334 (1991): 93–138

    Article  ADS  Google Scholar 

  9. Hutter, K., Koch, T., Plüss, C. and Savage, S. B., Dynamics of avalanches of granular materials from initiation to runout, Part II: Laboratory experiments, Acta Mechanica 109 (1995), 127–165

    Article  MathSciNet  Google Scholar 

  10. Koch, T., Greve, R. and Hutter, K., Unconfined flow of granular avalanches along a partly curved surface — Part II: Experiments and numerical computations, Proc. Royal Soc. London, 445A (1994), 415–435

    Article  ADS  MATH  Google Scholar 

  11. Savage, S. B. and Hutter, K., The motion of a finite mass of granular material down a rough incline, J. Fluid Mech. 199 (1989): 177–215

    Article  ADS  MATH  MathSciNet  Google Scholar 

  12. Savage, S. B. and Hutter, K., Dynamics of avalanches of granular materials from initiation to runout, Part: Analysis, Acta Mechanica, 86 (1991): 201–223

    Article  MATH  MathSciNet  Google Scholar 

  13. Tai, Y.C. An application of shock-capturing numerical schemes to the dynamics of granular material. Dissertation for the doctoral degree, TU Darmstadt, (in preparation).

    Google Scholar 

  14. Tai, Y.C., Gray, J.M.N.T. and Noelle, S., Front-tracking method with Nonoscilatory Central Scheme for the free moving boundary problem., (in preparation).

    Google Scholar 

  15. Wieland, M., Gray, J. M. N. T. and Hutter, K., Channelised free surface flow of cohesionless granular avalanche in a chute with shallow lateral curvature, J. Fluid Mech. (in press)

    Google Scholar 

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Authors and Affiliations

  1. Institute of Mechanics, Darmstadt University of Technology, Hochschulstraße 1, 64289, Darmstadt, Germany

    Yih-Chin Tai, Yongqi Wang, J. M. N. T. Gray & Kolumban Hutter

Authors
  1. Yih-Chin Tai
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  2. Yongqi Wang
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  3. J. M. N. T. Gray
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  4. Kolumban Hutter
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Editor information

Kolumban Hutter Yongqi Wang Hans Beer

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© 1999 Springer-Verlag

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Tai, YC., Wang, Y., Gray, J.M.N.T., Hutter, K. (1999). Methods of similitude in granular avalanche flows. In: Hutter, K., Wang, Y., Beer, H. (eds) Advances in Cold-Region Thermal Engineering and Sciences. Lecture Notes in Physics, vol 533. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0104200

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  • DOI: https://doi.org/10.1007/BFb0104200

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-66333-1

  • Online ISBN: 978-3-540-48410-3

  • eBook Packages: Springer Book Archive

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