OCEAN100 – M11 – Tides

OCEAN100 – M11 – Tides
Learning Objectives:
• Interpret tide charts and summarize basic patterns in time and space
• Appreciate gravitational basis of tidal forcing
• Relate spring and neap tides to moon phases using simple “equilibrium” model
• Evaluate short-comings of “equilibrium” model in light of “dynamic model”
• Visualize amphidromic systems and their production of three tide “regimes
A typical tide chart . . . Google away . . . common characteristics
Height
(Meters relative to MLLW)
Tidal highs, lows
Tidal range/height/amplitude
Tidal wavelength
Tidal period
From: tidesandcurrents.noaa.gov
Local tidal heights typically reported relative to local Mean Lower Low Water (MLLW)
MLLW is average height of lowest daily low tides for National Tidal Datum Epoch (1983-2001)
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MLLW and other tidal-based datums are important for legal and safety reasons
MHHW
MHW
MLW
MLLW
State/private property boundaries based on MLW, MHW, or MHHW
Navigation chart depths reported relative to MLLW
Bridge heights reported relative to MHHW
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Height
(Meters relative to MLLW)
Tides along our coastline may be best described as a _____ regime
Mixed Tide Regime
Diurnal Tide Regime
Semidiurnal Tide Regime
Tides are one of the most complex topics in oceanography
physics, vectors, etc. . . . We’ll explore concept through two models
Equilibrium Model of Tides:
• Proposed by Sir Isaac Newton in 1687
• Treated tides as deep-water waves; assumed no continents or friction
• In other words, tide crests “keep up” with attractive forces
• Relatively simple, but relatively inaccurate
Dynamic Model of Tides:
• Proposed by Pierre-Simon LaPlace in 1775
• Treated tides as shallow-water-waves; included
effects of continents, friction, and Coriolis
• Relatively complex, but relatively accurate
Lesson: Many simple models aren’t correct, more correct models often aren’t simple!
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Consider Newton’s Law of Gravity among you, Earth, Moon, and Sun
(Warning: Such newtonian “laws” fall apart near speed of light, so slow down!)
g=G
Mass Body 1 + Mass Body 2
(Distance between Body 1 and 2)2
gravitational attraction
between bodies in
=
“Newtons” (kg * m/s2)
(G = gravitational constant = 6.673 x 10-11 m3 kg-1 s-2)
Masses:
Mass of Student: 70 kg
Mass of Earth: 5.98 x 1024 kg
Mass of Moon: 7.35 x 1022 kg (~1.2% Earth)
Mass of Sun: 1.99 x 1030 kg (332,946X Earth)
Distances:
Student-Earth Distance: 6.40 x 106 m (Earth Radius)
Student–Moon Distance: 3.78 x 108 m (~59X Earth Radius)
Student-Sun Distance: 1.50 x 1011 m (~23,300X Earth Radius)
Gravitation Forces:
Student-Earth g: 9.8 m/s2 (look familiar?)
Student–Moon g: 3.0 x 10-5 m/s2 (0.0003% Student-Earth g)
Student-Sun g: 6.0 x 10-3 m/s2 (0.06% Student–Earth g)
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Basic idea in this
pile of numbers:
Moon and Sun’s gravitational
attraction of objects
on Earth’s surface is
relatively weak . . .
. . . yet sufficiently strong to
produces significant
amounts of water
motion as tides!
How?
We’ll first explore Earth-Moon interactions, then incorporate the Sun
All orbits of planets, moons,
satellites, asteroids, etc., result
from a balance between
inertial motion
and
gravitational force
So, in a sense,
orbiting objects
are forever
“falling around”
their host!
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Note: Earth-Moon distance scaled relaive to their size
Consider the Earth–Moon System
• Earth and Moon actually co-orbit around a common center-of-mass.
• As you might expect, this center-of-mass is slightly offset from center of Earth.
• Earth-Moon complete one co-orbit in 27.3 days (a “sidereal” month)
+
=
For Equilibrium Model, allow combined effects of gravity and inertia to produce
“Moon-facing” and “Moon-opposite” water bulges over Earth’s surface
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Earth would rotate through these two “water bulges” every 24:50
Why every 24:50 instead of 24:00?
Over 24 hours, the Earth rotates 360° E on its axis and the Moon co-orbits ~13.2° E
Thus, for a given location (I.e., man below) to again be directly under the Moon,
Earth must rotate another 13.2° E (24 hrs/360° = 0.88 hrs = ~50 minutes)
North-Pole 2-D view
(Note: Water bulges track Moon’s “overhead” position)
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Here comes the Sun . . .
