and the tide rises,

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et cetera, et cetera, et cetera

Fig. 8-2b

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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

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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?

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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

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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,

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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)

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Tides Across the Globe

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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 :

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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

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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

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Tidal Currents in the Chesapeake Bay

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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

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Tidal Predictions -• Measurement of tidal

component curves, a harmonic analysis– typically using 37+

cosine terms

• Lunar and solar components :complex astronomical tide predictions

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Tide Predictions and Real-Time Datahttp://www.opsd.nos.noaa.gov/

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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

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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

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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?

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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