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Re: double tide cause



At 03:03 PM 9/1/01 -0500, Kossom wrote:

Why does much of the Gulf of Mexico experience only one high and low tide
per day, rather than the usual two?

I'm still not convinced that "much" of the Gulf has diurnal tides, rather
than the usual semi-diurnal tides. But diurnal tides are certainly possible!

The physics is interesting. It goes something like this:

The usual textbook discussion tells you what the gravitational _potential_
looks like. This is pretty simple. In the absence of tides, the potential
is more-or-less spherical. And unchanging.

Now let's add in the tides. To make things even simpler, let's consider
the case where the sun and moon are colinear with the earth, i.e. new moon
or full moon. The tides squash the potential into a prolate
ellipsoid. The potential bulges up at the point right under the moon and
also bulges up at the antipodal point. It "tightens its belt" on the ring
of points 90 degrees away.

Let us imagine, temporarily, a planet which is earth-like EXCEPT that it
spins very slowly: slowly compared to the sloshing resonance frequency of
all the oceans and bays, and also slowly compared to any viscous relaxation
times. On such a planet, the water would come to equilibrium and would map
out the potential for us.

However, the slow-spin approximation is a terrible approximation for the
real earth. The earth spins quickly compared to oceanic slosh-times. To
make things reeeeeally messy, the spin axis isn't aligned with the axis the
aforementioned prolate spheroid. That's a point that people tend to
forget. And they forget that not everybody lives on the equator.

To be specific, suppose Moe is standing on Hainan island at noon on
midsummer's day. The sun is directly overhead. The sun is in the
constellation Gemini, right near the Taurus border, near the star cluster
M35. (Moe can't confirm that directly; it's hard to see stars in the
daytime.) At the very same instant, Joe is standing at the antipodal
point, namely Antofagasta, Chile. It is midnight there, and the full moon
is directly overhead, in the constellation Sagittarius.

(Draco) Cat's
eye
Eltanin o Polaris
* *


* Menkalinan
/
pinch/
|/
(Sag) Moon bulge-Earth-bulge Sun ** M35 (Gemini)
/|
/pinch
/

Now, the scary thing about this diagram is that it is NOT oriented
north/south. The usual definition of north/south is relative to the
earth's axis, which points to Polaris (roughly). In the diagram, the point
directly up the page from the center of the earth is the North Ecliptic
Pole (NEP) which is beautifully marked for us by the Cat's Eye nebula,
NGC6543 (an unforgettable number).
http://www.seds.org/messier/xtra/ngc/n6543.html
http://www.seds.org/messier/m/m035.html

The bulge in the potential stays put while the earth rotates under
it. From the earthlings' point of view, the potential bulge rotates.

So let's see how things look 12 hours later, when it is midnight at
Hainan. The moon will not be directly overhead. Not even close! It will
be in Sagittarius, about 45 degrees south of overhead.

The earth has rotated around its !tilted! axis. Hainan will be directly
underneath the star Eltanin (Gamma Draconis). This will not be associated
with the bulge in the potential. It will sit in the more-or-less neutral
regime between the bulge and the pinch. So Hainan will get a huge diurnal
driving force: large at noon, neutral at midnight. The situation is
similar at Antofagasta or any other location at comparable latitudes, north
or south. If you find some location where the local geography allows the
water to slosh with a resonant frequency near 24 hours, you will have a
huuuuge diurnal tide.

This is an example, i.e. a proof by construction that diurnal tides can
exist. The general case is, of course, quite a bit more complicated.