Geoscience Reference
In-Depth Information
Chapter 3
Role of the Compressibility of Water
and of Non-linear Effects in the Formation
of Tsunami Waves
Abstract The necessity is substantiated for taking into account the compressibil-
ity of water in describing behaviour of water column in tsunami source. Within
the framework of linear potential theory of a compressible liquid in a basin of fixed
depth, the general analytical solution is constructed for 2D and quasi-3D (cylindrical
symmetry) problems of the generation of acoustic-gravitational waves by bottom
deformations of small amplitudes. Manifestations of compressibility of the water
column in the problem of tsunami generation are studied, making use of the ex-
ample of model bottom deformation laws (piston, membrane and running displace-
ments). The main difference between the behaviour of a compressible water column
as compared to an incompressible model medium is shown to consist in the forma-
tion of elastic oscillations exhibiting significant amplitudes and a discrete spectrum.
Characteristic features of the dynamics of acoustic-gravitational waves in a basin
of variable depth are described. Records of bottom pressure gauges are used for
analysing manifestations of elastic oscillations of the water column at the source
of the 2003 Tokachi-Oki tsunami. The mechanism is considered of tsunami forma-
tion, related to non-linear energy transfer from 'high-frequency' induced or elastic
oscillations of the water column to 'low-frequency' gravitational waves.
Keywords Water compressibility
·
tsunami generation
·
T-phase
·
acoustic-gravity
waves
·
linear potential theory
·
Laplace transformation
·
Fourier transformation
·
analytical solution
·
bottom displacement
·
quarter-wave resonator
·
elastic oscil-
lations
·
normal modes
·
waveguide
·
numerical simulation
·
Tokachi-Oki 2003
·
JAMSTEC
·
bottom pressure
·
frequency spectra
·
non-linear effects
·
Euler's equa-
tions
·
non-linear tsunami source
The issue of accounting for the compressibility of water in the problem of tsunami
generation has been raised repeatedly in the literature [Sells (1965); Kajiura (1970);
Pod'yapolsky (1978); Yanushauskas (1981); Boorymskaia et al. (1981); Ewing
et al. (1950); Levin (1981); Selezov et al. (1982); Garber (1984); Zhmur (1987);
Nosov (1999), (2000); Nosov, Sammer (1998); Panza et al. (2000); Ohmachi (2001);
Nosov, Kolesov (2002), (2003); Nosov et al. (2005), (2007); Gisler (2008)]. How-
ever, in most of the tsunami models the ocean is considered to be an incompressible
