Geoscience Reference
In-Depth Information
to the problem being non-linear and the boundary, i.e. the shoreline, being movable.
The topic of tsunami run-ups on the coast is so vast that it could be the subject of
a separate monograph. In this section, we shall only briefly dwell upon some of
the main results of and approaches to resolving the tsunami run-up problem and
give references to key publications.
The well-known topic by J. Stoker [Stoker (1959)] contains the classical for-
mulation of the run-up problem. An extensive bibliography, reflecting development
of the issue up to the end of the 1980s of the twentieth century, can be found in
[Voltsinger et al. (1989)]. The most significant results achieved before 1995 are
presented in [Carrier, Greenspan (1958); Keller et al. (1960); Shen, Meyer (1963);
Sielecki, Wurtele (1970); Lyatkher, Militeev (1974); Spielvogel (1975); Hibberd,
Peregrine (1979); Pedersen, Gjevik (1983); Kim et al. (1983); Synolakis (1987);
Pelinovsky et al. (1993); Tadepalli, Synolakis (1994); Liu et al. (1995); Pelinovsky
(1995) and Titov, Synolakis (1995)]. A significant part of monographs written by
E. N. Pelinovsky [Pelinovsky (1996)] is devoted to analytical approaches to res-
olution of the tsunami run-up problem. Publications of the past decade demon-
strate significant progress in numerical simulation of the interaction of tsunamis
with coasts [Titov, Synolakis (1997), (1998); Fedotova (2002); Chubarov, Fedotova
(2003); Titov et al. (2003); Choi et al. (2007), (2008)]; the interest in analytical
and experimental studies in this field does also not weaken [Li, Raichlen (2002);
Jensen et al. (2003); Chanson et al. (2003); Liu et al. (2003); Carrier et al. (2003);
Kanoglu (2004); Tinti, Tonini (2005); Didenkulova et al. (2007)].
There exist different types of tsunami run-ups on a shore. They vary from gradual
flooding (like during the tide) to the onslaught on the coast of a vertical wall of
turbulent water—a bore. As a rule (in about 75% of events), tsunami waves flood
the shore without breaking [Mazova et al. (1983)]. Tsunami run-ups in the form of
a wall are quite rare, and usually in the case of waves of significant amplitude.
The three following main types of wave run-ups onto the coast can be identified
[Pelinovsky (1996)]:
1. Spilling—crest of wave breaks, foam flows down its frontal slope, peculiar to
gently sloping bottom
2. Plunging—crest of wave surpasses foot and curls down, peculiar to inclined bot-
tom slopes
3. Surging—wave floods coast without breaking, peculiar to steep slopes
One and the same tsunami may exhibit different run-up forms at different points of
the coast.
The most widespread mathematical model, applied in describing wave dynamics
in the coastal zone, makes use of the non-linear equations of long waves, (5.29)-
(5.31), in which the Coriolis force is usually neglected. In many cases, for reasons
of simplicity, bottom friction is also neglected, although this factor may actually in-
fluence the run-up value noticeably. The main ideas of the tsunami run-up process
can be understood by considering a one-dimensional problem along the axis perpen-
dicular to the shoreline. Most model studies are performed for a region, representing
a slope connected with a smooth horizontal ocean bottom (Fig. 5.12).
