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From: Trevor J. Kenchington (no email)
Date: Sun Aug 24 2003 - 23:28:22 EDT
Geoffrey Butt wrote:
> So, right or wrong, this is the
> way I explain two tides per day:
>
> * The Moon and Earth rotate around each other in the manner of a hammer-
> thrower before releasing the hammer
> * They both rotate about a point close to the surface of the Earth
> * The oceans are not rigidly connected to the Earth and are free to respond
> to the Moon's gravitational attraction by flowing towards the Moon
> * However if, with his second pair of hands, the hammer thrower was carrying
> a bowl of water as he rotated his eccentric motion would cause the water
> in the bowl to slosh outwards, away from the hammer
> * On the side of the Earth closest to the Moon the effect of Moon's gravity
> exceeds the sloshing effect and water levels are raised there - towards
> the Moon
> * On the side of the Earth remote from the Moon the sloshing effect exceeds
> the gravity effect and water levels are raised there also - away from the
> Moon
> * .. so there are two raised ocean levels opposite one another and as the
> Earth rotates beneath one experiences locally two tides per day
All of which is correct, as far as it goes into detail, save for the
very last part: As I wrote earlier today, these two "raised" areas do
not really exist. They are a very useful model for explaining the
effects of tide generating forces, which is why Newton came up with the
idea, but even Medieval knowledge of the tides of the English Channel
was sufficient to prove to any thinking person that there is not some
bulge moving westwards down channel at 15 degrees of longitude per hour.
> I haven't done the calculations myself but have read (somewhere) that the
> two causes for ocean raising have slightly different magnitudes - which
> explains why plotting sequential tidal ranges from tide tables results in
> the 'odd' tides following a slightly different curve from that for the 'even'
> tides.
That, in contrast, is false. In Newtonian theory the two bulges are of
exactly equal magnitude -- as is actually true of the tide generating
forces.
The Newtonian explanation for the diurnal tides (which in most areas
appear only as the diurnal inequality between the heights of successive
semi-diurnal high waters and ditto for low waters) is that the Moon (and
the Sun) rarely have zero declination. When the Moon has a northern
declination, for example, the "bulge" under the Moon will lie north of
the Equator, while the antipodean "bulge" will lie at some southern
latitude. Now imagine an observer at any temperate northern latitude.
When the Moon passes his meridian, the observer will be quite close to
the "bulge" and so will experience most of its height. When the Moon
passes a meridian 180 degrees away, the observer will again experience
high tide but the peak of the "bulge" will be far to his southward so
his water level won't rise as high as it did 12 hours (and about 25
minutes) earlier. The difference in height of the two high waters is the
diurnal inequality and is the result of superimposing the diurnal tide
on the semi-diurnal.
Again: These "bulges" don't exist but the forces that try to raise them
do and the magnitude of those forces varies with the same pattern as
Newtonian theory pretends that the "bulges" vary.
> " I understand that the Manual was produced at short notice in the early days
> " of the 1939-45 war to meet the sudden need to train up thousands of
> " officer-recruits for the Royal Navy. It's good to see it still being taken
> " as a reference.
>
> For this kind of project it is a wonderfully complete resource. However the
> mind boggles at the notion of 'thousands of officer-recruits' struggling
> with the chapters on the theory of harmonic analysis!
I agree. I had never heard that account of the origins of the Manual of
Tides before George posted it and I don't think that it is stated in the
preface to my copy, which details the development of the book. Still, I
don't doubt Georges' tale. I just rather suspect that the Liverpool
Tidal Observatory was asked for a textbook suited to officer-recruits
and, like too many scientists, they wrote the text that seemed, to them,
to convey the minimum amount of knowledge that an officer needed, even
though it far exceeded what almost any serving officer would have said
was required. (Here I must plead guilty: My own teaching, including
lectures on tidal phenomena, repeatedly falls into that mistake.)
I can confirm that, as an undergraduate oceanography student in the
1970s, we were pointed to the Manual as an ultimate reference on tides
but we were certainly not expected to master its content. I find it hard
to think that junior officers, even those with full peacetime training
at BRNC Dartmouth, were required to know more of the mathematics of
tides than oceanography students were.
Trevor Kenchington
--
Trevor J. Kenchington PhD
Gadus Associates, Office(902) 889-9250
R.R.#1, Musquodoboit Harbour, Fax (902) 889-9251
Nova Scotia B0J 2L0, CANADA Home (902) 889-3555
Science Serving the Fisheries
http://home.istar.ca/~gadus
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