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Landslide generated impulse waves.

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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. The challenges posed to the measurement system in an extremely unsteady three-phase flow consisting of granular matter, air, and water were considered. The complex flow phenomena in the first stage of impulse wave initiation are: high-speed granular slide impact, slide deformation and penetration into the fluid, flow separation, hydrodynamic impact crater formation, and wave generation. During this first stage the three phases are separated along sharp interfaces changing significantly within time and space. Digital masking techniques are applied to distinguish between phases thereafter allowing phase separated image processing. 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, elongational, and shear strain were extracted from the velocity vector fields. The fundamental assumption of irrotational flow in the Laplace equation was confirmed experimentally for these non-linear waves. Applicability of PIV at large scale as well as to flows with large velocity gradients is highlighted.

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Fig. 1.
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Fig. 3. a
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Fig. 6a–c.
Fig. 7a–c.
Fig. 8.
Fig. 9A–F.
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Fig. 11A–F.

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Abbreviations

a :

wave amplitude (L)

c :

wave celerity (LT−1)

d diff :

diffraction limited minimum particle image diameter (L)

d e :

diffracted particle image diameter (L)

d g :

granulate grain diameter (L)

d p :

seeding particle diameter (L)

d τ :

recorded particle image diameter (L)

f :

focal length (L)

f # :

f number (-)

F :

slide Froude number (-)

g :

gravitational acceleration (LT−2)

h :

still-water depth (L)

H :

wave height (L)

l s :

slide length (L)

L :

wavelength (L)

M :

magnification (-)

m s :

slide mass (M)

n :

refractive index (-)

n por :

slide porosity (-)

N iw :

number of seeding particles in an interrogation window (-)

N pair :

number of detected particle image pairs in window (-)

p :

interrogation window size p×p pixels; 1 pixel=9 μm (L)

P :

probability (-)

P il :

probability of in-plane loss of particle (-)

P ol :

probability of out-of-plane loss of particle (-)

s :

slide thickness (L)

S :

relative slide thickness (-)

t :

time after impact (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 py :

crosswise 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 iw :

interrogation volume (L3)

V s :

slide volume (L3)

x :

streamwise coordinate (L)

x ip :

area of view x dimension in image plane (L)

z :

vertical coordinate (L)

α :

slide impact angle (°)

δ :

bed friction angle (°)

δy :

depth of field (L)

Δt :

laser pulse separation (T)

Δx :

mean particle image x displacement in interrogation window (L)

ε Δx :

random displacement Δx error (L)

ε v :

random velocity v error (LT−1)

ε tot :

total random velocity v error (LT−1)

ε bias :

velocity v error due to biased correlation analysis (LT−1)

ε optics :

velocity v error due to optical imaging errors (LT−1)

ε track :

velocity v error due to particle flow tracking 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)

λ :

wavelength (L)

μ :

dynamic viscosity (ML−1T−1)

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. Laboratory of Hydraulics, Hydrology and Glaciology (VAW), Swiss Federal Institute of Technology (ETH), CH-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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Fritz, H.M., Hager, W.H. & Minor, HE. Landslide generated impulse waves. . Exp Fluids 35, 505–519 (2003). https://doi.org/10.1007/s00348-003-0659-0

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