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Re: Global oceanic tides,
From: Trevor Kenchington
Date: 2003 Aug 25, 00:28 -0300
From: Trevor Kenchington
Date: 2003 Aug 25, 00:28 -0300
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@iStar.ca 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