Dr. Benu Chatterjee
The final article in the present series on natural phenomena is about tsunami. The other articles in the series are based on Earthquake, Lightning, Natural Vortex (Cyclone and Tornado) and Colourful Optics of Nature.
history is known to mankind as the most destructive natural event which can
spread thousands of miles causing huge loss of life and property. Only the
giant tsunamis have arguably changed history. For instance, Mediterranean
tsunami struck the north shore of Crete over 3,500 years ago destroying the
sophisticated Minoan civilization into a tailspin leading it to succumb to
Mycenaea Greeks. In recent times, two huge tsunamis include
the Indian Ocean tsunami on Boxing Day in 2004 and the Pacific Ocean tsunami in
Tohoku, Japan on March11, 2011. Meaning of “tsunami”Tsunami is a
Japanese word meaning harbour (“tsu”) wave (“nami”),. It originates from fishermen’s
experience. While sailing for fishing, they would not encounter any unusual
waves while out at sea. But on coming back to land, they were sometimes
confused to find their village being devastated by huge waves at the harbour, and
hence the term tsunami. An explanation of this confused experience is given
Characteristics of Tsunami
global phenomenon, is different from normal sea waves at the beach. The ocean
waves that surfers ride are made by the blowing wind, while tsunami occurs
because of geological events.
associated with very long wavelengths,λ (crest to crest distance) in excess of 100 km and long period, t (time for a full wave cycle from crest through valley or trough
and back to crest) from several minutes to more than an hour.Tsunami moves very fast at a speedV around 200 m/sec.
height i.e. amplitude, L (trough to crest) of tens of metres had been
recorded in large events such as tsunami created by the landslide at Lituya Bay,
termed as “shallow water waves” which does not necessarily mean that the water is
shallow. By definition, a water wave with the depth of water (h) much less than λ i.e. small h/λ, is
defined as shallow, as it happens
near the coast. However, in deep ocean of some kilometres in depth
includingthe deepest part of world’s
oceans namely Mariana trench (in the western Pacific Ocean) ~ 11 kmdeep, water wave can still be defined asshallow because λ is
sufficiently larger (~100km) than h.
Devastation by tsunami
Two recent cases
Boxing day (Indian Ocean) earthquake
December, 2004, an undersea earthquake struck the coastal region of Indonesia
making it the most powerful ever recorded in the world in the last forty years
with magnitude 9.1 - 9.3.The movement
of the sea floor produced a tsunami with waves up to 30 metres along the
adjacent coast line, killing more than 240,000 people. Waves were registered
all over the World Ocean which spread outward from the source (the coast of
Sumatra), claiming 58,000 lives in Thailand, Sri Lanka and India within 2
Tohoku (Japan) earthquake and tsunami
On March 11,
2011, an earthquake of largest magnitude of 9.0 ever recorded in Japan produced
a huge tsunami in Tohoku. The combined impacts of earthquake and tsunami left
nearly 20,000 people dead, 130.000 displaced and a massive destruction along
the Tohoku coast of Japan. Autopsy results showed around 96% of the victim died
from drowning in tsunami waves.
Occurrence of tsunami
be linked either to a tidal or a seismic wave. Tides are formed only from an imbalanced
extraterrestrial gravitational influence of the moon, sun and planets, while seismic
waves by definition originate from earthquakes. In fact, as early as fifth
century B.C., the Greek historian Thucydides suggested a connection between
earthquakes and tsunamis. Tsunamis can
also develop from natural events such as cataclysmic volcanic eruption (namely
Thira eruption near Crete that triggered the Minoan tsunami), or enormous landslide
( Lituya Bay, Alaska in 1958when
massive rock of 40 million cubic metres plunged into water producing ahuge tsunami with the largest ever recorded wave of over 500 metres high).
Tsunami may also occur from unlikely events of cosmic collisions i.e. impacts
of meteorite disturbing the water below.The present article focuses only on
Tsunami from earthquake
mostly caused by sudden large-scale disturbances of the ocean by seafloor
earthquakes which are generated along faults called subduction zones. Such faults
are responsible for 90% of large earthquakes in the Pacific and Indian Oceans.
The process starts
when two giant flat slabs (tectonic plates) sliding past each other get stuck by
their jagged edges. The elastic energy stored in the stuck plates is enormous (equivalent
to 8000 Hiroshima bombs in Tohoku earthquake). This energy is suddenly released
with an enormous jolt via fracture of the plates, producing vibrations in the
form of shockwaves (seismic waves). Such disturbances can cause massive
vertical displacement of the overlying water to create tsunami.
It is worth
pointing out that If the earthquake occurs very deep inside the Earth, say more
than 100 km below the surface, a tsunami will not occur because of lack of enough
vertical displacement of water to come up to the surface.
