1. The Tides ... and the tide rises, et cetera, et cetera, et cetera
Fig. 8-2b
... and the tide rises,
and the tide falls ...
et cetera, et cetera, et cetera

2. And the Tides are ... And the Tides are not …
Slow, up and down movements of sea level
Once or Twice a day
And the Tides are not …
ocean waves, “tsunamis” or rip tides

3. 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
Doug Miller
4/22/2017 1:10 PM
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

6. Tide Records __________ _____ _______ Twice a day
Doug Miller
4/22/2017 1:10 PM
Tide Records
__________
Twice a day
_____
Twice a day with variations
_______
Once a day

7. Doug Miller
4/22/2017 1:10 PM
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
Gravitational Attraction and Centrifugal Force from sun and moon cause the Tides

9. 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)

10. 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’

11. The Barycenter is located near the earth, but not at the center.
The Earth - Moon System
Barycenter
Earth
Moon
Centrifugal
Force
Gravitational
Attraction
The Barycenter is located near the earth, but not at the center.

12. Equilibrium Model of Tides
Doug Miller
4/22/2017 1:10 PM
Equilibrium Model of Tides
Assumptions:
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 !)

13. Doug Miller
Equilibrium Model
4/22/2017 1:10 PM
Moon’s gravity pulls on the earth, the ocean and you.
Ocean water flows towards the Moon, accumulating and bulging up under it

14. Doug Miller
Equilibrium Model
4/22/2017 1:10 PM
Earth-Moon also rotate about a common centre of gravity causing centrifugal forces
Resulting in bulge away from Moon

15. Thus, we have Two Bulges As Earth rotates on its axis,
the point you stand on
passes beneath two bulges each 24 Hr
creating two tidal bulges each day.

16. Ever notice that high tide is about 50 minutes ahead each day?
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

17. 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

18. … 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

19. Types of Tides

20. 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

21. 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

22. or about half that of the Moon
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 massive
but 390 times further away
Thus, Sun’s Tidal Force is:
27,000,000 / (390)3 = 0.46
or about half that of the Moon

23. Combined Effects of Sun and Moon are additive
To Sun
Combined Effects of Sun and Moon are additive
Spring Tide
To Sun
Neap Tide

24. 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

25. Spring-Neap Tide Cycle

26. Spring-Neap Tidal Range

27. Two ‘king tides’ per year - one during summer and one during winter.
When would you get the Smallest and Highest Tides ?
Orbits are ellipses, not circles (29 days for moon, 365 days for sun)
Depends on Earth and Moon Orbits
Spring Tides occur when
Bodies are close together
Answer:
A spring tide with moon at Perigee and sun at Perihelion
Two ‘king tides’ per year - one during summer and one during winter.

28. 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?

29. 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

30. Dynamic Model of the Tides
Water confined to finite basins
High and Low Tides
on opposite sides of
basin
Rotate Counter- clockwise in N.H.
(due to Coriolis)

31. Rotary Tidal Motions in Amphidromic (rotation about a node) Systems
Cotidal lines
(high tide same time)
vs.
Corange lines
(equal tidal range)
Time = x
Time = x + 2Hr
Amphidromic Point
Rotary Wave – has attributes of both progressive and standing wave

32. 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

34. Global Amphidromic Systems
Bending of the cotidal line reflects wave refraction (2 = tide 2 hours later, 6 = tide 6 hours later etc.,)

35. 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

38. Severn Estuary :

39. Tidal Bore - Wall of water surging up-river
Large tidal range
+ tapering basin
+ decreasing depth
produces the wave
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)

40. Tidal Currents Flood currents move water landward
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 Data http://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

48. Is Tidal Power feasible and economic
Locations With Large Tidal Range
Is Tidal Power feasible and economic
At all these Locations?

49. La Rance River Tidal Power Plant
French Tidal Power Station
La Rance River Tidal Power Plant
at St. Malo

50. La Rance River Tidal Power Plant

51. 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