|Analysis of landslide generated tsunamis
and scaling the Lituya Bay Scenario
Landslide generated tsunamis, because they do not always cause as large of a water column displacement as earthquake generated tsunamis, are seen to have smaller wavelengths. However, the amplitude and wave run-up generated from landslide tsunamis is similar. The particular scaling involved with this analog model leaves many aspects of the necessary equation constant. The important components when dealing with landslide generated waves according to Kofoed-Hansen, Giménez and Kronborg in their work, is the instantaneous water depth, time varying bathymetry, surface evolution, flux densities, depth averaged velocities, acceleration due to gravity, wind friction, water density, and time. For the purpose of this experiment the surface evolution, flux density, averaged depth velocities, and wind friction are considered to be constant due to the system the waves were generated in. This gives a basic formula looking like: ∂h/∂t - ∂d/∂t; exhibiting the change in instantaneous water depth with a change in time and then subtract the change in bathymetry with a change in time. The particular bathymetry for the analog model is a flat plexi-glass surface, so this can be considered zero as well. The design of this analog was more to display wave amplitude change with mass influx increases and wave dynamics, not the prediction of wave amplitudes based on certain constraints.
Kofoed-Hansen, Giménez and Kronborg developed an actual equation using the integration of the conservation of mass and momentum to determine a vertical amplitude based on the time varying bathymetry of the area, as seen below:
Integration involving bathymetric parameters and wave factors to decipher probable wave dynamics based on mathematic data.
This model uses the basis of kinetic energy to describe the wave sizes and dynamics via the all possible variables in a wave interaction system. Conservation laws state that as the energy of the landslide transfers to the water it is converted into wave amplitude and turbulence, which can be viewed from the analog video. The forces involved in this transfer are the mass of the landslide and the drag force that is create beneath the surface as the water column is displaced. Wave turbulence and dynamic energy exchange can be seen in the analog lab as well as figure 2 below.
Figure 2: animation and bathymetry of Lituya Bay wave (http://students.washington.edu/hschwaig/webpage/research/mass_wasting/ls.html)
With this integration it is possible to determine many dynamic parts to landslide generated tsunamis if predictions can be made of where possible landslides will occur. The model indicated in figure 2, done by Washington University, discusses the scaling difficulty with simulating tsunami events triggered by landslides in a computer model, however using viscosity, density and initial mass distribution, calculated models can be made. Due to the fact that the models presented here are all done on the
Steven Ward, of the
University of California at Santa Cruz, used a numerical model to
develop a simulated video of
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