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Lectures 30: TIDES (cont'd)

Powerpoint Lecture Slides

Review:

"Spring" and "Neap" tides Actual tides (differ from the "equilibrium" theory we have developed)

Types of tides
Diurnal: 1 High & 1 Low per day . . . T 24 hr
Semidiurnal: 2 H & 2 L per day . . . T 12 hr
Semidiurnal, mixed:. . . unequal highs and lows

Equilibrium theory of tides- Consider the forces on the water, and assume the tidal bulges respond quickly to these forces and are in equilibrium with respect to them
Here are the components of the tides story: 1. Gravitational attraction (G) between Moon (M) and Earth (E) 2. Centrifugal force (C) of rotation of E-M system pulls in opposite direction 3. Earth's equator is at an angle to the planes of the orbits 4. Gravitational atttraction of the sun

A. Why are there two tidal bulges?

Excess G on the side closest to the Moon produces a bulge toward M
Excess C on side away from M produces a bulge
This gives us Semidiurnal tides- two bulges = 2 high tides per day
Earth rotates beneath the tidal bulges.

Time between high tides is 12 hr. 50 min.- the extra 50 min. is the extra rotation of the earth needed to "catch up" (the moon has progressed in its orbit since the last high tide)

B. Earth's equator is at an angle to the planes of the orbits- i.e., the sun and the moon are not directly above the equator and this causes...
Diurnal tides and semidiurnal mixed tides
Moon and Sun are in positions north or south of the Equator Therefore: One bulge mostly in the northern hemisphere, other is mostly in the southern hem. Diurnal tides immediately beneath each bulge (other bulge isn't noticed) Semidiurnal at the Equator Semidiurnal - mixed elsewhere
C. The sun has the same effect on tides as the moon, but weaker. 1. If the sun is close to the moon in the sky (new moon), the sun's tidal effect strengthens that of the moon- highs and lows are augmented (Spring tides) 2. If the sun is opposite the moon (full moon), the sun's tidal effect strengthens that of the moon (remember, there is a bulge on the side of the earth away from the moon) 3. Halfway in between these two cases (first or last quarter), the sun's tidal effect works against the moon's- highs and lows are weakened (Neap Tides) Two-week variations in tidal ranges (Spring and neap tides)
Actual tides and their prediction
The tides that we see at various places on the earth differ somewhat from what you would predict from the above model.

Actual tides in ocean basins and coastal areas
Each ocean basin and each coastal area responds uniquely to tidal forces. Heights and periods of actual tides do not exactly follow the "equilibrium" model.
1. Tides are shallow-water waves (both "standing" and moving) Cannot keep up with tide-raising forces (i.e., position of Moon) Direction and speed are altered: - - friction with bottom - - reflection from continents and continental margins - - refracted as they move into shallow, coastal waters
2. Continental barriers interrupt the passage of tides.
3. Tides are subject to the Coriolis effect Large distance and long duration of tidal motions Crests of tide waves "rotate" around central point like a stationary (standing) wave

Tidal prediction at any location (based on the l8.6-year lunar cycle)

1. Record observed tidal variations
2. Compare E-M-S motions to observations
3. Determine the specific components of E-M-S tide-raising
forces that contribute to tidal periods and heights
4. Determine local factors influencing tides
("dynamic responses" of ocean basin and coastal area)


(detailed notes (for lectures 29 and 30))

Tides

are the periodic rise and fall of water level along coastlines. The occurence of tides are related to the phases of the Moon, which was first recognized by Pliny the Elder in the first century. Tides result from the interaction (balance) of two celestrial processes:
Gravitational attraction between Earth and the Moon (and Sun). Centrifugal forces in the rotation of the Earth around the center of mass (center of gravity) of the Earth-Moon system.

Types of tides

are defined by their periods and by the "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.

2-week tides ("Spring" & "Neap" tides -- variation in high and low tidal levels with a period of about 2 weeks.

In order to explain tidal periods and inequalities, we consider the effects of tide-raising forces on a model Earth that is entirely covered by oceans. This approach is called the Equilibrium Theory of Tides.
Gravitational attraction (G) between the Moon (M) and Earth (E) holds the bodies together as they rotate around one another (actually, around their common center of mass). Gravitational attraction is directed along the "line of centers" between the two planets, i.e. between their respective centers of mass. But the gravitational attraction of the Moon is slightly different for all other points on and within the Earth. This is due to small but significant differences in the distance from those points to the Moon's center of mass.

