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

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

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

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?

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

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

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

Earth-Moon and Earth-Sun Systems Gravitational Attraction and Centrifugal Force from sun and moon cause the Tides

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)

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’

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.

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 !)

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

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

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.

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

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

… 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

Types of Tides

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

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

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

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

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

Spring-Neap Tide Cycle

Spring-Neap Tidal Range

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.

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?

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

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)

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

Dynamic Model Broad basins: Rotary wave about amphidromic point clock-like spokes of co-tidal lines progressive and standing Narrow basins: tidal bore,

Tides in Basins Gulf of St. Lawrence versus Bay of Fundy

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

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)

Tides Across the Globe

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

Severn Estuary :

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)

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

Tidal Currents in the Chesapeake Bay

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

Tidal Predictions - Measurement of tidal component curves, a harmonic analysis typically using 37+ cosine terms Lunar and solar components :complex astronomical tide predictions

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

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

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

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

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

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

La Rance River Tidal Power Plant

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