Transcript g104_class25-27_tides

Geography 104 - “Physical Geography of the World’s Oceans”
Ocean Tides and Sea Level
- tide – “daily rise and fall of sea level” (C&D)
- tide – distortions of sea by gravitational attraction of Moon and
Sun on every part of Earth
- tidal currents - small gravitational forces give rise to horizontal
water movement
- horizontal movement of water causes rise and and fall of sea level
gravitational
attraction
first order explanation of tidal patterns
daily tidal patterns
- horizontal movement of water causes rise and and fall of sea level
- can be represented as “waves” (periods ~12 or ~24 hours)
- classified by period
- diurnal tide (~1 cycle/day = 1 high, 1 low)
- semidiurnal tide (~2 cpd = 2 highs, 2 lows)
- mixed semidiurnal (2 highs and 2 lows not equal)
- tidal day – time for one complete revolution of Earth beneath
tidal bulges, ~24 hrs and 50 minutes
diurnal tide
tidal range = high tide water height – low tide water height
semi-diurnal tide
mixed tide
reference level for navigation:
mean lower low water
tidal components
mixed tide
diurnal tide + semidiurnal tide
mixed tide
Tab. 11.1
tidal patterns
Fig. 11.10
daily tidal pattern details
- actual tides depend on response of ocean to forcing
- tidal currents can be very strong (~5 knots)
- strongest currents typically near mouth of bays (i.e. SF Bay)
spring-neap tides Santa Barbara (tidal currents a few cm/s)
1
16 Jan – 11 Mar 2007
20 Jan
25
30
1 Feb
diurnal tide
5
10
15
20
25
1 Mar
5
semi-diurnal tide
10
tide generating and raising forces
- tides caused by gravitational attraction (tide generating force)
- mostly by moon, but also by sun, negligible contribution from other
bodies in solar system
- technically, difference between gravitational force at Earth’s
surface and Earth’s center gives rise to tides (tide raising forces)
- gravitational force between two masses
FG = G m1m2/d2
FG - gravitational force between two masses
G - gravitational constant
m1, m2 - masses
d - distance
earth & moon comparison
http://home.xtra.co.nz/hosts/Wingmakers/Moons
earth & moon distance
http://home.xtra.co.nz/hosts/Wingmakers/Moons
barycenter - the center of gravity where two or more celestial bodies orbit each
other. For example, the moon does not orbit the exact center of the earth, instead
orbiting a point outside the earth's center (but well below the surface of the Earth)
where their respective masses balance each other.
acceleration of earth due to moon’s gravity
Centripetal acceleration
centripetal acceleration and gravitational force
Centripetal acceleration
centripetal acceleration and gravitational force
apparent force due to
centripetal acceleration
Centripetal acceleration
tide raising force
G
tide raising force = G + C
C
TRF
Centripetal acceleration
C
distribution of tide raising forces
Centripetal acceleration
tide raising force
Centripetal acceleration
tide raising force
-Tide Raising Force (due to moon)
TRFm = 2 r G mm me/d3
(equation on page 227)
FG - gravitational force between two masses
G - gravitational constant
mm, me - masses
d - earth-moon distance
r - difference in earth-moon distance from Earth’s center
distribution of tide raising forces
Centripetal acceleration
tide raising force
horizontal component of tide raising force
tide raising force
horizontal component of tide raising force
local horizontal plane
horizontal component of tide raising force
horizontal component of tide raising force
earth’s gravitational force
>> vertical component
horizontal component of tide raising force
horizontal component
unbalanced – produces
water movement
pattern of horizontal components of tide raising forces
Tides are caused by the gravitational
attraction between the Earth and
other planetary bodies; primarily
between the Earth and Moon, and
the Earth and Sun.
