Tides
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
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
 m1m2 
T  G 3 
 r 
The Basic Physics of Tides
 m1m2 
T  G 3 
 r 
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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 sun’s influence on the tides is 46% of the
moon
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
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
Motion due to inertia
Motion due to gravity
Earth and moon revolve about
the SYSTEM’s center of gravity
The moon does NOT revolve
around the earth’s center of
gravity
The moon’s gravity attracts the
ocean surface toward the moon
Inertia causes ocean on opposite
side of the earth to bulge outward
Results in two high spots and two
low spots
A diagram of the force balance
The earth’s
rotation
produces the
rhythmic rise
and fall of the
tides
If tides simply result from the balance
of inertia and gravity, why are they so
complicated?
The Equilibrium Theory ignores
some important factors
• 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
Complication: The moon changes
position relative to the equator
28.5° N in winter, 28.5° S in summer
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.
Complication:The sun also causes the tides
to bulge
Opposition of sun and moon cancel gravitational pull.
Produce low (neap) tides every two weeks.
Complication: Orbits of earth
and moon are elliptical
r
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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
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.
• 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 wasn’t 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
Examples of tidal complexity
3 Classes of Tidal Patterns
Tidal patterns are determined
by GEOGRAPHY
• 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
Tidal waves circulate around Nodes
called Amphidromic Points
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
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
Geography controls the location
of Amphidromic points
• 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
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
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
Both amplitude
and speed of
tidal waves are
exaggerated by
bores
Tides affect marine organisms
• Zonation on rocky shores, estuaries and sandy
beaches
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
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