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Scale effects in subaerial landslide generated impulse waves

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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.

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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

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Acknowledgments

The first author was supported from the Swiss National Science Foundation, Grant 200020-103480/1.

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Authors and Affiliations

  1. Laboratory of Hydraulics, Hydrology and Glaciology (VAW), ETH Zurich, 8092, Zurich, Switzerland

    Valentin Heller, Willi H. Hager & Hans-Erwin Minor

Authors
  1. Valentin Heller
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  2. Willi H. Hager
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  3. Hans-Erwin Minor
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Correspondence to Valentin Heller.

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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

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