In case of a tsunami, would swimming out to sea be an escape strategy?
Several times I have been in locations where tsunami risks are either actively signaled or self-evident. Lima where I am right now has long beaches dominated by cliffs with exit routes about every km. Hiking the West Coast Trail in BC, Canada I have also been in situations where an extremely smooth cliff overlooks a low tide only trail. Leading to Tofino, Canada, you have a 40 km stretch of low lying lands before you see any higher ground. Depending on your location and how much advance warning you receive, you may not have the opportunity to reach higher ground in case of a tsunami warning.
If you have experience with big waves, near beaches, or especially near cliffs, you know that they are especially dangerous when they contact the shore. Both because that's when they break and because they can throw you against solid objects. In fact one of the best ways to safeguard yourself from a breaking wave is to dive under it, heading offshore (not something I suggest here, just an example of something very counterintuitive that works).
Looking at the videos shot of either the 2004 tsunami @ Phuket tsunami or the 2011 Tohuku, Japan earthquake the waves don't even look very big.
I know considerable effort since 2004 has been made to monitor for, and mitigate, tsunami risks. Has anyone looked into whether swimming a few hundred meters offshore and waiting out the main water disturbance would be a valid risk minimization strategy, if no timely route to safety was available?
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Imagine two strings of different densities, which are tied together at a point. Suppose you hit the string with the largest density several times with your hand, generating a sequence of traveling pulses. Due to conservation of momentum, when the pulses reach the lower density string, two things will happen: The wavelength will get shorter and the amplitude will get larger. This is the mechanism that forms a tsunami.
In extending the analogy above to a three dimensional continuous classical field, which in this case we usually address by the name of "water", the density remains the same, and the amplitude increase/wavelength decrease is caused by the shallow-ing of the sea floor: A set of traveling waves with huge wavelengths and tiny amplitudes is suddenly packed into a dense sequence of huge waves, because the momentum that was distributed along an immense mass of water has to be conserved when transitioning to a relatively smaller mass of water (which is all that's available in the coastal region).
I now address your question: As you swim deeper and deeper, you start to reach safer regions. The problem is that these regions form only when the seafloor is considerably deeper than at the coast. There are places on earth where the transition from shallow to deep water takes less than 1 or 2km, but in the general case you will be faced with having to swim several kilometers before the tsunami reaches you. As can be seen in several YouTube videos, ships that are far from the coast only notice a relatively abnormal amplitude in a forming tsunami, which is quite harmless. That's where you need to swim to. If the waves catch you midway, attempting to dive under them is a very efficient way of killing yourself faster, since their propagating speed is relatively homogeneous with respect to water depth.
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There are some good videos of the tsunami that hit Thailand some years ago. Thing to remember is that the waves are MILES long. The water rises and keeps rising.
I read recently of a similar question regarding boats. I think the recommended distance to get off shore was 15 miles. And from the time the water starts to retreat from shore you don't have a lot of time.
The water advances inland faster than you can swim, faster than you can walk, but if I remember correctly, it's a speed that is reasonable to bicycle.
If you have little time and no bike, look for a several floor high concrete building. Several people survived Thailand's wave by climbing big trees. They can be toppled. Or look for something that floats really well.
From the vids the biggest danger was getting hit by other floating debris.
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Even if you had time to swim a few hundred meters from shore, that would do you no good. The tsunami would just carry you right back to shore.
Go inland as quickly as possible. If that is not possible (or the wave is already nearly upon you), go up as high as possible. If you are already in the water, grab onto something that floats.
See the Homeland Security tsunami safety guidelines at: https://www.ready.gov/tsunamis
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