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1
et cetera, et cetera, et cetera
Fig. 8-2b
2
And the Tides are ...Slow, up and down movements of sea level
Once or Twice a day
And the Tides are not …ocean waves, “tsunamis” or rip tides
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Topics for Today• Tides are caused by the pull of the sun
and the moon• Two highs and two lows a “day” in most
places• Open ocean: tides are simple and single
waves that stretch across the entire ocean• Near coastline: tides are greatly altered by
bottom topography• Predictions are computed for particular
sites along coast
4
Tidal Characteristics• Tidal Range - vertical distance between high
and low tides (crest-trough)
• Wave period - time between high tides
• Tides are waves of very long period and a tremendous amount of energy
• Measured – onshore using tidal pen recorders – offshore pressure sensors
• Are tides deep water waves or shallow water waves?
5
Tidal Periods• Diurnal - about once a day
– 24 hours and 50 minutes
• Semidiurnal - about twice a day– 12 hours and 25 minutes (equal magnitude)
• Mixed - twice a day, but with unequal highs and lows
• Spring and neap tides following Moon’s phases
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Tide Records
_____
Twice a day with variations
__________Twice a day
_______Once a day
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Why do the Tides Occur ?
• Balance of forces as the moon orbits the earth and they Both go around the sun.
• What Forces ?– Gravity, Pulls Objects Together
– Centrifugal force Separates Objects
8
Earth-Moon and Earth-Sun Systems
SunEarth
Moon
Gravitational Attraction and Centrifugal Force from sun and moon
cause the Tides
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Tide Generating Forces
• Tides produced by gravitational and centrifugal force of both Earth-Moon and Earth-Sun systems.
• Despite the fact that the sun is 107 x more massive than the moon
• The moon still dominates Tides
Why? Moon is much closer to Earth
(384,835 km vs. 149,758,000 km)
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So, Consider First Just the Earth-Moon System
As Moon orbits the Earth they both rotate around the centre of mass of
the earth-moon system, the ‘balance point’
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Earth Moon
The Earth - Moon System
Barycenter
The Barycenter is located near the earth, but not at the center.
CentrifugalForce
Gravitational Attraction
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Equilibrium Model of Tides
• Earth is 100% covered by ocean of infinite depth– No bottom and no land masses
• Tides are assumed to be progressive waves
• Always in equilibrium with – Gravitational attraction of Moon
– Centrifugal force
• Neglect Effect of the sun (for now !)
Assumptions:
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Equilibrium Model
• Moon’s gravity pulls on the earth, the ocean and you.
• Ocean water flows towards the Moon, accumulating and bulging up under it
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Equilibrium Model
• Earth-Moon also rotate about a common centre of gravity causing centrifugal forces
• Resulting in bulge away from Moon
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Thus, we have Two Bulges
As Earth rotates on its axis,the point you stand on
passes beneath two bulges each 24 Hrcreating two tidal bulges each day.
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But Wait, There’s More
Ever notice that high tide is about 50 minutes ahead each day?
Why is that?
Because the lunar “day” is longer than the solar day by about 50 minutes
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The Lunar Day: 24h 50 min
• Moon moves 1/30 way around earth each hour
• 24 h / 30 = 0.8 h or about 50 min
• Lunar half-day is 12 hours 25 min
• This produces the first High Tide
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… and one more thing -
• Earth’s axis is tilted 28.5° to the plane of moon’s orbit (declination).
• Thus, the bulges that cause the tides are also at 28.5°.
• Leads to latitudinal variation of tides:– diurnal– mixed– semi-diurnal
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Types of Tides
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Equilibrium Model Summary and Questions
• Earth and Moon• Ocean: all over and infinitely deep• Bulges in balance with:
– Gravity & centrifugal forces and tilt of axis
• Explains:– diurnal– semidiurnal– mixed
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Here Comes the Problem• Similar Effects: two more factors• In 24 hours• Net tidal force of Sun is half that of the
Moon, thus:– Lower tidal amplitude for solar component
• Amplitudes for Moon and Sun are:– different– Not always in sync
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Why are the Solar Tidal Forces Less ?
Gravitational pull prop. to: (m1m2) / r3 (Dist. Between bodies more important for Tides)
Sun is 107 times more massivebut 390 times further away
Thus, Sun’s Tidal Force is:27,000,000 / (390)3 = 0.46
or about half that of the Moon
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To Sun
To Sun
Combined Effects of Sun and Moon are additive
Spring Tide
Neap Tide
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So, Moon & Sun effects are additive BUT
• Sun’s effects will pass in and out of phase with Moon’s effect
• New and Full Moons: forces additive , spring tides
• First and Last Quarter Moons: forces are subtractive: neap tides
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Spring-Neap Tide Cycle
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Spring-Neap Tidal Range
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When would you get the Smallest and Highest Tides ?
