Figure 1: Definition sketch for canonical bathymetry, i.e., sloping
beach connected to a constant-depth
In this set of experiments, the 31.73 m-long, 60.96 cm-deep, and
39.97 cm-wide California Institute of Technology, Pasadena,
California wave tank was used with water at varying depths (Fig. ).
The tank is described by Hammack (1972), Goring (1978), and
Synolakis (1986, 1987). The bottom of the tank consisted of painted
stainless steel plates. Carriage rails run along the whole length of
the tank, permitting the arbitrary movement of instrument carriages.
A ramp was installed at one end of the tank to model the bathymetry
of the canonical problem of a constant-depth region adjoining a
sloping beach. The ramp had a slope of 1:19.85. The ramp was sealed
to the tank side walls. The toe of the ramp was distant 14.95 m from
the rest position of the piston generator used to generate waves.
A total of more than 40 experiments with solitary waves running up
the sloping beach were performed, with wave depths ranging from
6.25 cm to 38.32 cm. Solitary waves are uniquely defined by their
maximum height to depth ratio and
the depth, i.e.,
and are sufficient to specify the wave.
ranged from to . Breaking occurs when
, for this particular beach. This
is the same set of experiments used to validate the maximum runup
analytical predictions presented in section A2.1.1.
Initial location, in the analytical consideration
(), changes with different wave heights. The reason distance varies is that solitary waves of different heights
have different effective ``wavelengths.'' A measure of the
``wavelength'' of a solitary wave is the distance between the point on the front and the tail where the local height is
1% of the maximum, i.e.,
distance is at an offshore location where only 5% of the
solitary wave is already over the beach, so that scaling can work.
Therefore, in the laboratory experiments initial wave heights are
identified at a point
In the laboratory, even
solitary waves can dissipate. If the wave height is measured far
offshore and used as an initial condition for non-dissipative
numerical models, the comparisons will be less meaningful, as the
solitary wave will slightly change as it propagates in the
laboratory. By keeping the same relative offshore distance for
defining the initial condition, meaningful comparisons are assured.
While only 10 wave gages were used in each experimental run, the
generation was extremely repeatable. As experiments were repeated
for each wave height, the wave gages were moved to different
locations, and the same
generated again until a sufficient number of data points existed to
resolve the entire wave profile. In Synolakis (1987) two different
comparisons are presented: one is the amplitude variation at
specific -locations, and the second is the amplitude variation at
specific -times, the latter resembling the image that a
photograph from the side with a large depth of field and angular
range would show.
Figure 2: Time evolution of = 0.0185 initial wave over a sloping
from to 65 with 10
increments. Constant depth-segment starts at . While
markers show experimental results of Synolakis (1986, 1987), solid
lines show nonlinear analytical solution of Synolakis (1986, 1987) Experimental data is provided from to 70
Synolakis, C.E. (1986): The Runup of Long
Ph.D. Thesis, California Institute of Technology, Pasadena,
California, 91125, 228 pp.
Synolakis, C.E. (1987): The runup of solitary
waves. J. Fluid Mech., 185, 523-545.