Tides
EPS 131: Intro. to Physical Oceanography
Douglas McClure
10/17/05
Outline
• Physical origin of tidal forces
• Global effects of tidal forces on Earth
– Over one day
– Over one lunar month
• Tides in Reality
• Outlook for the (distant) future
Origin of Tidal Forces
• Gravitational force between two masses falls off as
1/(distance)2: F  GmR m ; G  6.67 10
• Thus the Moon pulls more strongly on the Earth at
A than at B; indeed, the force difference is about
7%.
1 2
2
G
B
11
A
• The sun will have a similar but smaller effect; we will
come back to this.
Tidal Forces
• Compared to its force on the center of the
Earth, the Moon’s force along on the surface
looks as follows:
• Since rock is rigid
and water is not,
these forces will
cause oceans to rise
and fall relative to
(moon off to one side)
the crust.
(The crust rises and falls too, but only slightly.)
Effects of Tidal Forces: One Day
• The Earth completes a full rotation; the
moon completes only 1/29 of its orbit.
• Hence the two bulges remain almost still on
the timescale of the Earth’s rotation.
Effects of Tidal Forces: One Day
• In other words, a given point on the Earth’s surface will
experience both bulges and both troughs over one day.
• Small correction: after 1 day, the Moon (and thus the
bulges) will have advanced by 360o/29 ≈ 12o ≈ 48 min
• Thus high tides occur every 12 hrs 24 mins instead of
every 12 hrs.
Variation Over a Lunar Month
• The Sun contributes a tidal force slightly less than ½
of the Moon’s.
• At new Moon and full Moon,
the Sun’s contribution aligns
with the Moon’s, and so tides
are stronger (“spring tides”).
• At half Moons, the Sun’s
contribution partially cancels
the Moon’s, and so tides are
weaker (“neap tides”).
(Sun is to the right)
Variation due to Elliptical Orbits
• Since the Moon’s orbit is elliptical, it is
sometimes closer and sometimes farther;
particularly strong tides occur every several
months when the Moon reaches its closest
point (“perigee”) during a spring tide phase.
• Analogously, the Sun’s effect will be
strongest when the Earth is at perihelion.
Tides in Reality
• Tides are affected by regional topography.
• Resonance effects and the Bay of Fundy
Tides in Reality
• In most parts of the ocean, the effects are
much more complicated.
• Both timing and amplitude may vary; in
general, tides lag behind the Earth-Moon
axis.
• Tidal energy as a source of mixing.
Long-term Effects of Tidal Forces
• Because of the Earth’s fast rotation, the two “bulges”
actually lag behind the Earth-Moon axis.
• The resulting mutual tangential acceleration causes the
Earth to slow down and the Moon to speed up.
• The Earth will continue slowing until it becomes
tidally locked with the Moon.
• After then, the only source of tides will be the
Sun…if it is still around.
References
• Knauss, Chapter 10
• http://en.wikipedia.org/wiki/Tides
• http://www.jal.cc.il.us/~mikolajsawicki/tides_ne
w2.pdf
• http://oceanlink.island.net/oinfo/tides/tides.html
• http://homepage.eircom.net/~cronews/geog/tid
es/tide.html
• http://oceanworld.tamu.edu/resources/ocng_text
book/chapter17/chapter17_04.htm