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Lecture 29: TIDES

Powerpoint Lecture Slides

What are tides? What causes tides?
Types of tides
Tide-raising forces

Gravitational attraction
Centrifugal forces

Equilibrium Theory

Semi-diurnal tides and the lunar "tidal day"
Diurnal tides
["Spring" and "Neap" tides]
[Actual tides and their prediction]

 

 

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TIDES

Periodic rise and fall of water level along coastlines related to the phases of the Moon.
Cause -- balance of two celestrial forces:

1. Gravitational attraction between Earth and the Moon (and Sun).
2. Centrifugal forces in the rotation of the Earth around the center of mass (center of gravity) of the Earth-Moon system.

Types of tides -- periods and "inequalities" in high (H) and low (L) tidal levels.

Diurnal tides -- period of about 24 hr, with 1 H and 1 L per day
Semi-diurnal tides -- period of about 12 hr, with 2 H and 2 L per day
Semi-diurnal mixed tides -- same as semi-diurnal but with unequal high and low tides.
"Spring" & "Neap" tides -- variation in high and low tidal levels with a period of about 2 weeks.

Tidal periods and inequalities -- Equilibrium Theory of Tides.

Gravitational attraction (G) between the Moon (M) and Earth (E) holds the bodies together.
G is directed along the "line of centers."
G is slightly different for all other points on and within the Earth (due to small but significant differences in distance to the Moon's center of mass).

Centrifugal force (C) of rotation of the Earth-Moon system tends to pull the bodies apart.
E and M rotate about a common center of mass (T = 29.5 days).
C has same magnitude and direction for all parts of the Earth (the center and everywhere else).

G and C are exactly balanced (equal and opposite) at centers. But G and C are not balanced at Earth's surface.
Excess G immediately beneath the Moon produces a
bulge toward the Moon (and the Sun).
Excess C at the "antilunar" point produces a bulge away
from Moon (and the Sun).

 

Explaining types of tides from Equilibrium Theory:

Semi-diurnal tides . . occur as the Earth rotates beneath the tidal bulges.
Any location on Earth should experience 2 high tides and 2 low tides per revolution (per day).

Expected T = 12 hrs exactly -- the case for solar semi-diurnal tides.
Lunar semi-diurnal tides: T = 12 hr 25 min.
Moon revolves as Earth spins.

Any location on Earth's surface must rotate a little further each day (about 50 min. more rotation) to keep up.
"Lunar tidal day" = 24 hr 50 min.
Period of the lunar semi-diurnal tide is one-half of that, or 12 hr 25 min.

Diurnal tides and semidiurnal mixed tides . . occur because the Moon and the Sun are not directly overhead at the Equator, but at a different latitude. -- "Declination"

Sun's declination -- 23.5 deg N to 23.5 deg S, T = 1 year
Moon's declination -- 28.5 deg N to 28.5 deg S, T = l8.6 years (the "lunar cycle").
Tidal bulges are in both the N. and S. Hemispheres. Resulting tides as Earth rotates:
Diurnal immediately beneath the bulge
Semi-diurnal at the Equator
Semi-diurnal mixed elsewhere

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