Geoscience Reference
In-Depth Information
Fig. 2.8
The remains of the
Scotch Cap lighthouse, Unimak
island, Alaska, following the
April 1, 1946 Tsunami. A coast
guard station, situated at the top
of the cliff 32 m above sea level,
was also destroyed. Five men in
the lighthouse at the time
perished. Source United States
Department of Commerce,
National Geophysical Data
Center
Synolakis (
1994
) approximated run-ups for N-waves using
the following formulae:
Stem waves develop wherever the angle between the wave
crest and a cliff face is greater than 70. The portion of the
wave nearest the cliff continues to grow in amplitude even if
the cliff line curves back from the ocean. The Mach-Stem
wave process is insensitive to irregularities in the cliff face.
It can increase ocean swell by a factor of four times. The
process often accounts for fishermen being swept off rock
platforms during rough seas. The process explains how
cliffs 30 m or more in height can be overtopped by a
shoaling tsunami wave that produces run-up reaching only
one third as high elsewhere along the coast. Mach-Stem
waves play a significant role in the generation of high-speed
vortices responsible for bedrock sculpturing by large tsu-
nami—a process that will be described in the following
chapter.
All these processes, except Mach-Stem waves, are sen-
sitive to changes in shoreline geometry. This variability
accounts for the wide variation in tsunami wave heights over
short distances. Within some embayments, it takes several
waves to build up peak tsunami wave heights. Figure
2.10
maps the run-up heights around Hawaii for the Alaskan
Tsunami of April 1, 1946 (Shepard
1977
; Camfield
1994
).
The northern coastline facing the tsunami received the
highest run-up. However, there was also a tendency for
waves to wrap around the islands and reach higher run-ups at
supposedly protected sites, especially on the islands of Kauai
and Hawaii. Because of refraction effects, almost every
promontory also experienced large run-ups, often more than
Þ
0
:
5
H
1
:
25
t
Simple N-wave
H
rmax
¼
3
:
86 cot b
ð
ð
2
:
12
Þ
Þ
0
:
5
H
1
:
25
t
Double N-wave
H
rmax
¼
4
:
55 cot b
ð
ð
2
:
13
Þ
The two equations are similar in form to Eq.
2.11
for
solitary waves. However, they result in run-ups that are 36
and 62 % higher. In some cases, N-waves may account for
the large run-ups produced by small earthquakes. For
example, an earthquake (M
s
magnitude of 7.3) struck the
island of Pentecost, Vanuatu, on November 26, 1999
(Caminade et al.
2000
). Normally, an event of this magni-
tude would generate only a minor tsunami, if one at all.
Instead, run-up reached 5 m above sea level. The tsunami
was characterized by a distinct leading depression.
The run-up height of a tsunami also depends upon the
configuration of the shore, diffraction, standing wave reso-
nance, the generation of edge waves that run at right angles
to the shoreline, the trapping of incident wave energy by
refraction of reflected waves from the coast, and the for-
mation of Mach-Stem waves (Wiegel
1964
,
1970
; Camfield
1994
). Mach-Stem waves are not a well-recognized feature
in coastal dynamics. They have their origin in the study of
flow dynamics along the edge of airplane wings, where
energy tends to accumulate at the boundary between the
wing and air flowing past it. In the coastal zone, Mach-
