CHAPTER 9 Tides

Chapter Overview

• Tides are the cyclic rise and fall of sea level.

• Tides are very long-period (12 & 24 hr.) shallow-water waves

• Tides are caused by the gravitational attraction of the Sun, Moon, and Earth

• Idealistic tides are complicated by declination, elliptic orbits, continents, bathymetry and ocean friction.

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What are Tides?

• Tides – periodic raising and lowering of ocean sea level

• Occur daily

• Caused by combination of gravity and motion between Earth, Moon, and Sun

• Isaac Newton’s gravitational laws explain relationship

Tide-Generating Forces

• Barycenter between the Earth and Moon– Center-of-mass

between the Earth and Moon is inside the Earth

– Earth:Moon mass ratio is ~100:1

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Gravitational Forces• Every particle attracts

every other particle

• Gravitational force (Fg) proportional to product of masses– Increase mass,

increase force• Inversely proportional to

square of separation distance

• Fg=Gm1m2/r2

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Gravitational Forces• Greatest force at zenith – closest to moon• Least force at nadir – furthest from moon and

opposite zenith

Centripetal Force• Gravitational force that keeps planets (Earth) orbiting

stars (Sun), and satellites (Moon) orbiting planets• Tethers Earth and Moon to each other

Tidal Forces

• Tidal Forces are what you get when you subtract the center-of-mass (centripetal) force from the total gravitational force (Fgrav=Fcm+Ftidal) at each point

• Ftidal is small compared to the center-of-mass force Fcm that keeps objects in orbit (Fcm>>Ftidal)

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Tide-Generating Forces

• Resultant force has significant horizontal component

• Pushes water into two simultaneous bulges– One toward Moon– One away from Moon

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Tidal Bulges – Moon’s Effect

• Small horizontal forces push seawater into two bulges.

• Opposite sides of Earth

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Tidal Phenomena• Tidal period – time between high tides• Lunar day

– Time between two successive overhead moons– 24 hours, 50 minutes

• Moon orbits Earth• High tides are 12 hours and 25 minutes apart

Tidal Bulges – Sun’s Effect

• Similar to lunar bulges but ~half the size

• Why? Because even though the Sun is so much bigger, the Moon is a lot closer to the Earth and distance (r) matters more than mass (m) in Newton’s Universal Law of Gravitation (Fg=Gm1m2/r2)

Relative SIZE

Relative DISTANCE

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Earth’s Rotation and Tides

• Flood tide – water moves toward shore

• Ebb tide – water moves away from shore

• Tidal bulges are fixed relative to the Sun’s and Moon’s positions– Earth’s rotation moves different geographic

locations into bulges

Monthly Tidal Cycle

• Spring tides– New or full moons– Tidal range greatest

• Neap tides

– Quarter moons– Tidal range least

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Earth, Moon, and Sun Positions Relative to Spring and Neap Tides

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Complicating Factors…

• Declination – Angular distance of the Moon or Sun above or below Earth’s equator

• Sun to Earth: 23.5 degrees north or south of equator

• Moon to Earth: 28.5 degrees north or south of equator--need to add Moon to Earth declination (5 deg) to Sun to Earth declination (23.5 deg)

• Lunar and solar bulges shift from equator– Unequal tides

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Declination and Tidal Bulges

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Predicted Idealized Tides

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Complicating Factors• Elliptical orbits • Earth around Sun:

– Tidal range greatest at Tidal range greatest at perihelion (January) (January)– Tidal range least at Tidal range least at aphelionaphelion (July) (July)

• Moon around Earth:Moon around Earth:– Tidal range greatest at Tidal range greatest at perigee perigee (Moon closest to (Moon closest to

Earth)Earth)– Tidal range least at Tidal range least at apogeeapogee (Moon furthest from (Moon furthest from

Earth)Earth)– PerigeePerigee––apogee cycle is 27.5 daysapogee cycle is 27.5 days

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Effects of Elliptical Orbits

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Idealized Tide Prediction

• Two high tides/two low tides per lunar day

• Six lunar hours between high and low tides

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Real Tides

• Continents and friction with seafloor modify tidal bulges

• Tides are shallow-water waves with speed determined by depth of water

• Idealized tidal bulges cannot form– Cannot keep up with Earth’s rotation

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Real Tides

• Crests and troughs of tides rotate around amphidromic point– No tidal range at amphidromic points

• Cotidal lines – connect simultaneous high tide points

• Tide wave rotates once in 12 hours

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Cotidal Map

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Tidal Patterns

• Diurnal– One high tide/one low tide per day

• Semidiurnal– Two high tides/two low tides per day– Tidal range about same

• Mixed – Two high tides/two low tides per day– Tidal range different– Most common

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Tidal Patterns

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Monthly Tidal Curves

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Tides in Coastal Waters

• Standing Waves– Tide waves reflected by coast– Amplification of tidal range– Example: Bay of Fundy maximum tidal range

17 meters (56 feet)

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Bay of Fundy – World’s Largest Tidal Range

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Tides in Coastal Waters

• Tidal Bores– Wall of water– Moves up

certain rivers– Tide-generated

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Coastal Tidal Currents

• Rotary Current

• Reversing current– Flood current– Ebb current

– High velocity flow in restricted channels

• No current at high slack water or low slack water

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Coastal Tidal Currents

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Coastal Tidal Currents

• Whirlpool– Rapidly spinning

seawater– Restricted

channel connecting two basins with different tidal cycles

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Tides and Marine Life

• Tide pools and life• Grunion spawning

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Tide-Generated Power

• Does not produce power on demand

• Possible harmful environmental effects

• Renewable resource

• First Asian power plant in 2006

• United Kingdom proposed building world’s largest tidal power plant

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Power Plant at La Rance, France

• Successfully producing tidal power since 1967

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End of CHAPTER 9Tides

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Daily Assignment (8.1) for Nov. 15th, 2010:

1) Draw and label a picture to explain what a Spring Tide and a Neap Tide is. How are the two tides different in terms of observed water levels at the coast?

2) Draw and label a picture to explain what a Diurnal Tide and a Semi-Diurnal Tide is. How are the two tides different in terms of the observed daily water levels at the coast?