Ocean Waves
including tsunamis

 T
he recent "spillage" in the Indian Ocean prompted me to consider some of the aspects of waves in the open ocean in general. In the course of surfing (the web) for info, I came across a new word which I may have seen before but had long since forgotten. It is "Seiche" (pronounced "saysh"). This is the resonant frequency of a body of water (like your swimming pool, bathtub or Lake Geneva), i.e. it's the rate of "sloshing" which, if reinforced at each slosh, will make the slosh ever greater thereby causing the tub (or lake) to spill over its banks. Earthquakes have been known to do this to lakes and swimming pools.

It's about waves. Water waves. Specifically deep water, ocean waves. And something about tsunamis (just to be politically ... hmmmm ... morally correct).

I was looking for answers to these Q's :

... and a few more that they, in turn, generated.

1. Namely, if an ocean wave corresponds to a sine wave, how does it support the little circles that the water in a wave traces out? Shouldn't it go just up and down?
2. Can a wave be preceeded by a trough? Or, which comes first ... the crest or the trough? Does it make any difference?
3. Can a wave train have a trough on both ends ... or ... a crest on both ends?
4. Why is the little circle not exact? Why is the water displaced a tiny bit forward?
5. What happens on the bottom of the wave or on the bottom of the ocean floor in the case of a tsunami?
6. And what about Cumbra Vieja anyway? (the volcano in the Canary Islands off Morocco where the Tenerife Airport is ... where all those 500+ people got killed a few decades ago when the jumbo jets collided on the runway ... because El Capitan was tired of waiting for "clearance" to take off).

It's not a sine wave

It's called a "trochoid" wave form. It's a cycloid curve upside down. That's the curve you get when you trace out the path of a point on a wheel as it rolls along the ground. Actually, a point on the wheel's outside extremity traces out a "pointy" curved line which doesn't exist in nature. However, a point closer to the axle traces out the shape of a real ocean wave. They are somewhat steeper than a sine wave and more pointy too ... and ... they support that little circle that the water traces out.

Why is the little circle necessary anyway? Why CAN'T it be a sine wave? Here, web searches failed me. So, I did what I always do ... I was "forced" to figure it out for myself ... Aaaaaaaahhhh !!

Below is a rollover image that shows the circular motion of water in ocean waves. The "circle" isn't perfect unless it's a very deep wave. As you go deeper the ellipsoidal motion gets more and more eccentric and gets smaller too ... until it's just a line going back and forth. You can see why there are "surface" waves, eh? Way down deep there is no effect.

Now ... another question ...

Why the circle or ellipse? Why not just up and down? Why is the duck pushed forward and back to the starting point instead of just vertically? Here the web has no answer so I'll give it.

Imagine columns of water on a flat sea. To make a wave we must transport water from one column to the next ... to the next ... to the next, so that a hump (higher than sea level) is moved on down the line. Now, just how is the water in column A going to go to column B ... vertically?? Right, it can't. It has to go there laterally to advance to the next column. Remember, water is not a solid so it must move in tiny pieces (molecules) one at a time. This leaves a hole in the previous column that is lower than sea level. Thus, the logic of wave propagation in water requires that there be some sort of lateral back and forth movement as well as vertical ... in order to fill "up" the next column. Hey, we're talking "digital" waves now, aren't we?

Next: Which comes first the chicken or the egg?

In this case, crest or trough?

Well, here some symmetry principles come into play. Given the direction of the wave, we can't say that a wave can be propagated only with a leading trough and a trailing crest because this would violate T-symmetry, i.e. if you run a film backward, it would show the crest leading and the trough following on the end of the wave train. So, at this point, a wave can start with a crest or a trough equally as well.

How about a wave train with a crest on both ends? ... or

... a trough on both ends?

The problem here is that you have one extra of crests or troughs in the wave train. If you have an extra crest, it means that you have "bucket transport" by which I mean ... it's like carrying water in a bucket to some other place. A wave train doesn't transport water to another place, it transports energy in the form of waves. It can't transport water (bucket style) because water is not a solid and will fall down if you put it in a heap by itself. It doesn't "stack" like blocks. Thus, if you have an extra crest in a wave train, it's equivalent to having one lone bump on the water traveling by itself over an equi-potential. Such a "wave" will necessarily fall down and flatten out unless there is a corresponding hole (trough) to compliment it facilitating wave propagation in the physically allowable way, i.e. one crest to one trough. In opposite fashion, if there were an extra trough, it would be equivalent to a hole in the water which would necessarily fill up and level as well.

Note: The water falling down into the trough (below sea level) provides the energy to lift the water to the crest (above sea level). It's like a spring that doesn't lose energy very fast so it keeps going.

So, our answer here is that a wave train may be led by a crest or a trough, but whichever it is ... the end of the train must be the opposite form. For every up there must be a down. End of story.

Why is the circle not exact?

Physical measurements indicate that the duck pictured above will gradually be displaced in the direction of the wave. Ergo, things "wash up" on shore. Why?

Well, the waves are typically "driven" by something. That's why they go in some specific direction. Most often, it's the wind. As the wind blows, it pushes the water in the direction of "somewhere", i.e. it piles up the water in another place as in a hurricane "tidal surge". It's moving water "bucket style". Hence, there is a net push on an object in the direction of this driven current. That's all there is to it. The duck's progress over time looks more like this than the stationary circle.

What happens on the bottom of the wave?

If a wave bottom is just going back and forth with no circles, isn't there then some sort of conflict? Is the entire bottom going back and forth in unison? If some parts of the bottom are going one way and another the other way, there is a problem with the incompressibility of water.

