Tides
Tides are waves
Gravity waves
Restoring: Surface
Wind
waves
tension
Long period
waves
Tides
Tsunami
Disturbance:
Seiche and storm surge
Sun
and
moon
Energy
Wind
10
1
0.1s
1s
10-1
10-3
10-2
Wave frequency (s-1)
10s 30s
10-4
5min
12h 24h
Period
0.017m 1m 10m
10-5
1000m
Wavelength
Amplitude [m]
Wind
waves
Amplitude [m]
Tides vs wind waves
2
0
-2
0
50
100
150
Time [seconds]
200
2
Tides
0
-2
0
10
Time [days]
20
30
Tides are
✤
the longest ocean waves.
✤
have wavelengths of up to 12,000 miles.
✤
caused by the gravitational forces and motion of the
Earth-moon-sun system.
✤
never free of the forces that cause them -- they are
forced waves.
Using the force
Acceleration:
is a change in velocity (speed
and/or direction)
Looking down
from space, need
an acceleration
towards center to
move around the
circle.
Using the force
Acceleration:
is a change in velocity (speed
and/or direction)
On orbiting rock, feel
motion away from the
center.
Inertia / centrifugal
“force”
Earth-Moon system
rotates around center of gravity
However the earth is 81 times heavier than moon
Center of gravity
Simplest starting point
To start with
Consider the Earth as a ball uniformly covered by water.
(i.e., no land).
Consider just the Earth
and Moon.
Earth-Moon system
Gravitational forces want to pull the earth and moon
together.
but
because of inertia from the rotation of
the Earth-moon system
the distance between the Earth and moon is
constant.
Tide producing force
Centrifugal or Inertial
“force” is the same
everywhere on or within the
Earth.
Earth’s Center
Gravitational force
of the moon decreases with
the square of the distance
from the moon.
Forces balance for the planet as a whole,
but not on the surface.
Tide producing force
Extra gravity
Extra inertia
Difference between gravity and inertia produces a
net force on the oceans (and land).
Earth’s Center
Tide producing force
Vertical part of net force
(gravity minus inertia) is
much weaker than Earth’s
gravity, but horizontal part
moves water resulting in
tidal bulge (~2m high).
Almost two tides a day
Earth spins on it’s axis once a day.
Moon orbits earth once a lunar month.
H
H
24 hours later
H
24 hrs 50 min
Moon’s orbit
is not in the same plane as the Earth’s equator.
Over a month the moon cycle between 28oN and
28oS, affecting heights of low and high tide.
Now include the sun
✤
Sun is 27 million times larger than the moon.
✤
Sun is 368 times further from the Earth than the moon.
✤
Upshot is the sun’s affect on tides is about 40% of the
moons.
Spring and neap tides
Spring tide
higher highs
and
lower lows
Neap tide
Dynamic Tidal Theory
Real tides are more complicated than equilibrium tides
- Presence of land
- Tides travel as shallow-water waves
- Bottom friction
Coriolis Force
Types of tides
Amphidromes
✤
Result from combination of basin geometry and
Brooks/Cole
Coriolis.
Main semidiurnal
Main diurnal
Bay of Fundy (Canada)
has the world’s largest tides, up to 50 ft .
Funnel shaped bay has the same naturally resonates
(seiches) at the same period as the lunar tide.
Storm surges
Tides influence biology
Internal tides
Tidal energies
3.2 TW
(M2 = 2.5 TW)
Earth
Tides 0.2 TW
0.5 TW
0.02 TW
Atmospheric
Tides
11 TW
TW
Barotropic Tides: 3.5 TW
1 TW
Internal Tide
Local
Dissipation
e
av
w m
al ru
rn ct
te e
In sp
2.5 TW
Bottom
Friction
Boundary
Dissipation
Kρ >> 10-5 m2 s-1
Interior Dissipation
Kρ ~ 10-5 m2 s-1
Maintain Ocean Stratification
required Kρ = 10-4 m2 s-1
Some key ideas
✤
Tides are the longest ocean waves, and can have
wavelengths of up to 12,000 miles.
✤
Tides are shallow water waves.
✤
Tides are caused by the gravitational forces and motion of
the Earth-moon-sun system.
✤
Presence of land, and bottom friction makes global tidal
patterns complicated.
✤
High tides generally occur almost twice a day.
✤
Spring tides occur almost twice a month.
✤
Tides influences many things.