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Landslide generated impulse waves. 2. Hydrodynamic impact craters

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Abstract

Landslide generated impulse waves were investigated in a two-dimensional physical laboratory model based on the generalized Froude similarity. Digital particle image velocimetry (PIV) was applied to the landslide impact and wave generation. Areas of interest up to 0.8 m by 0.8 m were investigated. PIV provided instantaneous velocity vector fields in a large area of interest and gave insight into the kinematics of the wave generation process. Differential estimates such as vorticity, divergence, and elongational and shear strain were extracted from the velocity vector fields. At high impact velocities flow separation occurred on the slide shoulder resulting in a hydrodynamic impact crater, whereas at low impact velocities no flow detachment was observed. The hydrodynamic impact craters may be distinguished into outward and backward collapsing impact craters. The maximum crater volume, which corresponds to the water displacement volume, exceeded the landslide volume by up to an order of magnitude. The water displacement caused by the landslide generated the first wave crest and the collapse of the air cavity followed by a run-up along the slide ramp issued the second wave crest. The extracted water displacement curves may replace the complex wave generation process in numerical models. The water displacement and displacement rate were described by multiple regressions of the following three dimensionless quantities: the slide Froude number, the relative slide volume, and the relative slide thickness. The slide Froude number was identified as the dominant parameter.

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Abbreviations

a :

wave amplitude (L)

b :

slide width (L)

c :

wave celerity (LT−1)

d g :

granulate grain diameter (L)

d p :

seeding particle diameter (L)

F :

slide Froude number

g :

gravitational acceleration (LT−2)

h :

stillwater depth (L)

H :

wave height (L)

l s :

slide length (L)

L :

wave length (L)

M :

magnification

m s :

slide mass (M)

n por :

slide porosity

Q d :

water displacement rate (L3)

Q D :

maximum water displacement rate (L3)

Q s :

maximum slide displacement rate

s :

slide thickness (L)

S :

relative slide thickness

t :

time after impact (T)

t D :

time of maximum water displacement volume (L3)

t qD :

time of maximum water displacement rate (L3)

t si :

slide impact duration (T)

t sd :

duration of subaqueous slide motion (T)

T :

wave period (T)

v :

velocity (LT−1)

v p :

particle velocity (LT−1)

v px :

streamwise horizontal component of particle velocity (LT−1)

v pz :

vertical component of particle velocity (LT−1)

v s :

slide centroid velocity at impact (LT−1)

V :

dimensionless slide volume

V d :

water displacement volume (L3)

V D :

maximum water displacement volume (L3)

V s :

slide volume (L3)

x :

streamwise coordinate (L)

z :

vertical coordinate (L)

α :

slide impact angle (°)

δ :

bed friction angle (°)

Δx :

mean particle image x-displacement in interrogation window (L)

ε Δx :

random displacement Δx error (L)

ε tot :

total random velocity v error (LT−1)

ε xx :

streamwise horizontal elongational strain component (1/T)

ε xz :

shear strain component (1/T)

ε zx :

shear strain component (1/T)

ε zz :

vertical elongational strain component (1/T)

η :

water surface displacement (L)

ρ :

density (ML−3)

ρ g :

granulate density (ML−3)

ρ p :

particle density (ML−3)

ρ s :

mean slide density (ML−3)

ρ w :

water density (ML−3)

ϕ′:

granulate internal friction angle (°)

ω y :

vorticity vector component (out-of-plane) (1/T)

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Acknowledgements

The research work presented was supported by the Swiss National Science Foundation, grant number 2100-050586.97. The whole PIV system was generously funded by an extraordinary credit issued by the Swiss Federal Institute of Technology (ETH).

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  1. H. M. Fritz

    Present address: Georgia Institute of Technology, 210 Technology Circle, Savannah, GA, 31407, USA

Authors and Affiliations

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

    H. M. Fritz, W. H. Hager & H.-E. Minor

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  1. H. M. Fritz
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  2. W. H. Hager
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Correspondence to H. M. Fritz.

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Fritz, H.M., Hager, W.H. & Minor, HE. Landslide generated impulse waves. 2. Hydrodynamic impact craters. Exp Fluids 35, 520–532 (2003). https://doi.org/10.1007/s00348-003-0660-7

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