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 runup 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 KofoedHansen, 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 plexiglass 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.
KofoedHansen, 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.
http://www.dhisoftware.com/uc2001/Abstracts_Proceedigs/Papers01/036/036.htm
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 Lituya Bay
landslide, constants are held for mass influx and bathymetry, while
viscosity
and density variances are described to produce a wave similar to that
in Lituya Bay in 1958. With the analog experiment it was more
important for an overall view of landslide generated tsunamis and the
wave
amplitude changes with mass influx to be visualized.
Steven Ward, of the
University of California at Santa Cruz, used a numerical model to
develop a simulated video of
the Lituya Bay
tsunami based on the size of the landslide and the tsunami
wave
dynamics, seen here
or via Steven Ward's computer simulations http://www.es.ucsc.edu/~ward/.
This model is just a look into what
numerical
modeling can bring to the prediction of landslide tsunami hazard
zones.
Using the numerical model above and work like Ward's, it is possible to
look
into the devastation before it happens, allowing for precautions to be
taken
beforehand for a general populous in an area or structural stability.
Other work done by Eric W.
Weisstein and
Michael Trott using supercomputers with complicated programs, discuss
the
present problem of scaling tsunamis without the use of partial
differential
equations involving the many aspects that inhibit tsunami waves.
The
physics behind the tsunami is complicated and not fully understood as
of
yet. The problem being that every tsunami is different because it
is
based on the initiating seismic activity, mass influx variances, and
ocean floor
bathymetry for example. With these variables alone it is near
impossible to
predict the behavior of a tsunami wave and its dynamics without having
complex algorithms
and real spatial data to coincide with it.
Tsunami research is gaining
ground
and the realization for importance has become evident. This work
is made possible by the advancements
in today's computer systems as well as research development allowing
for
tsunami
prediction and calculation of magnitude based on the system in which
the wave interacts. Many pacific coast institutions have
begun funding for major work to be done into the prediction and
development of how these massive waves of destruction evolve and
function as to one day prevent the devastation that has taken place in
the past.
