Re: Bulges

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

John Mallinckrodt wrote:

> On Thu, 6 Mar 1997, David Bowman wrote:
>
> >                    Therefore it is no wonder that Jim doesn't see any
> > evidence of a tidal bulge in the oceanic tidal data that he has amassed.
> > The contribution of the (highly underdamped) oceans to the tidal bulge is too
> > small to show up in the time series for the ocean level at a typical
> > coastline which is dominated by other undamped resonant/sloshing and
> > continental reflection effects as well as extraneous wind effects, seasonal
> > ocean current effects, etc.  I suspect that if the time series for the ocean
> > height in the middle of an ocean was Fourier analyzed and its power spectrum
> > taken, that there would be a significant spike located at the lunar driving
> > frequency which would correspond to the presence of at least some of the
> > tidal bulge being present in the oceans.
>
> I don't understand this.  The time series for the ocean height at
> virtually *any* location--in the middle of the ocean, near a coast line,
> or even within highly protected bays--is, I believe, *overwhelmingly*
> dominated by spikes at the lunar and solar driving frequencies, isn't it?
> If anyone expects to find evidence against the tidal bulge theory in a
> lack of these components, I think they will be sorely disappointed.
>
> (Lest anyone misconstrue my remarks here, this is decidedly not to say
> that the *presence* of these components argues *for* the oversimplified
> tidal bulge model.)

When I said that Jim didn't see the lunar tidal bulge signal in the time
series  data that he had amassed for various continental shorelines I meant
that he doesn't see the bulge signal in the times series *itself* in the time
domain.  The reason that I suggested using ocean height data from a mid-ocean
location was that then the bulge signal would not be such a tiny part of the
overall motion and that the bulge signal would show up more clearly. I did
not mean to imply that no lunar frequency spike would be found elsewhere,
(although I'm not sure if its size would always be "*overwhelmingly*"
dominating).  One problem with the use of a coastline signal besides the
possibility of a weak signal is that of a strong phase shift.  A power
spectrum looses phase information.  Even if a decent-sized lunar (or solar)
frequency spike is found in the power spectrum of a shoreline ocean height
time series, it doesn't mean that the spike is directly due to the tidal
bulge itself.  It may be due to some multi-path phase-shifted reflected echo
signal (sort of like a TV ghost) which may be an indirect result of lunar or
solar driving force, but is not itself an indication of the presence of the
actual bulge itself.  Such complications would presumably be ameliorated by
using mid-ocean data.  I suppose it is possible to detect the presence of
such a phase-shifted signal relative to the actual bulge by not just looking
at the power spectrum, but by digitally filtering the time series with a
filter with a *very* narrow passband centered on the lunar (and/or solar)
driving frequencies.  Any signal which gets through the filter could have its
phase directly checked in the time domain against the proported location of
where the tidal bulges are supposed to be at those times, and then the
presence of the actual tidal bulge could possibly be seen.  I suspect that
doing this with shoreline data would show significant phase shifts caused by
reflections, refractions, and diffractions off of the local coastal
inhomogeneities.  Another problem with coastline data is that the ocean depth
there is so shallow along a continental shelf that there is not much of a
thickness of water available in situ to form into a bulge with the weak tidal
stress astronomically available.  Rather than the moon lifting a bulge from
pre-existent water, the water would have to be carried into and out of the
coastal region as some kind of one-sided (ocean-sided) time-delayed sloshing
action rather than as a moving high water bulge across the surface made from
in situ drawn up water.

IOW, I don't doubt that a lunar and a solar frequency signal can be detected
in the data "at virtually *any* location", but such a detection does not
necessarily indicate a bulge at the location of where it should be at the
right time.  Jim's incredulity about tidal bulges was not merely based on
asynchronicity with the astronomical driving frequencies, but on how the
various locally phase shifted (but synchronous with the astronomical driving 
frequencies) tides interact among themselves in ways that do not form bulges
when they are put all together.  My position is that underneath all the phase-
shifted, reflections, noise, resonances, diurnal subharmonics, and other
assorted (synchronous and asynchronous in frequency) crud, I expect that there
is still probably an actual bulge hidden under all the noisy background.
Jim's position is that any such bulge "is a myth".  In any event, the question
should be answerable by an appropriate signal processing of the ocean height
data extracted from the cleanest (bulge signalwise) regions.

David Bowman
dbowman@gtc.georgetown.ky.us