Depends on Earth and Moon Orbits
Orbits are ellipses, not circles (29 days for moon, 365 days for sun)
Answer:A spring tide with moon at Perigee and sun at Perihelion
Two ‘king tides’ per year - one during summer and one during winter.
Spring Tides occur whenBodies are close together
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Summary
• Spring and Neap Tides
• Tilt of Earth’s axis – Declination (celestial latitude)
• Inequality in bulges at any given spot– Diurnal tides at high latitudes– Mixed at mid-latitudes– Semidiurnal at low latitudes– Unequal tidal heights within a given day
• What if the Moon didn’t exist?
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Dynamic Model of Tides
• Water confined to bodies of finite depth
• Tidal bulge is squashed against basin’s western edge, flows downslope (pressure gradient) and to the right (Coriolis) in Northern Hemisphere
• Rotary waves move anticlockwise in Northern Hemisphere
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Dynamic Model of the TidesWater confined to finite basins
High and Low Tideson opposite sides of basin
Rotate Counter- clockwise in N.H. (due to Coriolis)
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Rotary Tidal Motions inAmphidromic (rotation about a node) Systems
Cotidal lines(high tide same time)
vs.Corange lines(equal tidal range)
Rotary Wave – has attributes of both progressive and standing wave
Time = x
Time = x + 2Hr
Amphidromic Point
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Dynamic Model
• Broad basins: – Rotary wave about amphidromic point– clock-like spokes of co-tidal lines – progressive and standing
• Narrow basins:– tidal bore,
33
Tides in Basins
• Gulf of St. Lawrence
versus
• Bay of Fundy
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Global Amphidromic Systems
Bending of the cotidal line reflects wave refraction (2 = tide 2 hours later, 6 = tide 6 hours later etc.,)
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Tides Near Amphidromic Point
• Tides are zero at the ‘node (amphidromic point) and increase to a maximum at antinodes (located at the edge of the basin)
36
Tides Across the Globe
37
Tidal Resonance
• Like sloshing in your bathtub
• If the natural resonance of the embayment and the tide are in phase -greatly amplified tidal range
• Most often used example is the Bay of Fundy or Severn Estuary
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Severn Estuary :
39
Tidal Bore - Wall of water surging up-river
Hardly noticeable 20 cm H,to 5-m in Amazon River, (20 km/h)to 7-8 m in Fu-Ch’un River, (25 km/h)
Large tidal range+ tapering basin+ decreasing depth produces the wave
40
Tidal Currents
• Sea’s rise and fall means water must move from place to place
• Flood currents move water landward
• Ebb currents move water seaward
• Strong near the coast, bays and inlets
• Rotary pattern in open ocean due to Coriolis force
41
Tidal Currents in the Chesapeake Bay
42
Prediction of Tides• Tabled for recording stations
• Predicted for other localities
• Newspapers
• Television and radio
• Marinas, bait shops
• Tables and calendars
• Web sites and programs– Government and commercial
43
Tidal Predictions -• Measurement of tidal
component curves, a harmonic analysis– typically using 37+
cosine terms
• Lunar and solar components :complex astronomical tide predictions
44
Tide Predictions and Real-Time Datahttp://www.opsd.nos.noaa.gov/
45
Atmospheric Conditions• Astronomical tide predictions versus Atmospheric Conditions
– Wind set-up (ordinary wind shear)– Storm surge (extra-ordinary)
• Wind shear• Low Atmospheric pressure• Ekman Transport (coriolis)
1999 Storm Surge
46
Tidal Rhythms and the Ecology of the Tides
• Rocky intertidal communities and zones
• Sandflats, mudflats and salt marshes
• Feeding and activity rhythms of fiddler crabs are attuned to the tides...
• Grunion spawning as well
• Horseshoe crab spawning and egg-laying
47
Energy from Tides
• Differences in tidal height drive generator turbines
• Although some 150 sites world-wide are suitable...
• Relatively few have been constructed
• http://www.darvill.clara.net/altenerg/tidal.htm
• http://www.energy.org.uk/EFTidal.htm
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Locations With Large Tidal Range
Is Tidal Power feasible and economicAt all these Locations?
49
French Tidal Power Station
La Rance River Tidal Power Plantat St. Malo
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La Rance River Tidal Power Plant
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Why so Few ?Consider the Problems:• Only a few suitable locations
– High tidal range required– Most of these not near major Pop Centers
• Cost Efficiency of Power Production• Environmental Impact
– Tidal time and range alteration
• Interferes with current dynamics of waterway– Navigation, commercial and recreational