Sun is much more massive than moon (27,000,000X), but much farther away (390X)
Recall how mass and distance control gravitational attraction between two objects
Result: Sun has only 46% the tidal-generating force of the Moon
g=G
Mass Body 1 + Mass Body 2
(Distance between Body 1 and
2)2
=
gravitational force
between bodies in
Newtons (kg * m/s2)
(G = gravitational constant = 6.673 x 10-11 m3 kg-1 s-2)
Earth–Moon–Sun System: One complete Earth-Moon co-orbit
around their center-of-mass in ~27.3 days (“sidereal month”) . . .
. . . but need another
~2.2 days (~29°) of co-orbit
for Earth-Moon-Sun
realignment . . .
(from Open University, 1999)
. . . thus, ~29.5 days
to cycle through
moon phases
(“synodic month”)
Equilibrium model explains Moon
phases and basic tidal patterns
resulting from E-M-S alignments
Spring Tides:
• E-M-S are lined up
• Moon and Sun bulges align
• Moon appear “new” or “full”
• Highest high tides
• Lowest low tides
• Largest tidal range
Neap Tides:
• E-M-S form 90° angle
• Moon 1/4 or 3/4 “full”
• Lowest high tides
• Highest low tides
• Smallest tidal range
Go to
BB animation!
(from Open University, 1999)
Net Result: Observed tidal patterns through time at a given location
OK, I see the general change in tidal range related to EMS relationships . . .
but what about the higher frequency “daily” variations?! (more variable than predicted)
Equilibrium model is reaching its limit . . shift to the dynamic model
which is way more complex but also way more realistic!
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“Real world” factors adequately incorporated into Dynamic Model of Tides
• Ocean depths force tides to be shallow water waves with friction
• Continental boundaries restriction free motion
• Coriolis deflection affects tides, essentially freely moving objects
• Variations in angle of Moon and Sun relative to Earth’s rotational axis
• Elliptical orbits of Earth around Sun and of Moon around Earth
Height
(Meters relative to MLLW)
Dynamic model is highly developed . . . used to predict future tides with great precision
Basic Idea of Dynamic Model of Tides:
Stuck within basins and limited in their speed, tides respond
“as best they can” to horizontal tide-generating forces from gravity
Amphidromic Point (AP): No tidal variation; “hub” around which wave rotates
Note that tidal forces and Coriolis produce a counter-clockwise rotation in NH!!!
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Net Result: Observed tidal patterns given continents and speed limits
Amphidromic Points (black dots): Minimal tidal variation; “hubs” around which waves rotate
Cotidal Lines (white lines): “Spokes” of same tide conditions (e.g. highest high tide)
at same time for a given amphidromic system
Colors: Blue = minimal tidal range; Brown = maximum tidal range
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Net Result: Observed tidal patterns given continents and speed limits
+9:18
+6:12
Focus on the North Atlantic - a “simple basin”
• If a high tide is along west Africa at 0:00 (star), then all locations along
0:00 cotidal line experience a local high tide and all points slightly NW
of ~6:12 experience a local low tide.
+3:06
0:00
• This high tide rotates counterclockwise around its amphidromic point,
reaching Scandinavian coast at ~6:12 and returning to the initial west
African location at ~12:25.
• So, over 24:50, two rotations of tidal crest produce “diurnal” regime
(two equal highs and two equal lows per tidal day) all around the
relatively “closed” North Atlantic
• Note: Tidal range (i.e., difference between high and low tides) generally
increases away from the amphidromic point in quasi-bull’s eye pattern.
• Note: Tidal ranges and rotation rates along coasts reflect complexities of
conservation of momentum, etc. as amphidromic system rotates
Amphidromic Points (black dots): Minimal tidal variation; “hubs” around which waves rotate
Cotidal Lines (white lines): “Spokes” of same tide conditions (e.g. highest high tide)
at same time for a given amphidromic system
Colors: Blue = minimal tidal range; Brown = maximum tidal range
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Net Result: Observed tidal patterns given continents and speed limits
The dozen plus amphidromic systems over the global ocean emerge from
continent blockages, coriolis deflections, and shallow-water-wave “speed-limits”
The tidal waves (where the crest is a high tide) associated with each of these
amphidromic systems interact just like wind-generated waves, with constructive
and destructive interference as they pass through one another.
Net Result: Observed tidal patterns given continents and speed limits
Complex globally . . . but at any location,
tides (generally) classifiable as diurnal, semidiurnal, or mixed
Why does our coastline have a mixed tide regime?
We are seeing the complex constructive and destructive interference of
multiple tidal waves rotating around their respective amphidromic points!
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Local effects in local basins: Bay of Fundy
Immense tidal range with very strong flood and ebb currents
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Can we capitalize on tides? Potential and problems
Can we capitalize on tides? Potential and problems
(Grunion) Sex on the Beach!
Basic research and monitoring matters: Sea level rise from tide gauges