Dr. Watson has arrived in front of the fireplace and made all preparations to ensure a successful evening.
After the previous drink disaster, resulting in the dismissal of the butler, Dr. Watson has prepared everything himself well ahead of Holmes` arrival. Drinks have been prepared; pipe and tobacco are already waiting for Sherlock Holmes.
Part 1: Sherlock Holmes and the Hippopotamus in the Basin
Part 2: Sherlock Holmes applies “meteorology” to geology
Holmes, upon arrival: You are early tonight, and I can see that you have made some preparations – even paper and pencils.
– Yes, Holmes, Dr. Watson replies.
– Your lecture on the Coriolis Effect and the adventures about the deep earth, kept me awake nearly all night. I had to get up early and do some thinking, writing and drawing. I could hardly wait to finish dinner and get back in business. I will now convince you that there are two working brains in this room. I am well prepared – what would you like to discuss Holmes, subduction, mantle upwelling or moving continental plates?
Holmes, looking back at Dr. Watson in astonishment and exclaiming: I say, dear chap – you are really going for it tonight. Well, I can hardly wait to hear your elaborations concerning mantle upwelling and its relation to dear old Coriolis.
– OK then, where on Earth do you want to start?
Holmes: Good question, how about starting just north of the Equator like I did in my discussion on the low-pressure systems in the atmosphere?
– OK, fasten your seatbelts, Holmes, and sharpen your brain.
Holmes, not used to that kind of lecturing: Quit being silly, Watson, get to the point!
– Well, you see, Holmes – OK, sorry about that.
– As you know, Holmes – from pole to pole, in the North and South Atlantic, there is a continuous upwelling zone. It is termed a mid-ocean spreading ridge created by an upwelling mantle.
Holmes interrupts: Do you really want to start there? You are aware that this is not upwelling caused by high fluid content in the mantle?
– I am aware of the fact that there might be other places to observe the evidence set in stone by the Coriolis Effect – but nevertheless, let`s start there, Dr. Watson adds.
– Close to the Equator, a vertical line – the direction of gravity or buoyancy, from the surface towards the centre of the Earth is close to being the same as the radius defining the rotational velocity. In other words, upwelling of masses from the mantle to the surface will move into regions with higher velocity, while staying within the same latitudinal plane. Due to the Coriolis Effect, the masses will deviate westwards because they ascend to regions that have increasing eastward rotational velocity. I made a drawing where you can see that the latitudinal angle of the location of the upwelling determines the rotational radius and velocity.
Dr. Watson presents his drawing:
– As we move closer to the North Pole, the radius defining the rotational velocity is proportional to the cosine of the latitudinal angle of the point in question, Watson explains.
Holmes: I already told you so last night.
– There is more – Dr. Watson states.
– We have to bear in mind that at a location further north, the vertical direction from the surface is at an angle different from 90 degrees relative to the axis of rotation. The upward, vertical direction will increasingly be pointing towards the North as we get closer to the pole. This is of significant importance because now the rising mantle plume not only approaches regions above that are rotating faster, but it simultaneously approaches regions at higher latitudes that are rotating slower. Whether the plume ends up deviating eastwards or westwards is determined by the gradients in the rotational velocity of the axis-perpendicular vector and the gradient of the rotational velocity along the surface direction.
– Simply put, it is determined by the angle between the axis of rotation and the direction of gravity. Thus, as we go northwards along the Mid-Atlantic Ridge from the Equator, we might observe the ridge becoming less and less pointing westwards and at some latitude start to point more eastwards.
– Of course I have not forgotten, Holmes, that the mantle plumes – if allowed to receive magma from all sides, will rotate counter-clockwise on the northern hemisphere, and clockwise on the southern hemisphere. I will tell you more about this in a minute.
Holmes: I dare say Watson – you have really thought hard about this. But – what happens with mantle upwelling and the spreading centre at the Equator itself – if I may ask: Can mantle plumes rise there?
– The Equatorial region is interesting, because exactly at the Equator the free flow of magma into an upwelling plume, would not be allowed to rotate. However, if we envision free inflow and upwelling of mantle plumes just north of, – and just south of the Equator, an interesting scenario would appear. The plume to the north of the Equator would tend to rotate slowly counter-clockwise, while the southern neighbour would rotate slowly clockwise. If the moving masses encountered each other, they would act like two gears engaging their teeth together and move masses in between them in an easterly direction.
– In addition, the two plumes would deviate westwards because of the Coriolis Effect in the vertical direction. Perhaps even more interesting, – on the east side of the two slowly rotating systems, the imaginary teeth would move away from each other and tend to transport masses northwards and southwards from the Equatorial line between the two.
Dr.Watson pulls out a second drawing he made during the night:
Holmes, exclaiming: Very nice Watson! And, where is the evidence in geology to prove your point?
– I anticipated that, and I have prepared more.
