Abstract
Hydraulic scale modelling involves scale effects. The limiting criteria for scale models of subaerial landslide generated impulse waves including solid, air, and water are discussed both based on a literature review and based on detailed two-dimensional experimentation. Seven scale series based on the Froude similitude were conducted involving the intermediate-water wave spectrum. Scale effects were primarily attributed to the impact crater formation, the air entrainment and detrainment, and the turbulent boundary layer as a function of surface tension and fluid viscosity. These effects reduce the relative wave amplitude and the wave attenuation as compared with reference experiments. Wave amplitude attenuation was found to be more than 70 times larger than predicted with the standard wave theory. Limitations for plane impulse wave generation on the basis of the present research are given by which scale effects can be avoided.
Similar content being viewed by others
Abbreviations
- a :
-
wave amplitude (L)
- a x′ :
-
wave amplitude at distance x′ from CWG1 (L)
- A :
-
relative wave amplitude (−)
- A 1d :
-
relative amplitude difference at CWG1 (%)
- A 1dtot :
-
total relative amplitude difference (%)
- A 1dZ :
-
relative amplitude difference according to Zweifel et al. (2006) (%)
- A 1ref :
-
relative reference amplitude at CWG1 (−)
- b :
-
channel width (L)
- c :
-
wave celerity (LT−1)
- C:
-
Cauchy number (−)
- d g :
-
grain diameter (L)
- D :
-
relative slide density (−)
- D g :
-
relative grain diameter (−)
- F:
-
slide Froude number (−)
- g :
-
gravitational acceleration (LT−2)
- h :
-
still water depth (L)
- H :
-
wave height (L)
- j :
-
number of governing dimensionless quantities (−)
- L :
-
wavelength (L)
- m :
-
number of governing independent parameters on impulse wave generation (–)
- m s :
-
slide mass (M)
- M :
-
relative slide mass (−)
- n :
-
bulk slide porosity (%)
- o :
-
number of fundamental units (−)
- p A :
-
box acceleration air pressure (ML−1T−2)
- R:
-
Reynolds number (−)
- s :
-
slide thickness (L)
- S :
-
relative slide thickness (−)
- t :
-
time (T)
- T :
-
wave period (T)
- T r :
-
relative time (−)
- Te :
-
water temperature (°C)
- V :
-
relative slide volume (−)
- V s :
-
slide impact velocity (LT−1)
- \( -\!\!\!\!V_{s} \) :
-
slide volume identical to box volume (L3)
- W:
-
Weber number (−)
- x :
-
streamwise coordinate (L)
- x′ :
-
distance from CWG1 (L)
- X :
-
relative streamwise distance (−)
- Y P :
-
relative primary wave height (−)
- z :
-
vertical coordinate (L)
- α :
-
slide impact angle (°)
- β :
-
average wave amplitude attenuation (%)
- δ :
-
dynamic bed friction angle (°)
- Δ:
-
time increment (T)
- Δx′ :
-
spacing between CWG1 and CWG7 (L)
- ΔX :
-
relative spacing between CWG1 and CWG7 (−)
- ϕ′:
-
internal friction angle (°)
- η :
-
water surface displacement (L)
- κ w :
-
water compressibility (LT2M−1)
- ν w :
-
kinematic viscosity for water (L2T−1)
- ρ :
-
density (ML−3)
- σ w :
-
surface tension for water (MT−2)
- A :
-
acceleration
- d :
-
difference
- g :
-
grain
- K :
-
Keulegan
- L :
-
limit
- M :
-
maximum
- P :
-
primary
- r :
-
relative
- ref :
-
reference
- s :
-
slide
- tot :
-
total
- w :
-
water
- Z :
-
Zweifel
- 1:
-
at CWG1
- 3:
-
at CWG3
- 5:
-
at CWG5
- 7:
-
at CWG7
References
Abelson HI (1970) Pressure measurements in the water-entry cavity. J Fluid Mech 44(1):129–144
Biesel F (1949) Calcul de l’amortissement d’une houle dans un liquide visqueux de profondeur finite (in French). La Houille Blanche 4(5):630–634
Buckingham E (1914) On physically similar systems. Phys Rev 4:354–376
De St Q Isaacson M (1976) The viscous dam** of cnoidal waves. J Fluid Mech 75(3):449–457
Dean RG, Dalrymple RA (2004) Water wave mechanics for engineers and scientists: advanced series on ocean engineering, vol 2. World Scientific, Singapore
Fritz HM (2002) Initial phase of landslide generated impulse waves. In: Minor H-E (ed) VAW-Mitteilung, vol 178. Versuchsanstalt für Wasserbau, Hydrologie und Glaziologie, ETH, Zurich
Fritz HM, Moser P (2003) Pneumatic landslide generator. Int J Fluid Power 4(1):49–57
Fritz HM, Hager WH, Minor H-E (2001) Lituya bay case: rockslide impact and wave run-up. Sci Tsunami Hazards 19(1):3–22
Fritz HM, Hager WH, Minor H-E (2003) Landslide generated impulse waves. Exp Fluids 35:505–532 doi:10.1007/s00348-003-0659-0