Here, I must assume that there is no exact straight line movement near the bottom of the wave. This is clearly incorrect. The action of water near the bottom of the wave must approach a straight line as a limit, i.e. as the ellipse gets more eccentric, it gets shorter till it's just an unmoving point.

Now, the problem can be solved. Where the movement of one part conflicts with another, the water goes up or down depending on whether the conflict is one of compression or expansion. Thus, if compression, a wave crest is on top of the conflict and vice versa for the trough. No problema.

Tsunami

There are three main classes of waves. Shallow, intermediate and deep. The above are all deep water waves. This means that the wavelength (maybe 10 meters) is small in comparison to the depth of the water it travels in (maybe 1000 meters). By contrast, a wave whose wavelength is great in comparison to the depth of the water it travels in is a "shallow" water wave. A tsunami is a shallow water wave because it is as much as a couple hundred kilometers long and the sea is only a couple kilometers deep.

There are equations for determining the velocity of waves which depend on what type they are. The greater the wavelength, in general, the greater is the velocity that the wave propagates. Hence, a tsunami may travel in open ocean at the speed of a jet liner.

When the tsunami gets to shallower water, it gets refracted (its wavelength shortens and its direction can also change depending on the angle of the obstructing sea bed. How the sea floor comes up to your position determines in large part whether you will just get a little wet or be swept away.

Here is a dude running away from the tsunami. Should he be afraid? Hell, no. In this container, the tsunami will just slosh back and forth and never bother anybody. You need to give it some way to climb out. Like this ...

The thing to remember is that this wave is 100 kilometers long and that wave is maybe two feet high. You can imagine how much water is in it. So it will continue to come up the beach and come up ... and come up ... and come up ... for maybe 30 minutes the water will pile up ... surging forward. Note that when a wave "breaks" on the shore, it doesn't do the little circle thingy anymore. The bottom of the circle gets traction so to speak and the whole wave rolls a-shore like a wheel whose lower part gets worn away. Thus, it is now doing "bucket transport". If you have a dike high enough it can repel the water back ... if ... the dike is very strong ... like a rock cliff. If not, it gets push along and is used like a bulldozer to knock down other homes, people, cars, cows, fences ... which all goes floating down main street.

You die mainly by being knocked out in water. This is always fatal because humans can't breathe under water and we tend to float face down when unconscious with arms and legs hanging down. (This is probably why whales have a blow hole on the top instead of a nose. They can doze off, hang limp and not drown.) So everybody who gets knocked out by a bump on the head ... dies ... unless they have a blow-hole too.

La Cumbra Vieja

This is a volcano in the south of La Palma Island (total surface area of 706 square kilometers and a population of 80.000). www.ing.iac.es/PR/lapalma/lapalma.html
"Any time in the next few thousand years a huge section of southern La Palma, weighing 500 thousand million tons, will fall into the Atlantic ocean. Scientists believe that waves could still be as much as 50 meters high when they reach the east coast of the United States."

I, of course, dispute the 50 meter quantifier.

Let's say 10 cubic kilometers of rock drop down a 1 kilometer potential (earth gravitational). How much water can this push up above sea level at what distance? Rock is about 2.8 times as dense as water so, if we put the rock on one end of the ocean and water on the other ... hmmmmm ... 10 CK (cubic kilometers) of rock dropping 1K will blast, at best, 28CK of water 1K high on the other side. Now, at 6000 kilometers distant, you have to stretch that 28CK out to cover an arc of similar magnitude ... 28/6000=4.6 meters. This means that the wave that reaches our shore (New York City) can be at most equivalent to a wall of water 1000 meters high and 4.6 meters thick.

Of course, it will come in the shape of a tidal surge like they got in Indonesia and elsewhere in the Indian Ocean for Christmas. So for every meter of ocean frontage at most 4600 cubic meters of water can come in (all together). Let's say it comes in at 40 kilometers per hour (faster than running speed) and it's 10 meters high. If it comes on for half an hour without stopping that would be 20,000 meters long x 10 meters high = 200,000 cubic meters of water all together. But we only have 4600 available for our wave. We're short about 193,400 cubic meters of H2O (plus the salt). My calculation says the "scientists" are all wet in their estimates by at least an order of magnitude.

The above is a drastic over-simplification ... (because the 1000 meter high water, falling down would provide energy to lift more water than the 4600) but it's just a ballpark guestimate. Look at the pics from Indonesia and that's probably just about what would happen in NYC and elsewhere. Some places would get it worse than others depending on the lay of the land. But ... be sure of this ... it won't look like that wave in

~~~~ "The Day After Tomorrow" ~~~~
And just what the hell did that wave have to do with atmospheric phenomena anyway?

In dealing with NPMD,s (Natural Phenomena of Mass Destruction), one should always divide by "10" since the scientist' natural tendency is to exaggerate the effect so as to increase his stature in the eyes of the public. So, the actual wave will be something like 5 meters high ... I mean here the maximum height of the surge like we saw in the Indian Ocean tsunami. That's still huge ... about 15 feet and will kill millions ... if ... they have no warning ... which won't happen in the USA ... however, you'll still have to run like a mutha' fucka' cause the freeways will be impassable with traffic jams and overloaded trailers of people trying to save their wide screen TVs (especially the plasma ones which are very expensive) ... so they can watch the carnage live on CNN and see their neighbors drown because they just had to save their stuff ... which is more important than the neighbors anyway ... Aaaaahhhhhhhh!!!!!!!

We're all gonna' die!!

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