About tides
Ilana Stern
upon the earth. It is hard to give a nontechnical explanation,
especially without diagrams or mathematical notation, so if you
are still confused after this article, I suggest an elementary
meteorology or physical oceanography textbook.
The tide-producing force, defined as that part of the attractive
force (gravity) of heavenly bodies (e.g. the moon) which doesn't
affect the earth as a whole, was defined and calculated by Laplace
in the late 18th century. The effect is symmetrical about the
line joining the earth to the attractor (moon or sun) which tends
to pull the ocean into an ellipsoidal shape -- but the response of
the ocean is limited by the speed at which the water can respond
and the complicated shape of ocean basins, so tides get more
complicated than this simple model. But as an ellipse has two
humps (sort of), you can see that the maximum (by simple model) tide
occurs both directly under the moon and also on the other side
of the earth, which is why there are two maxima each day.
The tide can be expressed as a series of spherical harmonics
(see, told you it gets technical quickly! Math gets confusing
when applied to the surface of a sphere) which have coefficients
relating to the basic frequencies of the solar system: the day,
the lunar month, and the year. The principal tidal component,
the lunar semidiurnal, has a period of 12.4 hours -- roughly twice
a day. There are 8 components which contribute at least 10% to the
tidal maximum; 4 are roughly semidiurnal (near 12 hours), 3 are
roughly diurnal (near 24 hours), and 1 is about 328 hours (13.6 days?
Maybe it's a semi-lunar-month? I don't know).
There are also way-long period effects at 8.85 years, 18.61 years,
and 21,000 years!
In bays and other coastline features, things get more complicated
because of boundary effects. One must solve (well, you don't have
to, but the people who produce tide tables do!) the forced shallow-water
equations with a complex boundary condition. This becomes a forced
oscillator problem, like the physics lab where you shake a spring
at different frequencies and try to get it completely damped or
wildly oscillating; if the natural mode of oscillation of a basin
(e.g. a bay), which is determined by its shape and size, is close to
a tidal frequency, the tides can be exaggerated (as happens for example
in the Bay of Fundy).
I hope this helps, or at least gives an idea of the scope of the
problem. If the group sci.geo.oceanography gets created (currently
under CFV), you might consider hanging out there for more details.
--
Boulder is so full of itself that if it drank a beer, it'd have to call itself
/\ on the cell-phone in the Beemer and arrange a power lunch with the broker
\_][ to consider the long-term effect on the portfolio, investment-wise,
\__________before belching.--Dick Dunn | il...@ncar.ucar.edu, Boulder CO