Führböter A (1970) Air entrainment and energy dissipation in breakers. In: Proceedings of the 12th coastal engineering conference, Washington DC, vol 1. ASCE, New York, pp 391–398
Hager WH, Bremen R (1989) Classical hydraulic jump: sequent depths. J Hydraul Res 27(5):565–585
Hampton MA, Lee HJ, Locat J (1996) Submarine landslides. Rev Geophys 34(1):33–59
Heinrich P (1992) Nonlinear water waves generated by submarine and aerial landslides. J Waterw Port Coast Ocean Eng 118(3):249–266
Heller V (2007a) Landslide generated impulse waves: prediction of near field characteristics. Dissertation 17531, ETH, Zurich (submitted)
Heller V (2007b) Massstabseffekte im hydraulischen Modell (in German). Wasser Energie Luft 99(2):153–159
Huber A (1976) Grenzen der Froude’schen Ähnlichkeit bei der Nachbildung flacher Wasserwellen im hydraulischen Modell (in German). In: Vischer D (ed) VAW-Mitteilung, vol 21. Versuchsanstalt für Wasserbau, Hydrologie und Glaziologie, ETH, Zurich
Huber A (1980) Schwallwellen in Seen als Folge von Bergstürzen (in German). In: Vischer D (ed) VAW-Mitteilung, vol 47. Versuchsanstalt für Wasserbau, Hydrologie und Glaziologie, ETH, Zurich
Hudson RY, Herrmann FA, Sager RA, Whalin RW, Keulegan GH, Chatham CE, Hales LZ (1979) Coastal hydraulic models. Special report no 5, US Army Engineer Waterways Experiment Station, Vicksburg, Mississippi
Hughes S (1993) Physical models and laboratory techniques in coastal engineering. Advanced series on ocean engineering, vol 7. World Scientific, Singapore
Ippen AT, Kulin G (1957) The effects of boundary resistance on the solitary wave. La Houille Blanche 12(3):390–407
Iwasa Y (1959) Attenuation of solitary waves on a smooth bed. Trans ASCE 124:193–206
Kamphuis JW, Bowering RJ (1972) Impulse waves generated by landslides. In: Proceedings of 12th Coastal Engineering Conference, Washington DC, vol 1. ASCE, New York, pp 575–588
Keulegan GH (1950) Wave motion. In: Rouse H (ed) Engineering hydraulics. Wiley, New York
Le Méhauté B (1976) An introduction to hydrodynamics and water waves. Springer, New York
Le Méhauté B (1990) Similitude. In: Le Méhauté B, Hanes DM (eds) The sea ocean engineering science, vol 9B. Wiley, New York, pp 955–980
Miles JW (1976) Dam** of weakly nonlinear shallow-water waves. J Fluid Mech 76(2):251–257
Miller DJ (1960) Giant waves in Lituya Bay, Alaska. Geological survey, Professional paper 354-C. US Government Printing Office, Washington DC
Miller RL (1972) The role of surface tension in breaking waves. In: Proceedings of the 13th coastal engineering conference, Vancouver BC, vol 1. ASCE, New York, pp 433–449
Noda E (1970) Water waves generated by landslides. J Waterw Harb Coast Eng Div ASCE 96(WW4):835–855
Panizzo A (2004) Physical and numerical modelling of subaerial landslide generated waves. Dissertation, Università degli studi, L’Aquila, Italy
Panizzo A, De Girolamo P (2005) Forecasting impulse waves generated by subaerial landslides. J Geophys Res 110(C12025):1–23 doi: 10.1029/2004JC002778
Panizzo A, Bellotti G, De Girolamo P (2002) Application of wavelet transform analysis to landslide generated waves. Coast Eng 44:321–338
Pugh FJ, Wilson KC (1999) Velocity and concentration distributions in sheet flow above plane beds. J Hydraul Eng 125(2):117–125
Skladnev MF, Popov IY (1969) Studies of wave loads on concrete slope protections of earth dams. In: Research on wave action, vol 2(7). Delft, The Netherlands, pp 1–11
Stive MJF (1985) A scale comparison of waves breaking on a beach. Coast Eng 9:151–158
Treloar PD, Brebner A (1970) Energy losses under wave action. In: Proceedings of the 12th coastal engineering conference, Washington DC, vol 1. ASCE, New York, pp 257–267
Walder JS, Watts P, Sorensen OE, Janssen K (2003) Tsunami generated by subaerial mass flows. J Geophys Res 108(B5):2.1–2.19
Zweifel A, Hager WH, Minor H-E (2006) Plane impulse waves in reservoirs. J Waterway Port Coast Ocean Eng 132(5):358–368
Acknowledgments
The first author was supported from the Swiss National Science Foundation, Grant 200020-103480/1.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Heller, V., Hager, W.H. & Minor, HE. Scale effects in subaerial landslide generated impulse waves. Exp Fluids 44, 691–703 (2008). https://doi.org/10.1007/s00348-007-0427-7
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00348-007-0427-7