Solitary Wave on a Canonical Beach
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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.,
. The
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
where
with
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
wave was
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.
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References:
Synolakis, C.E. (1986): The Runup of Long Waves. 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.