Tsunami Dynamics - Tsunami - page 18

2

Tsunami Dynamics

2.1 Introduction

In some cases, the waves in a tsunami wave train consist of an
initial peak that then tapers off in height exponentially over
four to 6 h. In other cases, the tsunami wave train consists of
a maximum wave peak well back in the wave sequence. The
time it takes for a pair of wave crests to pass by a point is
termed the wave period. This is a crucial parameter in
defining the nature of any wave. Tsunami typically
have periods of 100-2,000 s (1.6-33 min), referred to as the
tsunami window. Waves with this period travel at speeds of
600-900 km hr -1 (166-250 m s -1 ) in the deepest part of the
ocean, 100 -300 km hr -1 (28-83 m s -1 ) across the conti-
nental shelf, and 36 km hr -1 (10 m s -1 ) at shore (Iida and
Iwasaki 1983 ). The upper limit is the speed of a commercial
jet airplane. Because of the finite depth of the ocean and the
mechanics of wave generation by earthquakes, a tsunami's
wavelength—the distance between successive wave crests—
lies between 10 and 500 km. These long wavelengths make
tsunami profoundly different from swell or storm waves.
Tsunami waves can have different shapes depending
upon where they are placed with respect to the shore and
the depth of water (Geist 1997 ). The simplest form of
ocean waves is sinusoidal in shape and oscillatory
(Fig. 2.4 ). Water particles under oscillatory waves tran-
scribe closed orbits. Hence there is no mass transport of
water shoreward with the passage of the wave. Oscillatory
waves are described for convenience by three parameters:
their height or elevation above the free water surface, their
wavelength, and water depth (Fig. 2.2 ). These parameters
can be related to each other by three ratios as follows
(Komar 1998 ):

The approach of a tsunami wave towards shore can be an
awesome sight to those who have witnessed it and survived.
Figure 2.1 represents an artist's impression of a tsunami
wave approaching the coast of Unimak Island, Alaska, early
on April 1, 1946. Similar artists' impressions of breaking
tsunami will be presented throughout this text. The
impressions are accurate. Whereas ordinary storm waves or
swells break and dissipate most of their energy in a surf
zone, tsunami break at, or surge over, the shoreline. Hence,
they lose little energy as they approach a coast and can run
up to heights an order of magnitude greater than storm
waves. Much of this behavior relates to the fact that tsunami
are very long waves—kilometers in length. As shown in
Fig. 2.1 , this behavior also relates to the unusual shape of
tsunami wave crests as they approach shore. This chapter
describes these unique features of tsunami.

2.2 Tsunami Characteristics

Tsunami characteristics are described by many authors
(Wiegel 1964 ; Bolt et al. 1975 ; Shepard 1977 ; Myles 1985 ).
The terminology used in this text for tsunami waves is shown
schematically in Fig. 2.2 . Much of this terminology is the
same as that used for ordinary wind waves. Tsunami have a
wavelength, a period, and a deep-water or open-ocean
height. They can undergo shoaling, refraction, reflection and
diffraction (Murata et al. 2010 ). Most tsunami generated by
large earthquakes travel in wave trains containing several
large waves that in deep water are less than 0.4 m in height.
Figure 2.3 plots typical tidal gauge records or marigrams of
tsunami at various locations in the Pacific Ocean (Wiegel
1970 ). These records are taken close to shore and show that
tsunami wave heights increase substantially into shallow
water. Tsunami wave characteristics are highly variable.

ð 2 : 1 Þ

H : L ; H : d ; L : d

where

H = crest-to-trough wave height (m)

L = wavelength (m)

d = water depth (m)