Physics of tsunami
Speed and energy/power of tsunami
The speed with
which a shallow water wave moves is derived from Bernoulli’s theorem asV = √(g * h) where g is the acceleration due to gravity (9.8m/sec^2). In
the Pacific Ocean with water depth ~5 km, a tsunami would, therefore, gather a
speed ~221m/sec which is ~ 795 km/hr or close to 500 miles per hour, the speed
of a jetliner. This typical speed is fast enough for a tsunami wave to travel,
for instance, from Japan to the US in less than a day, or traverse the Pacific
Ocean in 10-12 hours.
enormous kinetic energy (K.E.) and power (P) are related to the huge mass of
water carried by tsunami in mid-ocean. On multiplying h (5000m) by the density of water (1000 kg/m^3) one obtains the
volume of water as 5*10^ 6 kg per square metre of ocean surface. Tsunamis
develop its high K.E. and P by moving this huge amount of water
at a very high speed through the deep ocean.
tsunami in 2011 is reported to generate ~3 petajoules i.e. 3*10^15 joules of
energy which is enough to power New York City for seven days. In comparison,
the total energy of the Boxing day tsunami waves in 2004 was ~ 5 megatons of
TNT (20 petajoules) which is more than the total explosive energy used during
the World War ll.
The rate at
which a wave loses its energy is inversely proportional to λ. This would imply that giant tsunamis with very high λ can travel great trans-oceanic
distances with only limited energy losses which could only arise from internal
friction and viscosity due tosolid-water friction.
The power P defined as the rate of transfer of K.E.is estimated in watts to be around one gigawatt i.e.10^9 watt per
kilometre of shoreline.
What happens as tsunami approaches the
approaching the coast, tsunami’s huge K.E.
is suddenly squeezed into a much smaller space at the shore. Based on
conservation of energy, all K.E. is
converted into potential energy. As a result, wave height is increased
producing huge walls of water which start to rise up at the coast.With tsunami’s speed decreasing and wave
height increasing (called shoaling) near the coast, Green’s law predicts L ~ 1/(h ^¼).The
consequence is striking. For example, if a tsunami is formed at a ocean depth ho with a wave height Lo, it will be related to the wave
height Lson the shore for a water depth hs asLo /Ls
= [ hs / ho] ^1/4
The above relation implies that a tsunami with a typical Lo of 1 m in the open ocean atho ~ 5 km, can end up with a final Ls around 8-9 m at hs ~ 1 m near the shore.The wave height Ls near the shore is thus deceptively many folds higher than Lo, and can sometimes be as high as 30
Deceptive nature of tsunami
1) On travelling along the ocean, tsunami is
typically associated with relatively small Lo~1 m. This would mean that at λ ~ 100 km, steepness of the wave in
the deep ocean given by 2π*(L/ λ) is
very low. Such tiny slope will manifest itself as small, harmless ripples
hardly visible let alone being dangerous to the fishermen’s ship on the ocean mentioned
earlier. Indeed, the deep ocean is one
of the safest places one can hang out when tsunamis are around.
reaching the shore tsunami wave could have wave height Ls reaching several tens of metres, causing havoc.Fishermen’s experience of devastation on returning
back to their harbour was thus confusedly related to something about the
harbour wave which did not show any sign of huge wave out in the sea.
2) Both V
and ho decrease as tsunami
approaches the shore. Based on V =√(g*h),
the travelling speed of tsunami at hs
=10 m slows downto ~ 10 m/sec ~ 36
km/hour compared to 795km/hour in the ocean. However, the speed is still high
enough to outrun a swimmer or a runner. This suddenness of speed along with
huge waves at the shore would take people by surprise at the coast with
3) Another deception of tsunami is related to
period t given by t = λ/V. The time required for a tsunami
wave to travel in the deep ocean with λ
and V around 100km and 200m/sec
respectively would be 500 sec or ~ 8 min. At
the shore, the depth of water and wave length if assumed to be 10m and ~ 5 km
compared to 5 km and 100 km respectively in the ocean, t will still be 500 sec as in the deep sea . The above
estimations indicate that the typical time separating the different events of a
tsunami whether it is in mid-ocean or by the coast is similar which is in
minutes or even hours, than 5-20 seconds for wind-generated waves. This long break
in time period can lead to tragic results by misjudging the tsunami behaviour.
An initial harmless drop in water heights for normal waves can attract people
to the beach which, after relatively long interval of time could follow with a
devastating massive wave that cannot be outrun.
Intensity and magnitude of tsunami
of the degree of tsunami damage is primarily based on the statistical analysis
of events that occurred in the past. Tsunami phenomenon is characterized, like
earthquake, by intensity based on objectives of measurable parameters (energy,
amplitude, period etc), and by magnitude derived from subjective descriptions
reflecting scale of destructions by the incoming massive waves on the coast.
Boxing Day superquake in 2004 and the Tohoku earthquake in 2011 stunned
scientists because neither region was thought to be capable of producing a
megathrust earthquake with a magnitude ~ 9. These recent incidents have prompted
urgently than ever the need for scientific understanding and modelling the
complicated physical phenomena associated with tsunami in order to prevent
unnecessary loss of life and property. One can appreciate the difficulty in
studying a full-scale physics and modelling of tsunamis that would require
supercomputers and complicated software.
Further reading on tsunami
Boxin g day (2004) and Tohoku (2011) events : 1, 2, 3, 4, 5, 6, 7, 8