1
et cetera, et cetera, et cetera
Fig. 8

2b
2
And the Tides are ...
Slow,
up and down movement
s of sea level
Once or Twice a
day
And the Tides are not …
ocean
waves,
“tsunamis”
or rip tides
3
Topics for Today
•
Tides are caused by the pull of the
sun
and the
moon
•
Two highs and two lows a “day” in most
places
•
Open ocean: tides are simple and single
waves that stretch across the entire
ocean
•
Near coastline: tides are greatly altered
by bottom topography
•
Predictions are computed for particular
sites along coast
4
Tidal Characteristics
•
Tidal Range

vertical distance between high
and low tides (crest

trough)
•
Wave period

time between high tides
•
Tides are waves of
very long
period and a
tremendous amount of energy
•
Measured
–
onshore using tidal pen
recorders
–
offshore pressure sensors
•
Are tides
deep water waves
or
shallow water
waves
?
5
Tidal Periods
•
Diurnal

about once a day
–
24 hours and 50 minutes
•
Semidiurnal

about twice a day
–
12 hours and 25 minutes (equal magnitude)
•
Mixed

twice a day, but with unequal
highs and lows
•
Spring
and
neap
tides following Moon’s
phases
6
Tide Records
_____
Twice a
day with
variations
__________
Twice
a day
_______
Once
a day
7
Why
do the Tides Occur ?
•
Balance of forces as the
moon
orbits the
earth
and they
Both
go
around the
sun
.
•
What Forces ?
–
Gravity
, Pulls Objects Together
–
Centrifugal force
Separates Objects
8
Earth

Moon
and
Earth

Sun
Systems
Sun
Earth
Moon
Gravitational Attraction and
Centrifugal Force from
sun and moon
cause the Tides
9
Tide Generating Forces
•
Tides produced by
gravitational
and
centrifugal force
of both Earth

Moon
and Earth

Sun systems.
•
Despite the fact that the sun is 10
7
x
more massive than the moon
•
The moon still dominates Tides
Why?
Moon is much
closer
to Earth
(
384,835 km vs. 149,758,000 km)
10
So, Consider First Just the
Earth

Moon
System
As Moon orbits the Earth they both
rotate around the
centre of mass
of
the earth

moon system, the
‘balance
point’
11
Earth
Moon
The Earth

Moon System
Barycenter
The
Barycenter
is located
near
the
earth, but
not
at the center.
Centrifugal
Force
Gravitational
Attraction
12
Equilibrium Model of Tides
•
Earth is 100% covered by ocean of
infinite depth
–
No bottom and no land masses
•
Tides are
assumed to be progressive
waves
•
Always in
equilibrium
with
–
Gravitational attraction of Moon
–
Centrifugal force
•
Neglect Effect of the
sun (for now !)
Assumptions:
13
Equilibrium Model
•
Moon’s
gravity
pulls on the
earth
, the
ocean and you.
•
Ocean water flows
towards
the Moon,
accumulating and
bulging up under it
14
Equilibrium Model
•
Earth

Moon also rotate about a common
centre of gravity
causing
centrifugal
forces
•
Resulting in
bulge
away from
Moon
15
Thus, we have
Two
Bulges
As Earth rotates on its axis,
the point you stand on
passes beneath two bulges each 24 Hr
creating
two tidal bulges
each day
.
16
But Wait, There’s More
Ever notice that high tide is about 50
minutes
ahead
each day?
Why is that?
Because the
lunar “day”
is longer than the
solar
day by about 50 minutes
17
The Lunar Day: 24h 50 min
•
Moon moves 1/30 way around earth
each hour
•
24 h / 30 = 0.8 h or about 50 min
•
Lunar half

day is
12 hours 25 min
•
This produces the
first
High Tide
18
… and one more thing

•
Earth’s axis is tilted
28.5
°
to the plane of
moon’s orbit (
declination
).
•
Thus, the bulges that cause the tides
are also
at 28.5
°
.
•
Leads to
latitudinal variation
of tides:
–
diurnal
–
mixed
–
semi

diurnal
19
Types of Tides
20
Equilibrium Model
Summary and Questions
•
Earth and Moon
•
Ocean: all over and infinitely deep
•
Bulges in balance with:
–
Gravity & centrifugal forces and tilt of axis
•
Explains:
–
diurnal
–
semidiurnal
–
mixed
21
Here Comes the
Problem
•
Similar Effects: two more
factors
•
In
24 hours
•
Net tidal force of Sun is
half
that of the
Moon, thus:
–
Lower tidal amplitude for solar component
•
Amplitudes for Moon and Sun are:
–
different
–
Not always
in sync
22
Why are the Solar Tidal Forces Less ?
Gravitational pull
prop. to: (m
1
m
2
) / r
3
(Dist. Between bodies more important for Tides)
Sun is 10
7
times more
massive
but
390 times
further away
Thus, Sun’s Tidal Force is:
27,000,000 / (390)
3
= 0.46
or about
half
that of the Moon
23
To Sun
To Sun
Combined Effects
of Sun and Moon
are
additive
Spring Tide
Neap Tide
24
So, Moon & Sun effects are
additive BUT
•
Sun’s effects will pass in and out of
phase
with Moon’s effect
•
New and Full Moons: forces
additive
,
spring
tides
•
First and Last Quarter Moons: forces
are
subtractive
:
neap
tides
25
Spring

