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TIDES
• Equilibrium Theory of Tides
– Earth-Moon Orbital System
– Added Affect of the Sun-Earth Orbital System
• Dynamic Theory of Tide (add continents)
– Amphidromic Points
– Daily Tidal Variation
Equilibrium Theory of Tides
Earth-Moon Orbital System:
• It is easiest to begin understanding the forces that
create tides by imagining an Earth entirely
covered with only water.
• The Earths gravitational force hold all objects to
the planet, including water. This is the restoring
force of most waves, including tides.
• Two primary disturbing forces cause ocean water
to slightly bulge outward on opposite sides of the
planet, creating two wave crests.
– Lunar Gravitational Attraction
– Inertia of the Earth Moon Orbital System
Just like any spinning or rotating object, there is an outward inertial
(centrifugal) force.
The position of the bulges is relative to the
moon's position. Three factors influence
the Moon's position relative to your
location on Earth:
• 1) Earths rotates: (time of day)
• 2) Moon's orbit: (moves 50 minutes later each day)
• 3) Moon's angle to equator (Lunar Declination)
(varies monthly N-S and annually in magnitude)
1) Earth’s Rotation: Think of the Earth as rotating "underneath" the
ocean water bulges, determining when the tide is high (at a ocean bulge
= wave crest) or low (between bulges = wave trough) for any given
position on Earth during a day.
2) Lunar Orbit: It takes about 29.5 days for the moon to
orbit the Earth. This results in the moon’s orbit progressing
12.2º arc further east of Earths daily rotation. This
discrepancy result in the moon rising in the night sky 50 min
later each day; thereby, the high tides shift 50 minutes later
each day. We say that the "tidal day" is 24h and 50 min.
Lunar Declination:
The moon changes
each month from
being above the
equator to below the
equator. The
maximum angle
above or below the
equator is 28.5º
degrees and this
happens every 18.5
years.
Added Affect of the Sun-Earth
Orbital System
Similar inertial/gravitational forces exist between the sun and the Earth
but because the sun is so far away, the effects are only about 50% of
the lunar effects. We call this the Solar Tide.
The net result of the solar tide is to modulate the amplitude of the
dominant lunar tide. Think of the Lunar tide as one wave and the
Solar Tide as a second wave. When they positively interfere the
amplitude of the wave crest (high tide) is increased. This happens to
the greatest extent when the three celestial bodies are in alignment.
In other words, the position of Sun and Moon to Earth dictate the
amplitude and timing of the tides. Again, when all three bodies are
aligned, the tidal variations are largest and are called SPRING tides.
When the three bodies form a 90 degree angle, tides are minimal and
called NEAP tides (think negative interference).
Tidal Records in graphic format. Tidal variation is reported as a change
in sea level relative to the tidal datum, which is defined as zero. Note
mean high water (MHW) and mean low water (MLW), and lunar cycle.
Flood currents exist on the rise, and ebb currents on the fall. There are
periods of little tidal current at the high and low slack tides.
Dynamic Theory of Tides
• Influence of Ocean Depth: Given the immense
wavelength of the tide and depth of the ocean, tides
act as shallow-water waves. Recall this means their
velocity depends on water depth.
• Influence of Continents: The tidal bulges (crests)
get diverted, slowed, reflected and otherwise
complicated by landmasses. The result is that ocean
basin shape can have a great influence on the realworld behavior of tidal crests.
Amphidromic Circulation
The Moon’s Gravity/Inertia over the ocean establishes the crest, but
this no longer has an influence when the Moon’s Gravity/Inertia
is over land. The restoring force of Earth's gravity acts on the
crest due to the "pressure gradient".
However, rather than simply sloshing across the basin, like a seiche
(think of the wave tank lab), the massive volume of water
involved gets deflect by the Coriolis effect as it moves.
The result is a tidal crest rotating around the basin due to Coriolis
effect. So we see tidal crests rotating or circulating within ocean
basins, in what is called amphidromic circulation.
Consider a simple box-shaped ocean basin in the Nhemisphere. Coriolis deflects to the right. Net
circulation of the crest is counter clockwise around the
wave node, or amphidromic point (AP), the point
where there is no tidal variation.
There are multiple major amphidromic points (nodes) in the global
ocean. The height of the tide wave, i.e. tidal range, is greatest the
farther away from the node. The time for a wave crest to travel around
a node is 12 h 25 min; or half the tidal (lunar) day.
Amphidromic circulation can occur on a more localized scale within
small broad basins along coastlines, e.g. Gulf of St Lawrence. This
can explain localized variation in tides along some coasts.
Vary narrow basins will not establish APs. However, such
basins may experience extreme tidal range due to a seiche
effect. The tidal wave can resonate when tidal wavelength
is half that of basin length, e.g. Bay of Fundy.
Another anomalous tidal event is the tidal bore, created by tidal crests
propagating up a narrowing river mouth. As the wave progresses into
narrower and shallower water a breaking wave is created and moves
upriver (in fact its surfable), e.g Severn R., SW England.
Daily Tidal Variations: Coastlines influenced by a single tidal
node have two high tides per day (semidiurnal tides). Other coastlines
influenced by more than one node may experience only a single high
tide per day (diurnal tides), and even other mixed combinations are
possible (mixed tides), all due to the degree and type of interference of
wave crests and distance from different amphidromic points.
NOTE: The tidal datum is established as the mean low water (MLW) for
diurnal and semidiurnal tides or as the average (mean) lower low water
(MLLW) in the case of mixed tides.
Note the pattern of APs (Fig 9.16) and the tide type globally. Most
diurnal and mixed tides on Pacific coasts, coincident with multiple
APs in the Pacific Ocean basin. Lunar declination can also be a factor.
Tidal Range and the Coastal Setting:
The tidal range for highest high and lowest low tides along any
given coastline is influenced monthly by the alignment of
Sun, Earth and Moon.
Differences in tidal range between different coastlines is
greatly influenced by the distance from amphidromic points
and localized effects.
We can classify coastlines in three ways relative to tidal range:
•
1) Macrotidal Coasts: > 4 m
•
2) Mesotidal Coasts: 2 to 4 m
•
3) Microtidal Coasts: < 2 m