Tsunami Propagation

Attenuation laws for tsunami

(SECTION TO BE ADDED)

Tsunami in shallow water

Whilst tsunami waves propagate at high speed over large distances in deep water, as a wave approaches shallower water it slows down (see equations), and the wavelength falls. In effect, the back of the wave catches up with the front. This, plus the decrease in water depth, causes the energy of the wave to be concentrated in a smaller volume of water: and so the amplitude has to increase. Tsunami waves that are barely detectable in deep ocean water become significant on the continental shelf and catastrophic as they impact the shore. It is for this reason that the established rule for shipping in the Pacific (where the shallow water coastal zones are narrow) is to put to sea on receipt of a tsunami warning. All the waves in a wave train will be similarly affected, in turn, so wave trains will also be compressed. If the wave is approaching a coastline, the process will continue until the amplitude increases to about 15% of the wavelength. For relatively short period waves passing over a shallowly sloping seabed (slope angles of 1-2° or less), this occurs when the amplitude is about 80% of the initial water depth. Where the seabed slopes more steeply, however, waves can build up to more impressive heights as solitary waves: waves moving up slopes of 5° or more can develop amplitudes of as much as 200% of initial water depth at the wave front before forming a plunging breaker.

In most cases the wave breaks as these limits are reached, the water within it is displaced forward at high speed, and it forms either a turbulent surge or, under certain conditions, a bore. These fast – moving, turbulent flows are the most destructive form of tsunami. Particularly violent bores develop when an incoming tsunami wave overrides the seaward – directed backflow from a preceding wave or the drawdown (negative wave) that commonly forms the leading element of tsunami wave trains: conversely, it has been proposed that waves which are not preceded by a drawdown (initial positive waves) break late and with comparatively little turbulence. Long – period, relatively low – amplitude tsunami can come ashore without breaking at all and these produce a rapid but tranquil rise in water level over a period of minutes, rather like a very fast tide. These are relatively rare, although in a number of cases a tranquil rise or fall in water level has preceded arrival of more turbulent and destructive waves.

FIGURE SHOWING EVOLUTION OF A TSUNAMI WAVE in shallow water

The dependence of wave velocity upon water depth, in conjunction with the complex submarine topography characteristic of most continental margins and island groups, produces a number of phenomena which lead to wide local variations in the amount of tsunami damage:

Wave refraction

As waves propagate towards and around points or islands surrounded by deeper water the variation in water velocity with depth causes parts of the waves to be bent around and towards the land. These areas therefore experience intensified tsunami damage. The effect is particularly pronounced in the case of more or less conical islands (including a large number of volcanic islands), in which the refracted waves converge at the side of island facing away from the direction of the tsunami source and produce particularly large waves and a concentration of destruction there. This occurred in the 1992 Flores tsunami. Narrow, low – lying points are vulnerable to a similar effect that arises during impact of tsunami wave trains: a wave early in the wave train refracts around the point, sweeps across it and collides with a later wave arriving on the front face. The combined waves then sweep up the length of the point. Wave collision of this type caused much destruction in the 1993 Japan Sea or Okushiri tsunami, and was responsible for a significant proportion (30% +) of the total losses: 230 deaths and $600 in economic and property losses. Wave refraction around offshore ridges and submarine mountains can also focus waves on particular sections of coastline. A ridge formed by a submerged delta offshore from Sissano, Papua New Guinea, is thought to have played an important role in focussing wave energy there during the 1998 New Guinea tsunami. Crescent City, California is especially vulnerable to tsunami generated in Alaska and the Aleutians because waves arriving from those directions are focussed on that section of coastline by offshore seamounts. Submarine canyons can have a similar effect, focussing waves into the regions on either side. On a much larger scale, the distribution of shallow and deep water in the Pacific is such that tsunami generated in Chile tend to focus in Japan: the 23rd May 1960 Chile tsunami, for example, produced 8 metre high waves at many places along the Pacific coast of Japan (higher than anywhere else outside Chile except Hawaii), causing 140 deaths and $50 million in property damage.THUMBNAIL SKETCH ILLUSTRATING WAVE REFRACTION

Wave reflection and interference.

Certain funnel – shaped, steep – sided bays are notorious for experiencing especially intense tsunami: the best – known example is Hilo Bay, Hawaii. The town of Hilo at the head of the bay experienced major, localised damage in both the 1946 Alaska (96 deaths), and 1960 Chile (61 deaths, $61 million in property damage) tsunami. In these bays, incoming waves arriving from particular directions are reflected sideways into the middle of the bay where they combine (constructively interfere) with later waves in the wave train to produce especially large waves towards the head of the bay. Such bay head areas tend to contain concentrations of economic activity and this phenomenon is therefore especially important for risk assessment. THUMBNAIL SKETCH SHOWING WAVE REFLECTION AND INTERFERENCE.

Wave resonance.

Certain harbours and largely enclosed bays have the unfortunate property that waves travel back and forward across them in a time equal to the period of long - period waves arriving at their mouth: the waves then repeatedly bounce back and forth across the harbour or bay, with newly - arriving waves adding to their energy each time. This phenomenon is known as resonance (an equivalent process occurs in lasers and badly - designed concert halls). Whilst the amplitudes of the waves rarely increase as a result, the repeated movement of the waves back and forth can cause substantially greater damage to boats and ships being swept around the harbour or bay than would be caused by the arriving waves alone. Harbours known to experience resonance during tsunami include Hilo Bay, Hawaii and Alberni Inlet, British Columbia.

These three phenomena, which may act in concert, greatly complicate evaluation of variation of tsunami hazards along coastlines. Their effects vary widely along the coast according to both its topography and the offshore bathymetry, which is not known with sufficient accuracy and detail along much of the world’s coastline, and according to the parameters of the waves themselves: amplitude, period and arrival direction. Evaluation of local variations in tsunami hazard is therefore a much more difficult exercise than, for example, evaluation of variations in earthquake hazard with soil geotechnical conditions. Although advances in computational power mean that the process is becoming easier, in the near future it is likely only to be of value for insurance purposes when dealing with risk estimation for major concentrations of value-at-risk such as ports and cities, or with facultative insurance of major coastal facilities.