The waves have fascinated humanity since time immemorial, both for their beauty and by its destructive strength. Today, that duality manifests itself rawly after the earthquake of magnitude 8.8 in Russia, which has unleashed Tsunami alerts throughout the Pacific and has forced to evacuate millions of people. This type of phenomena reminds us that, beyond its aesthetics, the waves can become implacable forces of nature.
The wave of an earthquake
The most powerful earthquake ever registered (Valdivia earthquake, Chile, 1960) released the energy equivalent to 20,000 Hiroshima atomic bombs. Such energy could cause a tsunami of only 4.55 meters high at sea, but that could rise up to 1.7 kilometers in coast. The increase is due to the call Shoaling effect o Asomeamiento: the waves increase in size as they approach the coast.
However, the real size was much smaller (about 10 meters) since the earthquake occurred on the mainland and not all energy went to a single wave. That does not mean that it was not a destroyer: the Tsunami crossed the Pacific Ocean, causing the death of more than 2,000 people in Chile, Peru, Hawaii and Japan.
Where wind and physics collide
Under normal conditions, most waves are generated by wind. They have a cycle of formation, growth and break that depends on the speed, scope and duration of the wind and the depth of the water. However, even in optimal conditions, the waves cannot grow indefinitely.
Physics establishes a limit proportion between the height of a wave and its wavelength: when that relationship exceeds 1/7, the wave becomes unstable and breaks. That is, the crest collapses forward because it can no longer be sustained.
In addition, there is another key factor: the depth of water. As a wave approaches the coast, the seabed slows its base while the crest continues to advance, which makes the wave lean and eventually break. In shallow waters, a wave cannot have a height greater than approximately 0.88 times the local depth. Thus, on a beach where water is 3 meters deep, the maximum theoretical wave that could break would be about 2.64 meters. This limit is observable and verifiable, and is frequently used in coastal engineering and in the prediction of waves.
Both phenomena establish some of the fundamental limits at the height of the waves in the sea.
Unexpected Giants: The Draupner wave
Now, there are times when the ocean seems to challenge these rules. So -called extreme waves or Rogue Waves (Monster waves) They are rare but very real events, in which a wave of huge size appears without warning, doubling or tripling the typical height of surrounding waves.
One of the best known was registered in 1995 by an oil platform in the North Sea: the Draupner wave, which reached 25.6 meters high. This event confirmed what until then many considered a sailor myth. Since then, several studies have shown that these extreme waves can be formed by the constructive combination of multiple waves, interaction with oceanic currents, or still study phenomena. However, in practice, its height does not usually exceed 30 meters in open sea.
When the earth creates waves: 520 meters high
Beyond what the wind can generate, there are waves of geological origin known as megatsunamis. These waves are produced by landslides, glacier collapses or meteorite impacts, which displace a huge amount of water suddenly.
A dramatic case occurred in Lithuya Bay, in Alaska, in 1958. An earthquake of 7.8 degrees on the Richter scale caused the detachment of a mountain. More than 30 million cubic meters of earth and stones fell into block to water, from a height of 900 meters. The collapse caused a wave that reached an estimated height of 524 meters.
This phenomenon, although real, was very different from the common waves since it did not occur in the ocean. It only affected the Fjord.
The energy necessary to form something similar in open sea is so colossal that it could only occur for extraordinary events, such as the impact of a large asteroid on the ocean.
The size of a megatsunami
Is there a physical limit to the size of a megatsunami? It is difficult to respond exactly. But we can make a simple estimate if we focus only on the associated energy.
Imagine a single “wave” that moves (also called Solitón u lonely wave) generated by an earthquake or the impact of a meteorite. By simplicity, we will ignore friction, turbulent flow and other complex factors. The height that it can reach will depend on its kinetic and potential energy. If we also know some parameters, such as its width or speed, we can estimate a value.
Therefore, we are going to enter the data corresponding to some of the greatest known tsunamis creative phenomena. Thus, we will see what maximum heights are physically possible. However, it is important to keep in mind that they overestimate real limits and are never reached.
The fall of a meteorite
On the other hand, the most energetic meteorite of which we have knowledge, (Chicxulub), popularly known for ending dinosaurs, released the energy equivalent to 67 billion Hiroshima bombs. So much energy could have generated a wave of no more than 16 kilometers in Costa, although in the literature it is estimated that “only” would have reached around 1 and 3 kilometers high.
There are no infinite waves
The waves cannot grow indefinitely. Its height is limited by factors such as wavelength, water depth and energy available.
In an open sea, wind generated waves hardly exceed 30 meters. Beyond that, we enter the field of tsunamis and megatsunamis, which can generate waves of hundreds of meters, but depend on violent and very rare geological processes.
In any case, in practice, there is a reasonable limit at the height of the waves that the sea can offer us.
We can go to the beach without fear, always, of course, that we do not live, at the moment, on the coast affected by the effect of the earthquake in Russia.
José Luis González Fernández, Assistant Professor Didactic Doctor of Mathematics, University of Castilla-La Mancha and Carlos Martínez-Conde Hernández, doctorate at the UCLM, Complutense University of Madrid
This article was originally published in The Conversation. Read the original.
