- Snapshots of modern mathematics
- Diderot Mathematical Forum 2013: “Mathematics of Planet Earth”
- Pierre de Fermat and Andrew Wiles in Czech Republic stamps
- Stefan Banach (March 30, 1892 – August 8, 1945)
- Diderot Mathematical Forums
- Guessing the Numbers
- What is mathematics for Ehrhard Behrends
- What is mathematics for Krzysztof Ciesielski
- The Three Ducks Trick
- What is mathematics for Franka Brueckler

# Where does river water go when it enters the ocean?

Dr Tom Crawford, aka the ‘Naked Mathematician’ and the person behind the award-winning website tomrocksmaths.com, has recently launched a new series of online articles explaining his PhD thesis in simple terms. If you’re feeling brave, you can tackle the full beast online here, but for most people we suggest starting with the first article outlining the motivation behind the work with the question ‘where does river water go when it enters the ocean?’

*“It might seem like a simple question, but just think
about it for a second… Water falls from the sky as rain, it flows over and
under the ground and enters into a river. The river flows downstream, maybe
passing through a few lakes along the way, until it reaches the ocean. Now what
happens? The water has to enter the sea and will eventually be evaporated by
heating from the sun and end up back in the atmosphere to form rain again. A
lovely full-circle route called the water cycle – you probably learnt about it
in Geography class. But, what if we could track a raindrop from the sky, into a
river and then into the ocean. What would happen? Does it just flow into the
ocean and then get mixed up and thrown around in the wind and waves? Or do
tides drag it out further to sea? And what about the fact that the Earth is
rotating? Perhaps not so simple after all…”*

The second article ‘how to build a river in the lab’ explains how laboratory experiments can be used to gain invaluable insights into the real-world situation, provided of course that they are suitably well-designed. Article number three, ‘the right ingredients’, moves onto the issue of how to decide which variables are most important in a given problem, touching on the incredibly powerful method of scaling analysis – an applied mathematicians favourite tool.

The fourth article introduces the experimental setup used to collect the data, which will ultimately prove or disprove the mathematical theory used to describe the problem. The title of the article ‘spinning a giant fish tank’ is a surprisingly accurate description of what is in fact a highly sophisticated scientific experiment (though maybe you’ll just have to take my word for it). Finally, ‘let the floodgates open’ features an explanation of an actual experiment in full detail, including a birds-eye view of the river current as it discharges into the rotating ocean.

*“This is a false colour image of an experiment viewed
from above. The freshwater from the river is dyed red with food colouring which
means that we can convert the colour intensity into a depth measurement. The
more intense the red food colouring, i.e. the more of it there is, the deeper
the current must be. The scale starts with black to represent no current (as is
the case for the saltwater ocean), then increases with the current depth
through red, yellow, green and finally blue for the deepest parts of the
current.”*

Tom plans to continue the series in the coming months so if you enjoy the first five articles please do keep your eyes peeled for when the next ones become available. Or better still, follow him on Facebook, Twitter, Instagram and YouTube @tomrocksmaths to be the first to hear when new material is posted!

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