Neap Tide Cycle
26
Spring

Neap Tidal Range
27
When would you get the Smallest and
Highest Tides ?
Depends on Earth and Moon Orbits
Orbits are
ellipses, not
circles (29
days for
moon, 365
days for sun)
Answer:
A
spring tide
with
moon
at Perigee and
sun
at Perihelion
Two ‘king tides’ per year

one during summer and one
during winter.
Spring
Tides
occur when
Bodies are
close
together
28
Summary
•
Spring and Neap Tides
•
Tilt of Earth’s axis
–
Declination (celestial latitude)
•
Inequality in bulges at any given spot
–
Diurnal tides at high latitudes
–
Mixed at mid

latitudes
–
Semidiurnal at low latitudes
–
Unequal tidal heights within a given day
•
What if the Moon didn’t exist?
29
Dynamic Model of Tides
•
Water confined to bodies of finite depth
•
Tidal bulge is squashed against basin’s
western
edge, flows
downslope
(pressure gradient)
and to the
right
(Coriolis)
in Northern Hemisphere
•
Rotary waves move
anticlockwise
in
Northern Hemisphere
30
Dynamic Model
of the Tides
Water confined to
finite basins
High and Low Tides
on
opposite sides
of
basin
Rotate Counter

clockwise in N.H.
(due to Coriolis)
31
Rotary Tidal Motions in
Amphidromic
(rotation about a node)
Systems
Cotidal
lines
(high tide same time)
vs.
Corange
lines
(equal tidal range)
Rotary Wave
–
has attributes
of both
progressive
and standing
wave
Time = x
Time = x + 2Hr
Amphidromic Point
32
Dynamic Model
•
Broad basins:
–
Rotary wave about amphidromic point
–
clock

like spokes of co

tidal lines
–
progressive and standing
•
Narrow basins:
–
tidal bore
,
33
Tides in Basins
•
Gulf of St.
Lawrence
versus
•
Bay of
Fundy
34
Global Amphidromic Systems
Bending of the cotidal line reflects wave refraction
(2 = tide 2 hours later, 6 = tide 6 hours later etc.,)
35
Tides Near Amphidromic Point
•
Tides are zero at the ‘node
(amphidromic point) and
increase to a maximum at
antinodes (located at the
edge of the basin)
36
Tides Across the Globe
37
Tidal Resonance
•
Like sloshing in your bathtub
•
If the natural resonance of the
embayment and the tide are in phase

greatly amplified tidal
range
•
Most often used example is the Bay of
Fundy or Severn Estuary
38
Severn Estuary :
39
Tidal Bore

Wall of water surging up

river
Hardly noticeable 20 cm H,
to 5

m in Amazon River,
(20 km/h)
to 7

8 m in Fu

Ch’un River,
(25 km/h)
Large tidal range
+ tapering basin
+ decreasing depth
produces the wave
40
Tidal Currents
•
Sea’s rise and fall means water must
move from place to place
•
Flood
currents move water landward
•
Ebb
currents move water seaward
•
Strong near the coast, bays and inlets
•
Rotary pattern in open ocean due to
Coriolis force
41
Tidal Currents in the Chesapeake Bay
42
Prediction of Tides
•
Tabled for
recording
stations
•
Predicted
for other localities
•
Newspapers
•
Television and radio
•
Marinas, bait shops
•
Tables and calendars
•
Web sites and programs
–
Government and commercial
43
Tidal Predictions

•
Measurement of
tidal component
curves, a
harmonic
analysis
–
typically using 37+
cosine terms
•
Lunar and solar
components
:complex
astronomical tide
predictions
44
Tide Predictions and Real

Time Data
http://www.opsd.nos.noaa.gov/
45
Atmospheric Conditions
•
Astronomical tide predictions
versus
Atmospheric Conditions
–
Wind set

up (ordinary wind shear)
–
Storm surge (extra

ordinary)
•
Wind shear
•
Low Atmospheric pressure
•
Ekman Transport (coriolis)
1999 Storm Surge
46
Tidal Rhythms and the
Ecology of the Tides
•
Rocky intertidal communities and zones
•
Sandflats, mudflats and salt marshes
•
Feeding and activity rhythms of fiddler
crabs are attuned to the tides...
•
Grunion spawning as well
•
Horseshoe crab spawning and egg

laying
47
Energy from Tides
•
Differences in
tidal height
drive generator
turbines
•
Although some 150 sites world

wide are
suitable...
•
Relatively few have been constructed
•
http://www.darvill.clara.net/altenerg/tidal.htm
•
http://www.energy.org.uk/EFTidal.htm
48
Locations With Large Tidal Range
Is Tidal Power
feasible
and
economic
At all these Locations?
49
French Tidal Power Station
La Rance River Tidal Power Plant
at St. Malo
50
La Rance River
Tidal Power Plant
51
Why so Few ?
Consider the Problems:
•
Only a few
suitable
locations
–
High tidal range required
–
Most of these not near major Pop Centers
•
Cost Efficiency
of Power Production
•
Environmental Impact
–
Tidal
time
and
range
alteration
•
Interferes with
current dynamics
of
waterway
–
Navigation, commercial and recreational
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