Tides

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Tides
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Tides are

• Periodic, short-term changes in height of the sea
  surface
• Caused by gravitational forces
• The longest of all waves
• Always shallow water waves
• Forced waves never free of the forces that cause
  them

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The Basic Physics of Tides

• Tides result from the COMBINED gravitational
  effects of the moon and sun acting on the earth
• Tidal force is
• Proportional to mass of earth, moon sun
• Inversely proportional to distance CUBED

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The Basic Physics of Tides

• Mass of the sun 27x106 moons
• Sun is 387 times farther away from earth
• Which exerts a stronger tidal force?
• R3 for the sun is 58x106
• The suns influence on the tides is 46 of the
  moon

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The Equilibrium Theory of Tides

• Developed by Issac Newton (17th Century)
• Describes first-order (most important) factors
  influencing tides
• Assumes
• Ocean depth is constant
• Ocean surface conforms instantaneously
• No continents
• All forces in equilibrium

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The moon and tractive forces

• Planetary motion is governed by the balance
  between gravitational and inertial forces
• What is inertia?
• tendancy for an object to move in a straight line
• Sometimes incorrectly called centrifugal force

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Motion due to inertia
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Motion due to gravity
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Earth and moon revolve about the SYSTEMs center
of gravity
The moon does NOT revolve around the earths
center of gravity
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The moons gravity attracts the ocean surface
toward the moon
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Inertia causes ocean on opposite side of the
earth to bulge outward
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Results in two high spots and two low spots
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A diagram of the force balance
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The earths rotation produces the rhythmic rise
and fall of the tides
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If tides simply result from the balance of
inertia and gravity, why are they so complicated?
The Equilibrium Theory ignores some important
factors
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• Complication The tidal day (time required for
  the earth-moon system to complete a single
  rotation) is 24 h 50 mi

The tide arrives 50 minutes later each day
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Complication The moon changes position relative
to the equator
28.5 N in winter, 28.5 S in summer
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Complication The sun also causes the tides to
bulge
Alignment of the sun and moon cause very high
(spring) tides. Spring tides occur every 2 weeks,
not just in the spring.
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ComplicationThe sun also causes the tides to
bulge
Opposition of sun and moon cancel gravitational
pull. Produce low (neap) tides every two weeks.
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Complication Orbits of earth and moon are
elliptical
r

• Distance (r) is not constant, T a 1/r3
• Apogee point where lunar r is greatest
• Perigee point where lunar r is smallest
• Aphelion point where solar distance is greatest
• Perihelion point where solar distance is
  smallest

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More complications

• Depth of the ocean is not constant
• Ocean basins
• Submerged mountain ridges
• Island arcs and trenches
• Continental shelves
• Continents
• Bays, inlets, river mouths, etc.

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• Newton knew his model (first proposed in 1687)
  was incomplete
• His theory predicted the maximum tidal range to
  be 79 cm (55 for moon, 24 for sun)
• Global average tide is 2 m
• But he wasnt primarily an oceanographer, and
  went on to solve problems that were more
  important (at least to him)
• The Dynamic Theory of Tides deals with these
  complications
• First developed by Laplace in 1775
• Subsequent refinements
• Improved prediction accuracy
• Increased model complexity

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Examples of tidal complexity
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3 Classes of Tidal Patterns
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Tidal patterns are determined by GEOGRAPHY
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• Tidal waves in the North Pacific Basin
• slosh back and forth within basins like seiches
• But feel the Coriolis effect, causing water to
  move to the right
• Reflects off N. America,
• Water moves to the left in the S. Hemisphere
• Rotate in a counterclockwise direction around
  AMPHIDROMIC POINTS

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Tidal waves circulate around Nodes called
Amphidromic Points
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The node of a seiche is the point where sea level
does not change

• Shallow-water wave
• Rocking of water confined to a small space
• Specific resonant frequency that changes with
• the amount of water or
• the size shape of the container
• A form of standing wave
• Node is the point of no vertical movement

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Amphidromic Circulation Develops Around Nodes
called Amphidromic Points
setting up a counterclockwise progression
Wave reflects off N. America,
Coriolis effect turns it to the right
Tidal wave enters N. Pacific Basin
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Geography controls the location of Amphidromic
points
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• The surface of the ocean is in constant motion
  (except at amphidromic points, APs)
• So, how do we define the height of the tide?
• APs represent the point of no tidal change, but
  height is affected by ocean gyres (why?), storms,
  etc.
• APs are often far out at sea difficult to survey
  actual height

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Tidal Datum

• Defined as the zero point on nautical charts,
  tide tables, etc.
• Reference point (datum) can be different in
  different locations
• Rarely defined as the mean sea level
• Defined as mean lower low water (MLLW) on coasts
  with mixed tides
• Defined as the average of all low tides (mean low
  water or MLW) on coasts with diurnal or
  semidiurnal tides

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In confined basins (e.g. bays)

• Tides can form bores
• A steep wave moving rapidly upstream
• Speeds exceed theoretical shallow water speed
• How is that possible?
• Tides are FORCED, not free waves
• Basin is often too narrow for formation of
  amphidromic point
• Tidal wave sloshes in and out

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Both amplitude and speed of tidal waves are
exaggerated by bores
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Tides affect marine organisms

• Zonation on rocky shores, estuaries and sandy
  beaches

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Tides affect marine organisms

• Grunion (Leuresthes spp.) spawn on the beach at
  low tide
• At night in California
• During the daytime in the Sea of Cortez

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Tides are a potential source of power

• Turbines convert water flow to electricity
• A form of hydropower
• Could provide 1 2 of global energy need
• Potential problems
• Fouling maintenance
• Flow restriction stagnation

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