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n cook wrote:


http://geography.berkeley.edu/people...am/2%20Literat
ure.pdf

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The Berkeley Geography Website was moved to a new server on February 4,
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The usenet 80 column limit perhaps.

I just downloaded and pdf-text converted the relevant page with mamgled
maths

page 42
reference to the phenomenon of "Perigean Spring Tides" (Wood 1976).
As noted before, tidal amplitude (and therefore range) is relatively large
during syzygy (period = ½ synodical month = 14.765294... MSD) and during
lunar perigee (period = 1 nodical month = 27.212220... MSD).
As is often the case with natural phenomena with independent origins, the
ratio of these periods (and hence their frequencies and angular speeds) is
an irrational number (T /T = 1.842985...).
Therefore, syzygy and lunar perigee will periodically approach and converge
(i.e. "beat"), but will literally never exactly coincide.
Their closest convergence during a beat will vary, and the strength of the
perigean spring tides will therefore also vary.
Wood, after an exhaustive historical and theoretical review of the
phenomenon (1976), classified perigean spring tides as 1) perigean (closest
coincidence is 6.5-23° geocentric longitude = moderately large amplitude);
2) proxigean (3.25-6.5°); and 3) extreme proxigean ( 3.25° coincidence =
greatest amplitude).
He also calculated the primary frequency sets that govern the closeness of
convergence during beats, based on the !! recognition that beats will occur
when n T (n+1) T , where n is an integer and T and T !! 1 2 1 2 are the
periods of the interacting waves.
When T T is irrational, there is no integer n 1/ 2 satisfying this
equation, but there will be sets of integers that satisfy the approximation
to any desired coincidence.
Using this method, Wood recognized major frequencies at multiples of about
31 years as well as shorter and longer frequencies and beats.
Wood and others researching extreme tides have noted that other cycles, at
other irrational period ratios, also generate beats and/or modulate the
magnitude of the beats generated by the syzygy and lunar perigee cycles
(Pugh 1987).
This means that the temporal structure of tidal beats, and therefore the
temporal patterns of the high tides that most influence marshes, is quite
complex.