Re: Bulges

[David Bowman <dbowman@tiger.gtc.georgetown.ky.us>]

John Mallinckrodt wrote:

> I understand what you are saying and I agree with you for the most part. 
> It's only your implication that one needs to do some kind of fancy signal
> analysis and even, perhaps, take a trip to Hawaii (not a bad idea, though) 
> to ferret out a supposedly weak "bulge signal" from the noise that I take
> exception to.

It's possible that we are each using the term "bulge signal" differently and
that is why you are taking exception to it.  As I tried to indicate in my
last post I do not consider any response at the astronomonical driving 
frequency the "bulge signal" but rather a specific such response, one whose
phase corresponds with where the actual bulge should be if such a thing
exists as the oceans' contribution to the overall tidal bulge of the earth
as a whole.  What I mean this "bulge signal" is is a contribution from the
oceans that on the average is a prolate distortion of the average earth's
shape which is induced primarily by the moon's tidal stress (with a
significant solar component) that is lined up mostly with the current earth-
moon line of sight but with a net average phase shift of about 6 degrees with
respect to that line of sight.  This phase shift is due to the finite response
response time of the earth to the tidal stresses coupled with the effect of
the rotation of the earth which rotates the bulge as it forms out ahead of the
moon's orbital position.  (This phase shift leads the moon's position as seen
from an external inertial coordinate system and lags the moon's position in
the sky as seen from a coordinate system fixed to the earth's rotation.)  It
this phase-shifted prolate distortion which has a net torque induced on it by
the moon's gravitational field gradient which brakes the earth's spin and
transfers its lost spin angular momentum to the orbital angular momentum of
the moon.  A local semi-diurnal ocean tide signal may either add to this
"bulge signal" or detract from it depending on the phase of its arrival.

> Quite the contrary, I think you'll find that the overwhelmingly dominant
> signature in the time signal at virtually *any* location on earth that has
> tides is that of the moon's drive frequency beating against that of the
> sun.

This is the usual case for the local response to the driving frequencies
but this response may not necessarily contribute to what I call the "bulge
signal" because of a large phase shift in its arrival time.  I also think
the emphatic term *any* above is too strong.  Certainly at the the so-called
amphidromic nodes such a response is missing altogether.  Additionally a
local response may be dominated by a nearby resonant mode of a local basin
structure.

>       In every tide table I've ever looked at this signature is
> immediately obvious.  Yes, there are phase shifts (in the Puget Sound the
> tides are almost exactly *out* of phase with those in the Pacific just the
> other side of the Olympic Penninsula) and harmonic distortions that cause
> typical waveforms to vary markedly from place to place, but the average
> time between successive high or low tides taken over any reasonable period
> is about 12h 25min (half the apparent lunar period) and the tides go
> through obvious cycles of varying heights about every 29 days, a very
> clear signature of beating with the sun's drive frequency.

I don't doubt any of this at all, but your *out* of phase example above just
shows the signal processing problem I was trying to discuss.  It doesn't
contribute to the "bulge" signal but subtracts from it.  Also as far as the
"bulge signal" is concerned the dominant solar/lunar beat modulation
frequency should be twice the rate above with a period of 14 1/2 days because
both full and new lunar phases induce a Spring tide and the 1st and 3rd
quarter phases induce a Neap tide.  A full 29 day subharmonic signal should
also be present due to the inclination of the moon's orbital plane with the
ecliptic as well as other higher order effects which produce the tidal 
stresses.

As happened last year in my discussion with Jack U. about the speed of light
c, I have nearly exhausted myself (and my free time) here trying to explain
my points.  So I plan to bow out of the bulge discussion at this point and
rest and devote my time to more productive things.  For some reason every
time Jim brings up the problem of tidal bulges the list goes into overdirve
in its flurry of tide thread responses.  I had tried to stay out of it this
time, but it didn't work, (Jim still sucked me in and John kept me there).
I think I need to show more will power in the future.  :-)

David Bowman
dbowman@gtc.georgetown.ky.us