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Chapter 11 – Tides
A tidal bore is formed
when a tide arrives to
an enclosed river
mouth. This is a
forced wave that
breaks.
Tidal range can be very large
The Coriolis Effect at Work!
http://www.youtube.com/watch?v=gccduFJSisI
Tide - rhythmic oscillation of the ocean surface due to gravitational &
centrifugal forces (‘inertia’) between the Earth, Moon and Sun.
Tide Patterns - regular, cyclic patterns of low water-high water
Tidal cycle – one low tide and one high tide consecutively
diurnal tide - one low tide, one high tide a day;
semidiurnal tide - high water-low water sequence twice a day;
2 high, 2 low, about the same level
semidiurnal mixed tide - same as semidiurnal but 2 highs and 2 lows
do not reach/drop to the same level; may be
the result of a combination of tide types
Tide Patterns - regular, cyclic patterns of low water-high water
diurnal tide
semidiurnal tide
semidiurnal mixed tide
Semidiurnal tides
Diurnal tides
Mixed tides
Most of
the world’s
ocean
coasts
have
semidiurnal
tides.
d
(ft)
14
10
6
4
0
–4
Mixed tide, Los Angeles
Diurnal tide, Mobile, Alabama Semidiurnal tide, Cape
Cod
Higher high tide
High tide
Lower high tide
High tide
Lower
low tide
Higher low
tide
(m)
4
3
2
1
0
–1
Low tide
Low tide
0 612 18 24 30 36 42 48
0 6 12 18 24 30 36 42 48 0 6 12 18 24 30 36 42 48
a
Time (hr)
b
Time (hr)
c
Time (hr)
Flood Tide: tide wave is propagating (onto shore) onshore –
water level is rising
High Tide: water level reaches highest point
Ebb Tide: tide is moving out to sea – water level is dropping
Low Tide: water level reaches lowest point
Slack tide: period when tide wave is reversing –
low current velocity
Water currents are generated by the tides, the speed of the incoming
tide is about the same but in the opposite direction of the outgoing
tide. Moving waters have to slow down and reverse, from flood to
ebb and vice versa (slack tide). This is a good time for navigation
through narrow places, particularly those characterized by strong
tides (East River, for example).
Mean Tide Level = MTL - computed from measurements taken at a
place over many years and averaging all water levels.
Mean High-Water = MHW.
Mean Low-Water = MLW.
For mixed tides:
Mean Higher High Water = MHHW
Mean Lower Low Water = MLLW
tidal range – difference between
MHW and MLW
(water level at high tide and
water level at low tide)
Examples of
typical tides - US
Study of Tides
Equilibrium Tidal Theory - ideal approach to understand basic
principles, assumes an earth covered with water
Assumptions:
1: entire Earth surface covered in water
2: infinitely deep basin (no shoaling)
3: tidal bulge fixed relative to the moon
Dynamical Tidal Analysis - realistic approach, studying the tides as
they occur on earth, accounts for modification due to landmasses,
geometry of ocean basins, earth’s rotation.
Tides are caused by the difference in gravitational forces resulting
from the change of position of the Sun and the Moon relative to
points on Earth
* centrifugal (‘inertia’) and gravitational forces*
universal law of gravitation
F= G m1 m2 / R2
G = universal gravitational constant
m1, m2 = mass of bodies
R = distance between centers of mass of bodies
B & C = gravitational forces
B’ & C’ = centrifugal forces
Figures in textbook
1,650 km
(1,023 mi)
Earth’s mass is 81 times
the mass of the moon
Moon
(81/82) r
(1/82) r
Average Earth–moon distance (r)
The moon’s gravity attracts the ocean toward it. The motion of Earth around
the center of mass of the Earth – moon system throws up a bulge on the side of
Earth opposite the moon. The combination of the two effects creates two tidal
bulges.
Add the Sun
A (and B & C) = gravitational forces
A’ (and B’ & C’) = centrifugal forces
(with figures 11.5 &
11.6 in textbook)
The Tide Producing Force
(difference between gravitational
forces and centrifugal forces at
the earth surface) is proportional
to GM/R3
The Moon Tide and how we get a ‘wave’
The Tidal Day = 24 hr 50 min
Diurnal = 24 hr 50 min
Semidiurnal = 12 hr 25 min
Lunar Cycle: the Earth –
Moon system has a period
of 29.5 days
The Sun Tide
Spring & Neap
Tides
Spring and Neap tides at two places on Earth
Dynamic Tidal Analysis
A mathematical study of tides as they occur. It looks at the tide wave,
which is similar to the tide wave of the ideal water covered earth, but
varies from place to place.
* Continents break up wave propagation
* Tide wave moves continuously around the globe only in the
Southern Ocean (Antarctica).
* shallow-water wave: speed is controlled by depth of ocean
* standing wave: oscillates because it is contained in ocean
basins (wave ‘contained’ in ocean basin)
* reflected by continents, refracted by changes in depth, and
diffracted (spread of energy sideways) as it passes through
gaps
* Coriolis affects the water movement because it is a large
scale phenomenon.
Amphidromic points are nodes at the center of ocean basins;
these are no-tide points.
The development of amphidromic circulation
(a) A tide wave crest enters an ocean basin in the Northern Hemisphere. The
wave trends to the right because of the Coriolis effect (b), causing a high tide
on the basin’s eastern shore. Unable to continue turning to the right because of
the interference of the shore, the crest moves northward, following the
shoreline (c) and causing a high tide on the basin’s northern shore. The wave
continues its progress around the basin in a counterclockwise direction (d),
forming a high tide on the western shore and completing the circuit. The point
around which the crest moves is an amphidromic point (AP).
How do tides behave in confined
basins?
The tidal range is determined by
basin configuration. (a) An
imaginary amphidromic system in a
broad, shallow basin. The numbers
indicate the hourly positions of
tide crests as a cycle progresses.
(b) The amphidromic system for
the Gulf of St. Lawrence between
New Brunswick and Newfoundland,
southeastern Canada. Dashed lines
show the tide heights when the
tide crest is passing.
Tides in a narrow basin. (a)
True amphidromic systems do
not develop in narrow basins
because there is no space for
rotation. (b) Tides in the Bay of
Fundy, Nova Scotia, are
extreme because water in the
bay naturally resonates
(seiches) at the same
frequency as the lunar tide.
Bay of Fundy
10 meter range
Tidal bore – Bay
of Fundy
Chapter 11 – Summary
Tides are huge shallow-water waves-the largest waves in the ocean.
Tides are caused by a combination of the gravitational force of the
moon and sun and the motion of Earth.
The moon's influence on tides is about twice that of the sun's.
The equilibrium theory of tides deals primarily with the position and
attraction of the Earth, moon, and sun. It assumes that the ocean
conforms instantly to the forces that affect the position of its
surface, and only approximately predicts the behavior of the tides.
The dynamic theory of tides takes into account the speed of the longwavelength tide wave in water of varying depth, the presence of
interfering continents, and the circular movement or rhythmic backand-forth rocking of water in ocean basins. It predicts the behavior
of the tides more accurately than the equilibrium theory.
Tides have the longest wavelengths of the ocean's waves.
These huge shallow-water waves are forced waves: never free of the
forces that cause them and so act in unusual but generally predictable
ways.