Tsunami Dynamics - Tsunami - page 23

Seiching was also induced in bays in Texas and the Great
Lakes of North America about 30 min after the Great
Alaskan Earthquake of 1964. Volcano-induced, atmo-
spheric pressure waves can generate seiching as well. The
eruption of Krakatau in 1883 produced a 0.5 m high seiche
in Lake Taupo in the middle of the North Island of New
Zealand via this process (Choi et al. 2003 ). Whether or not
either of these phenomena technically is a tsunami is a moot
point.
Resonance can also occur in any semi-enclosed body of
water with the forcing mechanism being a sudden change in
barometric pressure, semi- or diurnal tides, and tsunami. In
these cases, the wave period of the forcing mechanism
determines whether the semi-enclosed body of water will
undergo excitation. The effects can be quite dramatic. For
example, the predominant wave period of the tsunami that
hit Hawaii on April 1, 1946 was 15 min. The tsunami was
most devastating around Hilo Bay, which has a critical
resonant length of about 30 min. While most tsunami usu-
ally approach a coastline parallel to shore, those in Hilo Bay
often run obliquely alongshore because of resonance and
edge-wave formation. Damage in Hilo due to tsunami has
always been a combination of the tsunami and a tsunami-
generated seiche. The above treatment of resonance is
cursory. Harbor widths can also affect seiching and it is
possible to generate subharmonics of the main resonant
period that can complicate tsunami behavior in any harbor
or bay. These aspects are beyond the scope of this text.

from shore. They also show that, because of reflection, the
second and third waves in a tsunami wave train can be
amplified as the first wave in the train interacts with shelf
topography. If shallow-water long-wave equations include
vertical velocity components, they can describe wave
motion resulting from the formation of cavities in the ocean
surface (asteroid impacts); replicate wave profiles generated
by sea floor displacement, underwater landslides, or tsunami
traveling over submerged barriers; or simulate the behavior
of short-wavelength tsunami. Effectively, an underwater
barrier does not become significant in attenuating the tsu-
nami wave height until the barrier height is more than 50 %
the water depth. Even where the height of this barrier is
90 % of the water depth, half of the tsunami wave height
can be transmitted across it. Modeling using the full shal-
low-water, long-wave equations shows that submerged
offshore reefs do not necessarily protect a coast from the
effects of tsunami. This is important because it indicates
that a barrier such as the Great Barrier Reef of Australia
may not protect the mainland coast from tsunami.
Shallow-water, long-wave approximations are solved
using finite-difference techniques. Early models such as the
SWAN code used simple, regularly spaced grids of ocean
depths that incorporated Coriolis force and frictional effects
(Mader 1988 ). To overcome the loss of detail as water
shallowed, depth grids of increasing resolution were nested
within each other. These models have given way to more
advanced ones (Synolakis et al. 2008 ), which use triangular
(3-point) or polygonal (4- or more point) grid cells that
become smaller as bathymetry becomes more complex or
coastlines more irregular. This matches the quality of most
bathymetric data, which becomes more detailed towards
shore. For example, the Indian Ocean Tsunami event on
December 26, 2004 was modeled for the Banda Aceh region
of Indonesia using a triangular grid that started out at a
resolution of 14 km in the deep Indian Ocean, decreasing to
500 m near the coast and, finally, to 40 m at shore to model
inundation throughout the city (Fig. 2.6 ) (Harig et al. 2008 ).
Several advanced models are presently in use, including
MOST (Tito and Gonzalez 1997 ), TUNAMI-N2/TUNAMI-
N3 (Imamura et al. 2006 ) and SELFE (Zhang and Baptista
2008 ). The purpose of these models is to simulate accu-
rately tsunami evolution, its propagation across an ocean to
a coastline, its arrival time at shore and the limit of inun-
dation on dry land. The MOST (Method of Splitting
Tsunami) model can simulate all these components. An
example of its use is shown in Fig. 2.7 for the height of the
T ¯hoku Tsunami of March 11, 2011 as it propagated into
the Pacific Ocean from its source region on the east coast of
Japan. While the effect of the tsunami was significant on the
coast of Japan, this figure shows that there was minimal risk
to coastlines outside the immediate area. By pre-computing
hundreds of tsunami from possible earthquake scenarios, it

2.4 Modeling Tsunami

The preceding theories model either small amplitude or
long waves. They cannot do both at same time. Tsunami
behave as small amplitude, long waves. Their height-to-
length ratio may be smaller than 1:100,000. If tsunami are
modeled simply as long waves, they become too steep as
they shoal towards shore and break too early. This is called
the long-wave paradox. About 75 % of tsunami do not
break during run-up. Because their relative height is so low,
tsunami are also very shallow waves. Under these condi-
tions, tsunami characteristics can be modeled more realis-
tically by using non-linear, non-dispersive, shallow-water
approximations of the Navier-Stokes equations (Liu et al.
2008 ). The description of these equations is beyond the
scope of this topic.
These equations work well in the open ocean, on conti-
nent slopes, around islands, and in harbors (Mader 1974 ,
1988 ). On a steep continental slope greater than 4, the
techniques show that a tsunami wave will be amplified by a
factor of three to four times. Because they incorporate both
flooding and frictional dissipation, the equations overcome
problems with linear theory where the wave breaks too far