Back to the
Ask An Astronomer page.
Hello Claudine,
The tides are indeed an ellipsoidal function of your location on Earth
(with the major axis of the ellipsoid along the line joining the Earth and
the Moon), to first order. In fact, if the Earth had no land masses,
and the global ocean was much deeper than it really is (say about
25 km deep), then the tidal bulge would be an undistorted ellipsoid
pointing directly at the Moon. This is the "equilibrium model" of
ocean tides.
In reality, the ocean is shallow (typically 3 km deep), and there are
continents. The ocean floor and land masses rotate much faster than
the tidal bulge (the tidal bulge rotates once around the Earth in
about 27 days; the land masses rotate once per day). The land tries
to force the tidal bulge to keep up, so the true bulge tends to always
be slightly ahead of its equilibrium position, pointing directly at
the Moon. This is the "dynamical model" of the ocean tides. The
amount that the ocean is "out of equilibrium" is complicated, and
depends on the local structure of the ocean floor and shoreline. For
example, the land forces can dominate in areas where the ocean is
shallow and nearly surrounded by land (such as Cape Cod, Massachusetts
or the Gulf of Mexico), but the tidal bulge will be near equilibrium
in open ocean like the South Pacific.
All this sloshing about and movement of ocan against land causes some
interesting effects. Since the tidal bulge tends to always be ahead
of its equilibrium position, the Earth's rotation is exerting a torque
on the Moon. This is slowly causing the Moon to gain orbital energy,
resulting in an increasing distance between the Earth and the Moon (at
a rate of about 4 cm per year!). This increase in orbital energy has
to come from somewhere (since energy must be conserved; it cannot be
created nor destroyed), and it turns out that it comes from the
Earth's rotational energy. Therefore, the Earth's rotation is being
slowed, and the length of a day is slowly increasing (at a rate of
about 1.5 milliseconds per century!). The rotation is also slowing
because energy is lost to frictional rubbing of the oceans against the
land and seafloor. This energy exchange will continue until the
Earth's rotational period is equal to the orbital period of the Moon.
After that, the continents will not be rotating faster than the tidal
bulge, and the tides will finally be in equilibrium.
Back to the
Ask An Astronomer page.