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

POSTED BY: Marco Thiel
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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

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 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

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

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
POSTED BY: Marco Thiel
POSTED BY: Marco Thiel

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
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