Tides
Type of shallow water waves
Wavelength = _ circumference of earth (20,000 km)
- Shallow water wave
- Water depth < 1/20 wavelength
< 20,000km/20
Daily rise and fall of the sea surface
Caused by gravitational attraction between:
Equilibrium Theory of Tides (Newton)
Assumes earth covered by uniform layer of water
No effect from:
Interaction with the seafloor
Influence of basins (land)
Sloshing
- Contrasts to Dynamic theory of Tides (Laplace)
Tidal Forces
Gravitational attraction between 2 bodies
Proportional to mass of the bodies
Inversely related to the distance between the 2 bodies
Tidal generating force
= G(m1m2/r3)
G = universal gravitational constant
m1 and m2= masses of the 2 bodies
r = distance between the centers of the two bodies*
Earth-Moon attraction
Moon orbits Earth due to gravitational attraction
Why don’t they collide?
Additional force=
Centrifugal force — inertial force
= tendency for objects to continue to move in a straight line
Inertial Force
Force outward from the center of mass of the Earth-moon system
Earth 81x more massive than moon
Center of mass located within the Earth
Center of Mass (Barycenter)
Gravitational Tidal Forces
Tractive Forces
Inward pull of gravitational tide generating force and outward force of inertial force are not always balanced (equal and opposite)
- Forces generated by this lack of balance = tractive forces
Tractive Forces on Earth
Sum of the gravitational and centrifugal forces (tractive forces)
Creates 2 bulges in the ocean (~2m)
- At the center of mass — 0 tractive force
- On the side facing the moon- gravitational force = 1 bulge
- On the side away from the moon- inertial force = 1 bulge
Tidal Bulges
Solid Earth = small response to these forces (10-12")
Oceans and atmosphere = fluids
= greater response to forces (ocean = ~2m/ atm = miles)
Bulges tend to stay aligned with the moon as Earth spins
Earth turns beneath the bulges
Equilibrium Theory of Tides
Earth turns beneath the bulge
Crest = high tide
Trough = low tide
Moon is also moving- tidal crest follows that motion
- In the time it takes the Earth to make one revolution the moon has advanced
Equilibrium Tides
Additional complication
Moon does not orbit directly over the equator
Ranges 28 _ degrees above and below
- So, one region may see 1 high high tide and 1 not so high tide during a day
Add the Sun
Tide generating force of the sun also a factor, but less important than the moon
F = G(m1m2/r3)
Sun is 27,000,000x more massive than moon
Sun is 387 X farther away than the moon
(3873 = 58,000,000)
Affect of the sun
= 27 million/58 million
= .46
= effect of sun = 46% effect of moon (~1/2)
Sun also creates a tidal bulge, but smaller than the bulge from the moon
Solar Tides
Gravitational and inertial interactions between the sun and moon
- Smaller solar bulge follows the Sun (and Earth revolves under it)
Combined Tides
When sun-moon-Earth aligned (new or full moon)
Solar tide added to lunar tide
Max high tides and min low tides
Spring tides
When sun-moon-Earth at right angles (first and last quarter)
Solar trough coincides with lunar crest (and visa versa)
High tides not very high
Low tides not very low
Neap tides
Dynamic Theory of Tides
Equilibrium model- idealized
- Dynamic model- add landmasses, ocean basins, friction
~150 tide generating/tide altering forces- very complicated
Can’t predict tides mathematically
Tide charts based on studies of past patterns
Tides are shallow water waves
Speed is a function of depth
C= ˆ gd
Crest of the wave (tidal bulge) tries to stay below the moon, but friction slows it down
Basin Effects
Water can slosh back and forth in a basin
Tides can resonate across a basin, shape of the margins can affect the rhythm
Tidal Patterns
Equilibrium theory predicts 2 high tides per day
Semidiurnal tide (twice daily)
Also observe:
Diurnal - one high tide per day
Mixed — one high high tide and one low high tide per day
Tidal Range
Varies with the shape of the basin
- Extremes develop where inlets focus tidal energy
and
- Water resonates at frequency of tidal cycle
Tidal Bore
Front wave of the tide moving up an inlet or river
If the tide moves faster than the shallow water wave speed
Wave will oversteepen and break (spilling wave)
Tidal Friction
Bulge trying to stay aligned with the moon while the Earth rotates under it- friction
- Tidal friction is slowing down the rotation of the Earth
Slow process
~1/200 sec per 100 yrs
350 million yrs ago- 400days/yr
22hrs/day
4.5 billion yrs ago — 10 hr days
Tidal Energy
Incredible amount of energy in tides
Non-polluting
Renewable
Limitations
Limited locations- near area with large tidal range (all locations à
1% of current energy needs)
Expense
Effect resonance in the bay or estuary
Effect on marine life