maximum tide generating force a midlatitudes
equilibrium lunar tides
equilibrium lunar tides
to remain under
moon tide wave
would have to
propagate 442 m/s
eastward at equator
at equator
velocity = 442 m/s
lunar day
53
53
- 1 lunar day = 24 hours + 53 minutes
- 2 high & 2 low tides per lunar day
- called the M2 tide with period of 12.42 hours (see Table 11.1)
example of semi-diurnal tide
effect of moon’s declination
- moon’s declination causes unequal tide heights
(zero declination)
tidal inequality
tidal inequality
tidal inequality
lunar hours =
large tidal
inequality –
diurnal tides
small tidal
inequality semi-diurnal
tides
example of diurnal tide
synodic month
- 2 spring-neap tide cycles/ synodic month
time between new moons
solar tide & spring neap cycle
spring tide
neap tide
earth-moon system
(moon’s orbit around earth)
center of mass
of earth
center of mass of
earth-moon system
earth, moon, & sun
earth, moon, & sun
around sun
Path of moon
around earth
earth, moon, & sun
around sun
Path of earth
around sun
Path of moon
around earth
earth, moon, & sun
around sun
Path of earth
around sun
Path of moon
around earth
earth, moon, & sun
around sun
Path of earth
around sun
29.53 days =
lunar month
Path of moon
around earth
earth, moon, & sun monthly (29.53 days) cycle
spring-neap tides Santa Barbara
1
16 Jan – 11 Mar 2007
20 Jan
25
30
1 Feb
diurnal tide
5
10
15
20
25
1 Mar
5
semi-diurnal tide
10
changing earth-moon distance
dA = 405,800 km
dP = 375,200
TRF at perigee = dA 3 = 1.073 = 1.21
dP
TRF at apogee
( )
 21% variation in TRF due to changing earth-moon distance
declination of moon & tidal inequality
= max. angle
above equator
(always changing)
0 years
18.6 years
4.65 years
9.3 years
moon’s changing declination
Earth
moon’s changing declination
0 years
(blue)
moon’s changing declination
0 years
4.65 years
moon’s changing declination
changing earth-sun distance
153x106 km
149x106 km
 ~8% variation in TRF due to changing earth-sun distance
tidal components
distribution of tide raising forces
global distribution of tide types
consideration of ocean basin geometry and the Coliolis force
results in amphidromic systems
co-tidal lines
amphidromic M2 tide
M2 amphidromic
systems
tidal amplitude
CCW
tidal phase
CW
amphidromic system – M2 tide
Kelvin Wave – northern hemisphere
Kelvin waves and amphidromic systems
Kelvin waves and amphidromic systems
pressure
Coriolis
tidal current
Tides for Santa Monica, Municipal Pier starting with December 5, 2008.
Day
High
Tide Height % Moon
/Low
Time Feet Visible
F
5
5
5
5
High
Low
High
Low
3:37 AM
9:09 AM
2:01 PM
9:00 PM
4.1
2.9
3.7
1.0
40
Tides for Santa Barbara starting with December 5, 2008.
Day
High
Tide Height % Moon
/Low
Time Feet
Visible
F
5
5
5
5
F 12
12
12
12
High
Low
High
Low
3:57 AM
9:27 AM
2:21 PM
9:18 PM
4.0
3.0
3.6
1.0
Low
High
Low
High
1:50 AM 2.2
8:16 AM 7.2
3:38 PM -1.9
10:16 PM 3.8
40
99
20 minute difference; 150km/20 min = 125 m/s; sqrt(9.8m/sx1500m = 121 m/s)
The End
Class Summary (it really does all fit together):
- position on earth, navigation
- water properties
- bathymetry (water depth; Geology)
- sea water, solubility (Chemistry)
- gasses & nutrients (oxygen & primary production; Biology)
- seawater density, temperature and salinity effects
- vertical structure of ocean (mixed layer, pycno, halo, and thermo –clines)
- specific heat of water
- solar radiation (where ocean circulation begins)
- air-sea heat budget (heat from ocean drives atmosphere)
- atmospheric circulation
- Coriolis force
- tropical cyclones and El Nino
- direct wind driven Ekman flow (upper ocean mixed layer)
- large scale wind driven circulation, sea level set up, subtropical gyres
- western and eastern boundary currents (coastal upwelling/downwelling)
- thermohaline circulation
- waves (development, propagation, dissipation)
- tides (forces, time scales, amphidromic systems, Kelvin waves)