et cetera, et cetera, et cetera

lameubiquityΜηχανική

21 Φεβ 2014 (πριν από 3 χρόνια και 6 μήνες)

47 εμφανίσεις

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