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 Geography 104 - “Physical Geography of the World’s Oceans”
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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.
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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
Geography 104 - “Physical Geography of the World’s Oceans”
first order explanation of tidal patterns
gravitational attraction
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
diurnal tide + semidiurnal tide mixed 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)
20 Jan 25 30 1 Feb 5 10 15 20 25 1 Mar 5 10
16 Jan – 11 Mar 2007
1
spring-neap tides Santa Barbara (tidal currents a few cm/s)
diurnal tide semi-diurnal tide
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
http://home.xtra.co.nz/hosts/Wingmakers/Moons
earth & moon comparison
http://home.xtra.co.nz/hosts/Wingmakers/Moons
earth & moon distance
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
Centripetal acceleration
C
tide raising force = G + CG
CTRF
tide raising force
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
verti
cal
com
ponent
horizontal
component
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
at equator velocity = 442 m/s
to remain under moon tide wave would have to propagate 442 m/s eastward at equator
lunar day
5353
- 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)
21% variation in TRF due to changing earth-moon distance
3
declination of moon & tidal inequality
= max. angle above equator(always changing)
0 years18.6 years
4.65 years
9.3 years
moon’s changing declination
moon’s changing declination
Earth
0 years
moon’s changing declination
(blue)
(yellow)
0 years
4.65 years
moon’s changing declination
153x106 km 149x106 km
~8% variation in TRF due to changing earth-sun distance
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
CCW
CW
tidal amplitude
tidal phase
amphidromic system – M2 tide
Kelvin Wave – northern hemisphere
Kelvin waves and amphidromic systems
Kelvin waves and amphidromic systems
tidal current
Coriolis pressure
Tides for Santa Monica, Municipal Pier starting with December 5, 2008.Day High Tide Height % Moon /Low Time Feet VisibleF 5 High 3:37 AM 4.1 40 5 Low 9:09 AM 2.9 5 High 2:01 PM 3.7 5 Low 9:00 PM 1.0
Tides for Santa Barbara starting with December 5, 2008.Day High Tide Height % Moon /Low Time Feet VisibleF 5 High 3:57 AM 4.0 40 5 Low 9:27 AM 3.0 5 High 2:21 PM 3.6 5 Low 9:18 PM 1.0
F 12 Low 1:50 AM 2.2 99 12 High 8:16 AM 7.2 12 Low 3:38 PM -1.9 12 High 10:16 PM 3.8