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Tides

- Periodic waves caused by the gravitational pull of the moon and sun on the earth
- Timing set by earth\'s rotation
- Long wave lengths—up to 1/2 the circumference of the earth

Major tidal influences on Earth

Major tidal influences on Earth

The tide-producing force (F) is proportional to the product of the masses (m1 and m2) over the CUBE of the distance (r).

Types of Tide Patterns

- Diurnal tide—one high and one low daily
- Semidiurnal—two cycles daily, with the two highs about the same height and the two lows drop to about the same level
- Semidiurnal mixed—two cycles daily, but the two high tides reach different heights and the two low tides drop to different levels

Tide Levels:Diurnal or Semidiurnal

- High water—greatest height to which the water rises on any day
- Low water—lowest point to which the tide falls on any day

Tide Levels:Semidiurnal Mixed

- Higher high water—higher of the two highs
- Lower high water—lower of the two highs
- Higher low water—higher of the two lows
- Lower low water—lower of the two lows

More Tide Terminology I

- Average (or mean) tides—average of all water levels taken over many years
- Mean high water—average high water level
- Mean low water—average low water level
- Tidal datum—reference depth for reporting water depth (for navigation safety, mean low water is usually the tidal datum)

More Tide Terminology II

- Minus tide—when water level falls below the mean value
- Flood tide—when water level is rising
- Ebb tide—when water level is falling

Tidal Currents

- Currents associated with rising or falling of the tides
- Important currents for nearshore navigation
- Flood tide current—water level rising and current is toward the land
- Ebb tide current—water level falling and current is toward the sea
- Slack water—turning tide, between ebb/flood or flood/ebb

Two Ways to Study Tides

- Equilibrium Tidal Theory
- Mathematical idealized principles
- Dynamic Tidal Analysis
- Measure the real world

Equilibrium Tidal Theory

- Mathematically ideal wave
- Assumes uniform layer of water covering Earth
- Used to simplify Earth, Moon, Sun relationships
- Good for illustration of principles, but not good for predicting actual tides

Dynamic Tidal Analysis

- Study of tides as they occur naturally
- Modified by landmasses, shape of ocean basins, and Earth’s rotation

Equilibrium Tidal Theory

- Equilibrium tide theory explains:
- effects of the Sun’s and Moon’s gravity
- effects of rotation
- Consider Earth and Moon as a single unit, the Earth-Moon system orbiting the Sun

Moon

- Orbits Earth
- Held by Earth’s gravitational force
- Force acting to pull Moon away from Earth is centrifugal force
- The two forces balance

Earth-Moon System

- Earth and Moon rotate about a common center of mass
- Held in orbit about the Sun by the Sun’s gravitational attraction
- Sun’s gravitational attraction balanced by a centrifugal force acting to pull Earth-Moon system away from the sun

The Moon Tide

- Water on Earth’s surface closer to the moon (side of Earth facing Moon) acted on by excess gravitational force
- Water moves along Earth surface toward a point directly under the Moon
- Produces a bulge in the water covering the Earth
- Called the gravitational bulge

Moon and Centrifugal Force

- Centrifugal force is equal to the gravitational attraction of the Moon, but operates in the opposite direction
- Causes an opposing bulge on Earth’s surface away from the Moon
- Called the centrifugal bulge or inertial bulge

C

C = Centrifugal Force G = Gravitational Attraction

The opposing gravitational and centrifugal forces create two tidal bulges

Earth’s rotation under the tidal bulge gives the observer two high tides and two low tides each day

Lunar Complications to Equilibrium Tidal Theory

- Lunar Day
- Caused by timing of Moon’s orbit of Earth
- Moon’s declination
- Moon above or below celestial plain
- Moon’s elliptical orbit
- Distance from Earth varies

Lunar Day (or Tidal Day)= Time for completion of each day’s entire tidal cycle, diurnal or semidiurnal, from high tide to the next day’s high tide. See the observer on the diagram below.

- Observer begins at high tide, aligned with moon.
- Earth rotates once in 24 hours, and Moon orbits Earth in about 28 days
- After 24 hours, Moon has moved forward 1/28th of the way around Earth, which is 1/28th of 24 hours, or about 50 minutes
- Thus, Earth must rotate 50 minutes more so the observer on Earth is aligned with the moon and thus at the next high tide
- Thus, Lunar Day = 24 hours 50 minutes

When the moon is closest to Earth (perigee), the tide-producing force is increased by 20%

When the moon is farthest from Earth (apogee), the tide-producing force is decreased by 20%

This drawing is to scale. Note the variation in the distance of the moon from the earth and the distance of the moon above and below the orbital plane.

Complications of the Sun

- Like the Moon, the Sun also produces two equilibrium tidal bulges
- Even though the Sun is huge, it is so far away that it has only 46% of the tide-producing effect of the Moon
- Tides vary with phase of the Moon as Earth-Moon system orbits the Sun

As the Moon revolves around the Earth, the Earth-Moon system is revolving around the Sun. In a lunar month, the moon passes through a series of “phases” as seen from Earth.

Spring Tides

- Occur at New Moon and Full Moon phases
- Earth, Moon, and Sun aligned
- Moon’s tidal bulge adds to Sun’s
- Higher high tides
- Lower low tides
- Nothing to do with seasons. The word “Spring” is from Old English word “springere” meaning to rise or spring up

Neap Tides

- Occur at 1st quarter and 3rd quarter phases
- Earth, Moon, and Sun at right angles
- Moon tidal bulge subtracts from Sun’s
- Lower high tides
- Higher low tides
- Neap—acronym for near even as possible

Which tidal records show diurnal tides? Semidiurnal? Semidiurnal mixed?

Note the timing of spring and neap tides and lunar phases.

Perigean Spring Tides

- A spring tide during moon’s perigee.
- Higher highs and lower lows
- Occurs a few times per year

http://oceanservice.noaa.gov/

facts/perigean-spring-tide.html

Proxigean Spring Tide

- A rare, unusually high tide
- Occurs when the moon is both unusually close to the Earth (at its closest perigee, called the proxigee) and in the New Moon phase (when the Moon is between the Sun and the Earth)
- 25% increase in tides
- The proxigean spring tide occurs at most once every 1.5 years

Dynamic Tidal Analysis

- Needed to explain the real tides on Earth
- There are many complications with Equilibrium Tidal Theory

Real Factors Controlling Tides

- Size of basin (lakes have no tides)
- Width of continental shelf (wider shelves = higher tides)
- Shape of shoreline, concave embayments = higher tides
- Water depth variations deep water nearshore = higher tides

The Tidal Wave

- Wavelength is one-half Earth’s circumference
- Shallow-water wave

Courtesy of Dr. Tom Garrison

Predicting Tides

- Can’t use Equilibrium Tidal Theory alone
- Need to combine years of local observations with astronomical data
- Minimum 19-year record to allow for 18.6-year declinational period of the Moon
- Result is Tide Tables with local predictions of water level and timing of tides

What Really Happens

- Tides in individual basins are deflected by the Coriolis Effect
- Also blocked by continents
- Results in a rotary wave going around the basin
- Two daily cycles around the basin = semidiurnal
- One daily cycle around the basin = diurnal

Amphidromic System

Amphidromic Point (node)—no change in water level

Cotidal lines—tide occurs at the same time along each line

Corange lines—tides of same amplitude along each circle

Tidal Bore

A tidal bore is a wall of water that surges upriver with the advancing high tide.

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