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Re: double tide cause

Regarding Jim Green's comment about the significance of Jupiter's tidal
effect:

You would expect the tides to be somewhat attenuated, because the Gulf
is
fairly small, and connected to the open ocean only by rather narrow
straits.

Yes, conceivably, but these are subordinate questions: First ask how
close
does the resonant frequency of the body of water match one of the many
driving frequencies of the forces due to the Moon, Sun, and possibly
Jupiter in some cases. True the net force due to Jupiter is much
smaller
than those due to the Moon or Sun, but it is the frequency match that
matters most.

Here a physics text IS helpful -- Look at the equation for a driven
damped
harmonic oscillator. That is what the tides on the Gulf (or anywhere
else) are.

Jim Green

Over 5 years ago in a previous incarnation of our periodically perennial
discussion of tides Jim had also mentioned the relevance of Jupiter's
tidal effect. In a note to Jim dated 3 JUL 96 I commented on that
possibility. I include below a copy of that message and so demonstrate
that there is not much new under the Sun concerning Jim's thinking about
tides.

Jim,

Concerning my comment:

BTW for Jim G., the gravitational field gradient of Jupiter
at the location of the earth varies somewhat with the
relative orbital positions of the Earth and Jupiter,
but its average value is about 6 or 7 x 10^-6 that of
the sun. This I *would* call "tiny".

you said:

Me too BUT the magnitude is not as important as is the frequency -
remember the Tacoma Narrows Bridge (:-) This is the point I keep
trying to make -- and will try no more (at least til next year (:-)
-- if the oceans are systems of complicated damped driven nearly
harmonic oscillators, any of the many frequencies of the several
forces can be paramount. Not just the Moon.

I hope you don't keep making this point in public. It is true that
the upper layers of the earth can be modeled in terms of a complicated
coupled set of damped, driven oscillators with a wide range of damping
rates, resonant frequencies, and Q's. It is not true that this
coupled system is driven by a broad-band spectrum of driving
frequencies. The average driving frequencies for the sun, moon, and
Jupiter's tidal effects are:
f_sun = 2.000 cycles/day
f_moon = 1.932 cycles/day
f_jup = 2.005 cycles/day

Notice that these frequencies are narrowly centered on the semi-diurnal
rate due to the earth's rotation. There does happen to be a very slow
FM modulation to these driving terms due to the elliptical nature of
the orbits of the earth and moon and the relative motions of Jupiter
w.r.t. the earth. For instance, even though on the average the Sun
undergoes meridian transit (crosses high noon in the sky) every 24 hr.,
over the course of a year it sometimes runs a few minutes fast and
sometimes a few minutes slow due to the earth speeding up and slowing
down in its elliptical path around the sun. On top of the FM
modulation is also a corresponding slow and weak AM modulation of these
driving terms due to the small differences which occur in the distances
to these celestial bodies (again due primarily to elliptical orbits).
These modulation rates are so slight that the entire band of driving
frequencies is still sharply centered around 2. cycles/day when all the
sidebands are included. You appealed to the effect of a sharp
resonance to make the weak driving amplitude of Jupiter result in a
significant response. I am *highly* suspicious of this to the point of
incredulity. As mentioned above, the average driving amplitude for
Jupiter is about 150000 times weaker than that of the Sun (which is
*itself* some 2 1/2 times weaker than the Moon). Suppose that some bay
or estuary had a main resonant frequency EXACTLY at the average driving
rate for Jupiter of 2.005 cycles/day and the bay's response to Jupiter
was comparable in amplitude to its response to the Sun's driving term
(which itself is only 40% of the amplitude of the Moon's). This means
that the Q of the bay must be about 78000 for this kind of frequency
discrimination. I think that this is probably quite unrealistic. (Here
we have neglected any other complicating random effects such as wind,
non-tidally induced currents, etc.) I wish my windup alarm clock could
keep anywhere near as good of time as this bay would be capable of
doing as a resonant free oscillator.

Now it seems that dissipative losses in the sloshing of water in a bay
are probably relatively low. But it is still hard for me to believe
that such a mode would have a Q on the order of 78000 when we realize
that the bay is probably relatively shallow and friction on the bottom
along the shoreline would seem to be significant enough to greatly
lower the Q well below such a large figure.

David Bowman
David_Bowman@georgetowncollege.edu