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Ocean currents: from Fukushima and rubbish, to Malaysian airplane MH370

POSTED BY: Marco Thiel
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Marco and Bjoern, This is an incredible post.

About the data relevant to the MH370 flight, do you know if the data from 2014 is available? Or is there a way for you to post some small amount of data like average currents for the Indian ocean?

Searching for ocean current pictures, they seem to vary in some important details, but it appears that the wreckage appearing on Reunion island is close to several divergent integral curves. Also it looks like there is a lot of turbulence. Just based on what I see there, I'd expect sensitive dependence and the wreckage conceivably could have come from where the authorities say it crashed but just from the currents a case could be made for anywhere in the Indian Ocean, or even the South China sea which is where it was supposed to be flying.

That's just a guess, and it would be interesting to quantify that.
POSTED BY: Todd Rowland

Dear Todd,

thank you very much for your encouraging words.

About the data relevant to the MH370 flight, do you know if the data from 2014 is available? Or is there a way for you to post some small amount of data like average currents for the Indian ocean?

There is indeed some more data available on the website. If you go to this page, which I used for the download, you will see that there is data available for up to the end of October 2014.

enter image description here

You seen that the last file name ends in 20140124.nc, which indicates the date.That end data is, of course, not quite enough to follow the debris of the plane through the ocean, but you can use is for the first couple of months and then use the older data from previous years and make a sort of ensemble prediction over the flow in different years.

This is also what could be done in case of an oilspill, where flow data for predictions is not readily available. It is also interesting to study how different the paths of the particles are if you study at different times, i.e. current conditions.

Another interesting thing to try might be to use the data for different depths. If you open a file the top of it looks like this:

enter image description here

so we get all sorts of data for various different depths, not only the surface. This could be quite valuable for applications.

There are lots of other things to try. Here I have a gif-animation of the particle movements for the Fukushima scenario:

Export["~/Desktop/swarm.gif", 
 Table[Graphics[{RGBColor[i/1238., 1. - i/1238., 0.], Opacity[0.8], 
      Disk[#, 3]} & /@ trajectories[[i, 1 ;; 1000, {3, 2}]], 
   PlotRange -> {{470, 950}, {380, 570}}, ImageSize -> Full, 
   Background -> Black], {i, 1, 1236, 5}]]

enter image description here

You can use Image3D to get a representation of it, which can (after slight modification) be 3D printed.

Image3D[Import["~/Desktop/swarm.gif"]]

enter image description here

The "green top" shows the earlier times, and the "red bottom" the later ones.

Thanks a lot for your comments; I really appreciate it.

Cheers,

Marco

BTW, you can get pretty nice effects with ContourPlot:

ListContourPlot[veltottot, AspectRatio -> 1/2, ImageSize -> Full, ColorFunction -> "TemperatureMap", Frame -> None, Contours -> 7]

enter image description here
POSTED BY: Marco Thiel

Dear Marco and Bjoern,

this - as usual! - is a remarkable post! Thank you very much for sharing! I started out for this "MH370 challenge", but soon I got stuck at the rubbish problem: Assuming the plastic garbage stays next to the surface but the water moves up and down, i.e. on the surface there are (so to say) wells and sinks - or more mathematically speaking: $\nabla\vec{v}_{\scriptsize horiz}\neq0$. I thought the rubbish should accumulate on places where there is a sink. So I downloaded the data for vertical velocities for most of the year 2014. Because the data change over the year but the rubbish stay stationary, I calculated the mean value of all the data. The result looks like this (shown are only the sign of the horizontal velocity!):

enter image description here

I was very surprised to find wells and sinks mixed on a very fine scale! And the overall result is not really suited to give the nice result of the original post. Only very roughly the garbage "piles up" on places without vertical motion.

Regard -- Henrik

EDIT: There is an effect called "salt fingering", which is a mechanism for mixing water in the ocean. Maybe this is what we are seeing here. Regarding the shown horizontal motion: I expected to see the famous Humboldt current (along the west coast of South America) - what is NASA hiding?
POSTED BY: Henrik Schachner

Just wanted to say: very nice job! Perhaps you could add the border of the countries, such that there are clear distinct lines between land and sea.

POSTED BY: Sander Huisman

Dear Henrik,

Thank you very much for your post and for your time looking into this. The figure you show is really interesting. The extreme fine structure, I think I understand. It appears that the rubbish accumulate in the areas that have no pronounced fine structure (the large white areas in the oceans). I believe that there are numerical studies of much simpler situations that show that (massive?) particles often accumulate in the larger vortices, which is consistent with that I see. You are mostly seeing the very fine structure, which is the most fleeting structure. There appears to be a "fractal" pattern/scaling in the vortex size etc. It would be quite useful to see the code that you used. I

I have a rough idea what the answer to your question is, but I am not sure enough to post it here. I have a colleague, Alessandro de Moura here at the University of Aberdeen, who is an expert in this area. He has published a lot in this field, and is co-author on this paper. I have asked him for an explanation, and will post it when I get a confirmation from him.

I also fully agree with you that 3D is probably important here. It would be really nice to study the complete 3 dimensional system. As I said, the data files do contain (some of) the information we would need. I do have access to more CPU time, and one could combine efforts here in the community to sort this out.

I will try to come up with something as soon as I can.

Thanks a lot again for commenting,

Marco
POSTED BY: Marco Thiel

Dear Marco,

thank you very much for you informative answer. Of course it was naive to think there are "big" areas with wells or sinks. And one should not post a picture without any code! See the attachment, the code is quite simple. Without seeing your code I never ever would have been able to do the download - thank you for this as well! The papers you supplied seem basically to be about Hamiltonian chaos - decades ago I was quite interested in that field. I hope I find the time reading them! All in all a very nice stimulation!

Regards -- Henrik

Attachments:
POSTED BY: Henrik Schachner

Dear Henrik,

thank you very much for your notebook. It is very interesting indeed. I spoke with Alessandro, who promised to post an explanation, but apparently has not gotten around to it. I had suspected that the problem is that the flow is non-autonomous, i.e. time dependent, and that it is a 2D slice of a 3D system.

It appears that the attractors for the advection of particles can be really complicated and it is by no means clear that the "sinks" are the actual attractors. From what I understand the implications of these very complex flows are not fully understood and even much more simplified systems are rather difficult to understand.

I think that it should be possible to produce simple models to study some aspects of these flows. I am, however, not familiar with these types of simulations.

It would be great to see what type of fluid-mechanical simulations people have implemented in Mathematica. I know the demonstrations, and this beautiful 2013 blog entry.

I also had some students who used windspeed data to simulate distribution of ash from a volcanic eruption and they got excellent results. But similarly to my simulation, they basically used the flow and put particles in it.

Cheers,

Marco
POSTED BY: Marco Thiel

Dear Sander

you are quite right. I tried to do that, but had trouble aligning the images properly. It is certainly possible, but requires some fiddling with projections.

Cheers,

Marco
POSTED BY: Marco Thiel

enter image description here - this post earned "Featured Contributor" badge, congratulations !

Dear @Marco Thiel, you are the first person on Wolfram Community to be repeatedly selected as a "Featured Contributor". This is a great post and it is now featured the curated Staff Picks group. Thank you for your excellent contributions!
POSTED BY: Vitaliy Kaurov
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