Tides

1
Tides

• EPS 131 Intro. to Physical Oceanography
• Douglas McClure
• 10/17/05

2
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

3
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.

4
Tidal Forces

• Compared to its force on the center of the Earth,
  the Moons 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.)
5
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 Earths rotation.

6
Effects of Tidal Forces One Day

• In other words, a given point on the Earths
  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.

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Variation Over a Lunar Month

• The Sun contributes a tidal force slightly less
  than ½ of the Moons.

• At new Moon and full Moon, the Suns contribution
  aligns with the Moons, and so tides are stronger
  (spring tides).
• At half Moons, the Suns contribution partially
  cancels the Moons, and so tides are weaker
  (neap tides).

(Sun is to the right)
8
Variation due to Elliptical Orbits

• Since the Moons 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 Suns effect will be strongest
  when the Earth is at perihelion.

9
Tides in Reality

• Tides are affected by regional topography.
• Resonance effects and the Bay of Fundy

10
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.

11
Long-term Effects of Tidal Forces

• Because of the Earths 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
  Sunif it is still around.

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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/tid
  e.html
• http//oceanworld.tamu.edu/resources/ocng_textbook
  /chapter17/chapter17_04.htm