TIDES
Objectives
1. Learn the terminology used to describe the
regular rise and fall of the tides.
2. To understand the tides we would expect to find
on a non-rotating planet that is uniformly covered
with water (equilibrium theory).
3. 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).
1. Definitions
- 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 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.
2. Equilibrium Theory
- Theoretical description of idealized tides.
- Assumes earth is covered with a uniform layer of water.
- Newton's 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 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.
3. Dynamic Tidal Analysis
- Mathematical description of observed tides.
- Equilibrium theory does not include Continents or Friction.
- Effects 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 - the 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.
4. Near Shore Effects
- Every basin has a natural period based on its shape. If the tide forces
the basin near its natural period, tidal ranges are increased.
- Bay 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.
5. Review Questions
- 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.
- 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?