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: • Thus the Moon pulls more strongly on the Earth at A than at B; indeed, the force difference is about 7%. • 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 the crust. (moon off to one side) (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_new2.pdf • http://oceanlink.island.net/oinfo/tides/tides.html • http://homepage.eircom.net/~cronews/geog/tides/tide.html • http://oceanworld.tamu.edu/resources/ocng_textbook/chapter17/chapter17_04.htm