1. The Heartbeat of the Ocean

2. Introduction Tides are one of the most obvious features of the oceans. Natural rhythms can easily be observed. Long term records of amplitudes and predictions made since 13th century. 1687 Newton applies his law of gravitation to tides Visual of seasons

3. II. TIDES Write this rhythmic rise and fall of water at a fixed location (handout in student binder) Lunar day 24 hrs. 50 min. Tides are linked to lunar cycle 28 days for moon to circle the earth (and be over the exact same spot)

5. Tidal Theories There are two tidal theories. Equilibrium theory by Newton Dynamic theory by Laplace Each have there own assumptions.

6. Equilibrium theory by Newton Assumptions: Forget Sun for a minute. Totally fluid earth, no land and no boundaries. In fact lets make the ocean infinitely deep and homogeneous. If we allow an infinite time, we will reach equilibrium where surface bulges can keep up with the moon.

7. A. EXPLANATION Write this 1. Equilibrium Model-theory that proposes reasons for large scale patterns. There is a variation in the gravitational effects of...... EARTH MOON 2/3 EARTH SUN 1/3

8. Visual on the next slide Write this The earth moon are a system like a spinning "barbell" through space. They rotate around each other. The gravitational midpoint of this unit is the "barycenter"

9. The Earth-Moon System The Earth and Moon orbit their common center of gravity, the barycenter (3000 miles from Earth’s center, or 900 miles from Earth’s surface)

10. F g = Gravitational Force M 1 = Mass of Earth M 2 = Mass of Moon r = Distance between Earth & Moon

11. Inertial forces on Earth due to the Earth-Moon System Force is the same everywhere on Earth Force is directed perpendicular to Earth’s center everywhere on Earth

12. Inertial Force Balances the Lunar Gravitational Force at the Barycenter (Center of Mass of the Earth-Moon System

13. Resultant forces Resultant Resultant forces are: The difference between gravitational (G) and Inertial (C) forces Directed away from Moon on the side of Earth opposite Moon Directed toward Moon on the side of Earth facing Moon

14. Write this a. Inertia and gravity work against each other but are over all equal. This allows a consistent pattern of tides as the earth orbits the sun

15. The Tide Generating Force

17. Equilibrium Theory

18. But wait… there’s more to TIDES!

19. Sun’s Influence

20. Neep tide- first and last 1/4 low HIGH TIDE high LOW TIDE Spring tide- new and full very HIGH TIDE very LOW TIDE

22. Dynamic Theory by Laplace Equilibrium theory is not very realistic, so 100 years after Newton, Laplace developed the Dynamic theory. Assumptions: Still homogeneous ocean (barotropic) No coriolis accelerations. No analytical solution to Laplace equations, use numerical approximations and simple boundaries

23. 2. Dynamic model- based on observations Write this

24. a. Types of tides Write this Diurnal Tide – One high and low per day Gulf of Mexico Semi-diurnal Tide – Two highs and lows per day, nearly equal in magnitude Bahamas Mixed Tide – Two highs and lows per day, with conspicuous inequality in successive high and low water elevations West Coast of USA (Tidal Datum – The average, over a 19-year period, of water height at a particular stage of the tide (i.e., mean high water, mean low water, mean lower low water, etc.))

26. b. why? Write this friction of the ocean floor and coast lines distort the "expected" high and low. Historical records " Empirical data" is collected for 100's of years. Computer programs help project future tidal patterns.

28. Tidal patterns in the U.S.

29. n The Inertial force which offsets lunar gravitation is due to the orbit of the Earth around the barycenter … it is not due to the spin of the Earth on its axis. n Due to much greater mass, the gravitational force of the Sun (F=GM 1 M 2 /r 2 ) is greater than that of the Moon. n So why are lunar tides greater than solar tides? Because the tractive force (proportional to 1/r 3 ) exerted by the Sun is only about 40-50% as strong as that of the Moon.

30. Tidal measurement

31. Lord Kelvin’s Tide Predictor http://www.ams.org/featurecolumn/archive/tidesIII3.html http://www.ams.org/featurecolumn/archive/tidesIII3.html Each pulley represents a harmonic constituent of the tide. A wire running through the pulleys was connected to a pen which traced the shape of the tide. First conceived in 1872, similar machines were in use until the 1960s.

32. U.S. Coast and Geodetic Survey Tide-Predicting Machine No. 2 Built 1910, in use until 1966 37 Harmonic Constituents 11’ x 2’ x 6’ 2500 lbs

33. Global Ocean Tides from TOPEX/Poseidon