Centrifugal force (C) of rotation of the Earth-Moon system tends to pull the bodies apart. As noted above, the Earth and Moon rotate about a common center of mass with period of 29.5 days. This is commonly referred to as the "lunar month." Centrifugal forces have the same magnitude and direction for all parts of the Earth (the center and everywhere else).

Centrifugal and gravitational forces between the Earth and Moon are exactly balanced (equal and opposite) at their centers. But the forces 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).
With this explanation of tide-raising forces from the Equilibrium Theory, let's see why we get different types of tides. Semi-diurnal tides . . occur as the Earth rotates beneath the tidal bulges. This means that any location on Earth should experience 2 high tides and 2 low tides per revolution (per day). If this were the case, we would expect the period of semi-diurnal tides (the interval between high tides or low tides) to be exactly 12 hours, one-half of the Earth's rotational period. This is indeed the case for solar semi-diurnal tides, tides produced by the Sun's gravitational attraction. But the period of most lunar semi-diurnal tides is 12 hr 25 min, a little longer than expected. Why does this happen? The Moon is not stationary. It rotates around the Earth (actually, the common center of mass) with a period of 29.5 days. Any location on Earth's surface must rotate a little further each day (about 50 min. more rotation) to keep up with the passage of the Moon overhead. So, the "lunar tidal day" is 24 hr 50 min.; and the 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 in a position that is either north or south of the Equator. That is, the Moon and Sun are not directly overhead at the Equator, but at a different latitude. We call the position with respect to the Equator the "declination" of the Moon and/or Sun. Sun's declination -- 23.5 deg N to 23.5 deg S, with a period of 1 year Moon's declination -- 28.5 deg N to 28.5 deg S, with a period of l8.6 years (the "lunar cycle"). Because of declination, the tidal bulges are not at the Equator but rather in both the Northern and Southern Hemisphere. As the Earth rotates beneath these (hemispheric) bulges, the resulting tides are: Diurnal immediately beneath the bulge Semi-diurnal at the Equator Semi-diurnal mixed elsewhere
Two-week variations in tidal ranges -- spring and neap tides -- are caused by changes in the alignment of the Earth-Moon-Sun (EMS) system. When the three bodies are oriented along a straight line, lunar and solar tides reinforce one another to produce a maximum in tidal range -- spring tides. This alignment occurs at the time of a "Full Moon" and "New Moon." When the EMS system forms a right angle, lunar and solar tides interfere with one another to produce a minimum in tidal range -- neap tides. This alignment occurs at the time of a "First-Quarter Moon" and "Third-Quarter Moon."

Actual tides in ocean basins and coastal areas.

Observed tides are more complex than predicted by the Equilibrium Theory. Tidal periods and ranges do not exactly follow this simple model. The general explanation is that any given ocean basin and coastal area responds differently to the tide-generating foces.

Continents are barriers to the passage of tidal bulges.

Tides behave as shallow water waves -- their wavelength is about one-half Earth's diameter! Therefore, tidal "waves" cannot keep up with the passage of the Moon (and Sun) overhead. The direction and speed of tidal waves are altered by: friction with the sea floor reflection from continents and continental margins refraction as they move into shallow, coastal waters Tides are subject to the Coriolis effect because of the long distances and long durations of tidal motions. Because of Coriolis deflection, tides in some basins tend to rotate around a central node just like a standing wave.
Tidal prediction . . is an ancient art, and one that is essential for a maritime community. Sailors have tranditionally time their exit from a port for the falling tide, and their entry to a rising tide.

Tidal predictions are made for the l8.6 year lunar cycle; over that interval, the Moon completes all possible positions with respect to the Earth. Tidal predictions are done as follows: 1. Record observed tides (period, tidal range, inequalities, etc.) 2. Compare observations to E-M-S positions at the exact time. 3. Determine the specific components of E-M-S tide-raising forces that contribute to tidal periods and ranges. 4. Determine the local factors influencing tides; these are the "dynamic responses"of an ocean basin or a particular coastal area to tide-raising forces.

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