Tsunami Dynamics - Tsunami - page 22

Island causing significant destruction on the lee side (Yeh
et al. 1994 ). It also occurred on the south and west coasts of
Sri Lanka during the Indian Ocean Tsunami of 2004.
Finally, diffraction allows tsunami waves to bend around
shielding land such as long headlands or islands more than
0.5 km in length.
Not all tsunami behave as sinusoidal waves. Many
observations of tsunami approaching shore note that water
is drawn down before the wave crest arrives. This charac-
teristic can be due to non-linear effects that produce a
trough in front of the wave. Solitons or N-waves mimic
these features (Fig. 2.4 ) (Geist 1997 ; Tadepalli and Syn-
olakis 1994 ). These type of waves will be discussed further
when run-up is described.

α o

Depth contour

d

o

α o

α i

d i

α i

Direction of
wave travel

Shoreline

2.3.1 Resonance

Fig. 2.5 Refraction of a tsunami wave crest as it approaches shore

Tsunami, having long periods of 100-2,000 s, can also be
excited or amplified in height within harbors and bays if
their period approximates some harmonic of the natural
frequency of the basin—termed resonance (Wiegel 1964 ,
1970 ). The word tsunami in Japanese literally means harbor
wave because of this phenomenon. Here tsunami can
oscillate back and forth for 24 h or more. The oscillations
are termed seiches, a German word used to describe long,
atmospherically induced waves in Swiss alpine lakes. Sei-
ches are independent of the forcing mechanism and are
related simply to the 3-dimensional form of the bay or
harbor as follows:

where

= (sin D) -0.5

K sp

K sp = coefficient of geometrical spreading on a sphere

(dimensionless)

D = angle of spreading on a sphere relative to a wave's

direction of travel

In a large ocean, bathymetric obstacles such as island
chains, rises, and seamounts can refract a tsunami wave such
that its energy is concentrated or focused upon a distant
shoreline (Okal 1988 ). These are known as teleseismic tsu-
nami because the effect of the tsunami is translated long
distances across an ocean. Japan is particularly prone to tsu-
nami originating from the west coast of the Americas, despite
this coastline laying half a hemisphere away. On the other
hand, bottom topography can spread tsunami wave crests,
dispersing wave energy over a larger area. This process is
called defocussing. Tahiti, but not necessarily other parts of
French Polynesia, is protected from large tsunami generated
around the Pacific Rim because of this latter process.
Headlands are particularly prone to the amplification of
tsunami height due to refraction However, this does not
mean that bays are protected from tsunami. Reflection
becomes a significant process for long waves such as tsu-
nami that do not break at shore as wind waves do (Murata
et al. 2010 ). The tsunami wave is reflected from the sides of
an embayment towards shore. At shore, the wave is
reflected seawards, then bent back to shore by refraction.
This traps and concentrates the energy of tsunami waves
along a bay's shoreline increasing the amplitude of suc-
ceeding waves. Trapping by this process can also occur
around islands. This was particularly significant during the
December 12, 1992 tsunami along the north coast of Flores
Island, Indonesia, when the tsunami wrapped around Babi

Closed basin : T s ¼ 2L b g ðÞ 0 : 5 ð 2 : 9 Þ

Open basin : T s ¼ 4L b g ðÞ 0 : 5

ð 2 : 10 Þ

where

L b = length of a basin or harbor (m)

T s = wave period of seiching in a bay, basin, or harbor(s)

Equation 2.9 is appropriate for enclosed basins and is
known as Merian's Formula. In this case, the forcing
mechanism need have no link to the open ocean. As an
example, an Olympic-sized swimming pool measuring
50 m long and 2 m deep would have a natural resonance
period of 22.6 s. Any vibration with a periodicity of 5.6,
11.3, and 22.6 s could induce water motion back and forth
along the length of the pool. If sustained, the oscillations or
seiching would increase in amplitude and water could spill
out of the pool. Seismic waves from earthquakes can pro-
vide the energy for seiching in swimming pools, and the
Northridge earthquake of January 17, 1994 was very
effective at emptying pools in Los Angeles (Bryant 2005 ).