Dr. Watson pulls out yet another figure:
Holmes: What is that?
– That is a small section from the bottom of the sea, along the mid-ocean ridge in the South Atlantic. The present time Equator is running directly along that big, open canyon in the middle, Dr. Watson explains.
– And would you believe it – if we continue along the Equator westwards, we end up where the Amazon River meets the sea! As you know, rivers tend to follow valleys – and to begin with, they need a valley to follow.
Holmes: OK Watson, are there more peculiarities along the Mid-Atlantic Spreading Ridge?
– There is – and in theory, there should be, Dr.Watson explains.
– You see, the only place where we might encounter “cooperating gears” – is at the Equator itself. Further away from the Equator, free-flowing mantle masses would create mantle plumes that oppose each other along the line of contact, because all plumes rotate in the same direction there. The newly formed oceanic crust will become segmented into smaller rotational sections with dimensions determined by crimping during the cooling of the lava, the strength of the rocks and the forces created by the Coriolis Effect.
– I think this is the reason we get the formation of what is called “transforms”. These are interesting creatures because they have an individual life until they are subducted as so-called slabs in the distant future. The “sideways” stepping of the spreading axis along the transforms ought to be a function of the combined, east-/westwards deviation in the vertical plane and the propelling forces created between segments due to the direction of rotation of the upwelling magma.
– By the way, Holmes – I have to make a serious complaint about your lecturing about the low-pressure systems in the Northern Hemisphere.
Holmes: I beg your pardon Watson –what on earth, are you aiming at?
– Well, you omitted a piece of vital information; maybe thinking I would understand it by myself – which by the way is correct, Dr. Watson has to admit.
Dr. Watson continues as Sherlock Holmes watches his every move in great anticipation.
– You told me that the rotational velocity of different points on the Earth is proportional to the cosine of the latitudinal angle.
Holmes, exclaiming: And – what is wrong with that?
– Nothing is wrong with that, but you did not explain that because of this; the change, or the gradient in rotational velocity, is proportional to the sine of the latitude when going northwards or southwards from point to point. A sine function has zero value at zero angle and a value of one at 90 degrees angle. Dr. Watson explains.
Holmes: Of course, I know that – get to the point.
– The point is that the Coriolis Effect along the horizontal plane will end up producing slightly – or, if I may say so, profoundly different results at different latitudes, Dr. Watson says.
– When moving masses towards a point where upwelling is occurring near the Equator, the deviation due to changes in rotational velocity is very small – because as I said, the value of sine at small angles is small. The consequence of this is little and slow rotation within the upwelling magma around the Equator. The change in rotational velocity in the vertical direction is at its greatest near the Equator, therefore the westward deviating part of the Coriolis Effect will dominate there.
– If we consider the inflow of magma towards a ridge segment, a bit further north than the Equator, the southbound flow will experience a greater Coriolis Effect than the northbound flow. This is because the rotational velocity is proportional to the cosine of the latitudinal angle. The sine of this latitudinal angle is the derivative of cosine and defines the change in velocity per degree of change in latitude along the surface. A sine function goes from zero at zero degrees latitude and ends up at one at 90 degrees latitude.
– The implication of this is that as we move northwards, the symmetry in deviation towards the upwelling zone becomes lost. The south-directed flow deviates sharper to the west than the eastwards deviation of the northwards flowing masses. The combined effect of this might be a more elliptic rotation and a change in angle from the north-south direction of the spreading centre segments closer to the Equator.
– I will sum this up to you Holmes – because this is exciting, Dr Watson says with his most insisting voice.
– If we start moving along the Mid Atlantic Ridge from the Equator and towards the North Pole, we should expect to see something like this:
- Large westwards deviation and stepping of the spreading axis just north of the Equator.
- Diminishing, westwards stepping of the spreading centre further to the north.
- Entering a region of no westwards vertical deviation of the ascending plume.
- Increasing mantle plume deviation eastwards.
- Before entering a region having a decreasing eastwards deviation
- Finally, at the North Pole itself – no east-west deviation from vertical movements – just a bit of twisting from horizontal movements.
– A similar process ought to occur in the Southern Hemisphere although as you know, the Coriolis Effect does not produce the exact same results on both hemispheres. The changes in westwards deviation due to the Coriolis Effect in the vertical plane are virtually the same. Still, the rotation in the horizontal plane is opposite of the Northern Hemisphere. This does not allow the two hemispheres to become mirror images of each other.
– There is so much more to talk about, Holmes – but it is getting late, Dr. Watson concludes.
Holmes: This has been a most interesting evening, also for me. There might be more to discuss tomorrow. I am getting a bit interested in the shape of the eastern coast of Africa. Maybe I will be the one not being able to sleep tonight. Anyway – let`s call it a day my dear friend.
HANS K JOHNSEN
Inspired by Arthur Conan Doyle