A. Learn the terminology used to describe the regular rise and fall of the tides.

B. To understand the tides we would expect to find on a non-rotating planet that is uniformly covered with water (equilibrium theory).

C. To understand the tides that actually occur and are made more complex by the presence of continents, ocean basins, and the earth's rotation (dynamic tidal analysis).

Diurnal - one high and one low tide per day
Semi-diurnal - two high and two low tides per day
Semi-diurnal mixed - highs and lows are not equal

Low Water - lowest point of diurnal or semi-diurnal tide
High Water - highest point of diurnal or semi-diurnal tide
Lower Low Water - lower low of semi-diurnal mixed tide
Higher Low Water - higher low of semi-diurnal mixed tide
Lower High Water - lower high low of semi-diurnal mixed tide
Higher High Water - higher high low of semi-diurnal mixed tide

Tidal Datum - Long term (about 20 years) average of Low Water
(diurnal or semi-diurnal) or Lower Low Water (semi-diurnal
mixed)

Flood Tide - sea level rising
Ebb Tide - sea level falling
Slack Water - time of low currents when tide changes from flood to ebb

3. Equilibrium Theory - theoretical description of idealized tides.
Assumes earth is covered with a uniform layer of water.

Newtons Universal Law of Gravity F = G (m₁m₂)/R²
F = gravitational force
G = universal gravitational constant
m₁ = mass of body 1
m₂ = mass of body 2
R = distance between body 1 and 2
Increase in R results in decrease in F.

Forcing for Moon Tides:

At the center of the earth, Gravitational Force towards the moon is exactly balanced by the oppositely directed centrifugal force.

On the side of the earth closer to the moon, R is decreased, so the gravitational force exceeds the centrifugal. Water in this region is pulled toward the moon.

On the side of the earth away from the moon, R is increased, so the centrifugal force exceeds the gravitational force. Water in this region is forced out away from the moon.

Result is a tidal bulge on opposite sides of the Earth.

As the earth rotates underneath the tidal bulges, an observer on the earth will experience 2 high tides and 2 low tides.

But it takes about 30 days for the moon to orbit the earth, so in the 1 day it takes the earth to complete a revolution, the moon must also move 1/30 of the distance around the earth, or 12 degrees.

It takes the earth an another 50 minutes to rotate the additional 12 degrees, so a Tidal Day actually is 24 hours 50 minutes long.

Sun Tide:

Forcing is similar to moon tide, but even though the Sun is much bigger than the Moon, it is much farther away (very large R).
Amplitude of the Sun tide is less than half the amplitude of the moon tide.

Superposition of Moon and Sun Tides:

Tides behave like a shallow water wave, which are linear, so the two tides can be added.

Spring Tide -
If the Moon and Sun are lined up, the Moon tide crests line up with the sun tide crests, so the resultant tidal range is increased

Neap Tide -
If the Moon and Sun are at right angles, the Moon tide crests line up with the sun tide troughs, so the resultant tidal range is reduced.

Declination Angles:

Declination is the angle between the earth's equator and the moon or sun above or below the equatorial plane.

Moon's declination +/- 28.5 degrees, Sun's declination +/- 23.5 degrees.

When the moon's declination is large, mid-latitude tides appear more diurnal, while tides at the equator still appear semi-diurnal.

It requires 18.6 years for the Moon and Sun declination cycles to repeat.

4. Dynamic Tidal Analysis - Mathematical description of observed tides
Equilibrium theory does not include Continents or Friction

Effect of Friction:

Tides are a shallow water wave (D < L/20).
L=1/2 of the circumference of the earth (20,000 km). D is about 4000 m.

Near the poles, the earth is spinning slower than the shallow water wave velocity, the tide can propagate as a free wave, and the high tide is lined up directly with the moon.

Near the equator, the earth is spinning faster than the shallow water wave velocity, the tide propagates as a forced wave, but friction drags the high tides to the east of the moon.

Definitions:

Cotidal line - line showing location of tide crest at set time intervals
Corange line - line of equal tidal ranges
Progressive Tide - travels like a surface wave in one direction.
Water particles travel back and forth in flattened
elliptical orbits, but Coriolis force turns them to
right. Result is a clockwise rotation in the
horizontal plane.
Example - South Atlantic
Standing Wave Tide - due to reflection off continents.
High water rotates counterclockwise around the
AMPHIDROMIC POINT.
Water particles, however, are still turned to
the right by Coriolis Force, so the tidal
currents again rotate clockwise.

Every basin has a natural period based on its shape. If the tide forces the basin near its natural period, tidal ranges are increased.
Bat of Fundy - 10 m tidal range.

Tidal Bore - When the tidal wave must move faster than the shallow water wave speed, it can break, forming a spilling wave front.
Tsientang River - 8 m tidal bore.

a) Draw and compare a series of tidal records for the New Jersey coast for spring tides, neap tides, low declination tides and high declination tides.

b) Would the equilibrium theory tide offshore New Jersey travel as a forced or a free wave? Does the real tide travel as a progressive wave or is it a rotary standing wave?