Understanding the wave nature of a tsunami

Paul Nachman writes:

Yesterday Peter H. wrote:

See this horrifying video, one of the most instructive I’ve seen, in which we see some of what you’ve discussed previously (here and here), that the tsunami is not, in any way, a “wave” in the normal sense, but a sudden rise in the level of the entire surrounding sea resulting in the pouring of sea water down into the city, which is now below the level of the sea.

No, it really is a wave. But the wavelength (crest-to-crest or trough-to-trough distance) is a couple of hundred of kilometers [about 120 miles] long. And with a wave speed of about 800 km/hour [500 miles per hour], that means that the period (cycle time) of the wave is a about a quarter of an hour or 15 minutes. So it’s “up” for about 7.5 minutes, “down” for the next 7.5 minutes, etc.

And this really means that its height increases approximately sinusoidally from “zero” for 3.75 minutes (half of 7.5 minutes) to the maximum, decreases back to “zero” for the next 3.75 minutes, further decreases to the bottom of the trough during the next 3.75 minutes, and then returns to “zero” during the “final” 3.75 minutes, whereupon the cycle repeats if there are multiple waves in the train.

As this Wikipedia article makes clear, the amplitude (up and down disturbance) of the waves can easily be less than a meter far out at sea. Thus people on a ship encountering such a wave would most likely be unaware of it (given the approximately 15-minute cycle time). But waves “shoal” when they reach shore (not a phenomenon I’ve ever tried to think about enough to understand), which means the amplitude of the wave grows dramatically, even as the wavelength shortens. But what’s preserved is the period, so now you have a huge wave that’s “up” for 7.5 minutes, then recedes for the next 7.5 minutes, etc. (My use of 7.5 minutes isn’t meant to be exact and the same value among all such waves—it merely comes from those starting values of 200-km wavelength and 800-km/hour wave speed.)

Here’s the key part of the Wikipedia article:

Tsunamis cause damage by two mechanisms: the smashing force of a wall of water travelling at high speed, and the destructive power of a large volume of water draining off the land and carrying all with it, even if the wave did not look large.

While everyday wind waves have a wavelength (from crest to crest) of about 100 metres (330 ft) and a height of roughly 2 metres (6.6 ft), a tsunami in the deep ocean has a wavelength of about 200 kilometres (120 mi). Such a wave travels at well over 800 kilometres per hour (500 mph), but owing to the enormous wavelength the wave oscillation at any given point takes 20 or 30 minutes to complete a cycle and has an amplitude of only about 1 metre (3.3 ft).[20] This makes tsunamis difficult

to detect over deep water. Ships rarely notice their passage.

As the tsunami approaches the coast and the waters become shallow, wave shoaling compresses the wave and its velocity slows below 80 kilometres per hour (50 mph). Its wavelength diminishes to less than 20 kilometres (12 mi) and its amplitude grows enormously. Since the wave still has the same very long period, the tsunami may take minutes to reach full height. Except for the very largest tsunamis, the approaching wave does not break, but rather appears like a fast-moving tidal bore.[21] Open bays and coastlines adjacent to very deep water may shape the tsunami further into a step-like wave with a steep-breaking front.

When the tsunami’s wave peak reaches the shore, the resulting temporary rise in sea level is termed run up. Run up is measured in metres above a reference sea level.[21] A large tsunami may feature multiple waves arriving over a period of hours, with significant time between the wave crests. The first wave to reach the shore may not have the highest run up.[22]

I don’t know what accounts for the high speed of the tsunami waves. If those “everyday wind waves” they write about traveled at the same speed, then more than 100 of them per minute would rush by.

LA replies:

Thank you for this helpful explanation, which is much clearer than the Wikipedia article I had read (as I discussed with Peter H. in the entry yesterday). The confusion was initially created a few days ago by the article at American Thinker we discussed which pointed out that the “wave” seems to have no trough behind it, but rather is a very large area of raised water, which made it seem to be not a wave, but something else. The contradiction is resolved by the fact that the tsunami wave is around 120 miles long. It is both a wave, and a huge raised area of the ocean encompassing perhaps thousands of square miles.

Peter H. writes:

Thanks to Mr. Nachman for his helpful information and explanation. I do understand what he’s saying, that a tsunami is a wave with a very long wavelength. It seems to me, however, that the effect of a Tsunami is closer to what happens during tidal surges than it is to what happens in a typical wave. In a thrust-type quake, the ocean floor pushes the sea. In tidal movements, the gravitational pull of the moon “pulls” the sea. But a tide must also have a peak and a trough. Both tides and tsunamis, then, are special waves with very long wavelengths albeit, in the case of tsunamis, much more rapid and exaggerated. It is for this reason that I like the term “tidal wave,” implying something abnormal and unusual.

Also, I wonder if Mr. Nachman can clarify if there is not only a horizontal movement of the land, but a vertical one as well, whether the land is actually lowered as is implied in the Wikipedia article. It seems to me that this could be a significant factor in the run-up to a tsunami.

LA replies:

By coincidence (no, by synchronicity), just a minute before receiving Peter’s above comment, I added a comment in the previous tsunami entry saying that I prefer the term “tidal wave” to tsunami. Now I’ll go further and say that we should resist fashion and start bringing back the term tidal wave.

LA replies:

The more I think about it, the more I prefer “tidal wave.” Yes, of course, a tsunami is not literally a tide, but it is “tide-like” in that it consists of a raising of the level of the ocean. It’s a combination of a wave and of a tide-like raising of a large part of the ocean. Tidal wave also poetically suggests the hugeness and force of the thing. Far from being inaccurate or non-descriptive, it is probably the best possible term for the phenomenon. I say it’s time to start bringing it back.

March 20

Paul Nachman writes (March 19):

I want to acknowledge Peter H’s questions and admit that I can’t answer them very well. My best attempts are as follows:

1. Since Peter wrote:

Also, I wonder if Mr. Nachman can clarify if there is not only a horizontal movement of the land, but a vertical one as well, whether the land is actually lowered as is implied in the Wikipedia article.

… I can refer him to another paragraph in that Wikipedia article:

In the 1950s, it was discovered that larger tsunamis than had previously been believed possible could be caused by giant landslides. These phenomena rapidly displace large water volumes, as energy from falling debris or expansion transfers to the water at a rate faster than the water can absorb. Their existence was confirmed in 1958, when a giant landslide in Lituya Bay, Alaska, caused the highest wave ever recorded, which had a height of 524 metres (over 1700 feet). The wave didn’t travel far, as it struck land almost immediately. Two people fishing in the bay were killed, but another boat amazingly managed to ride the wave. Scientists named these waves megatsunami.

So that’s not an earthquake effect, but it’s a vertical disturbance, which is what Peter seemed essentially to be asking about.

Before this recent Japanese tsunami, I’d seen an online video about that astonishing Alaska wave—ah, yes, here it is, but there’s a puzzle, since the narrating survivors in the video are named Ulrich whereas the sole survivors in this Wikipedia account are named “Swanson.” What Wikipedia provides is extracted from this Los Alamos publication.

2. Regarding terminology, the first of those Wikipedia articles says that “tsunami” is Japanese for “harbor wave,” which seems no more appropriate to me than “tidal wave.” And I think “tidal wave” captures the draconian sense of the things better than “harbor wave.”

Posted by Lawrence Auster at March 19, 2011 09:22 AM | Send