Key Notes from 10/19/00
Ocean Circulation
1) Upwelling occurs in regions where surface waters diverge.
Coastal upwelling (CA) occurs as surface water is forced offshore.
Deep waters rise to replace diverging water.
2) El Nino is a climatic phenomena which occurs every 3-8 years
in the equatorial Pacific. During an El Nino, surface wind patterns
and currents change direction and allow warm water to flow eastward towards
S. America. This reversed circulation eliminates upwelling in equatorial
Pacific and coast of Peru.
_______________________________________
What is a Wave?
Dictionary says: "a disturbance or variation that transfers energy
progressively from point to point in a medium. The form is that
of an
elastic deformation ..."
In the ocean, a wave produces circular motion of water but the water
does not move forward with wave.
Wave Production/Dissipation
There are two forces which make and break waves:
1) Disturbing Force eg wind, earthquakes, moon's
gravitational pull, landslides
2) Restoring Force usually gravity
How do we classify waves?
Basic measures of a wave are the wavelength (L), the wave height (H),
the velocity of the wave (normally use celerity as velocity implies direction
but we'll stick with book notation here) (V), and the frequency of the
wave (v) which is the inverse of the period (T)
T = 1/v (note capital V is velocity and small v is frequency)
Since we are talking about different types of waves propagating through sea water, there are some easy equations which can be used to better understand wave propagation in sea water.
One easy characteristic of a deep water wave (water depth > 1/2L) to
measure is the period (T) (time for two sucessive wave crests (or troughs)
to pass a certain fixed point. Knowing the period (T) we can estimate the
velocity of the deep water wave (V)
V = 1.56T (in meters per second)
Maximum wave heights (H) of deep water waves are 1/7 of the wavelength. Reasonable estimate of largest wind generated storm waves: Period = 12 seconds, wavelength = 225meters, V= 1.56 (12 seconds) = 18.8 meters/second = 42 mph
Max height = 1/7(225m) = 32m = 105 ft (about 35 yards) Most wind waves are deep water waves (d>L/2) which travel at a speed which is = 1.568( the period T). Longer wavelengths travel at faster speeds.
Waves tend to group themselves by wavelength (and speed). These groups are called wave trains which actually travel at 50% of the speed of the individual waves.
Wave Interference
When one wave train overtakes another, the resultant surface waves
are distorted relative to either train.
a) Constructive interference occurs when crests
and troughs are roughly in phase.
b) Destructive interference occurs when the waves
are ~180 degrees out of phase
If the wave is a shallow water wave (water depth < 1/20 of L), V=
3.1 x water depth0.5 (meters per second) As a deep water wave
approaches the shore, the period remains constant. As the wave "feels bottom"
the frictional drag of the wave on the bottom slows the wave down. In order
to maintain period, the wavelength must decrease. The waves tend to bunch
up against one another as they approach the shore. In addition, the heights
of the waves will increase as the deep water waves approach the shore.
The wave will break when water depth is 4/3 of the wave height. (a wave
3m high will break in 4m of water).
BENDING AND BOUNCING WAVES
Refraction is the tendency to bend a wave which approaches shore at an angle. The human wave in Beaver stadium can be viewed as a refracted wave. Wave velocity in the upper sections is greater than that near the field.
Diffraction occurs when a wave train runs into an object(s) which interrups the train. In some cases, the interruption will set up a new set of waves which are the diffracted waves. Reflection of the incident wave occurs when a wave impacts a barrier head-on. Under these special conditions, much, if not all, of the incident energy is reflected. In some special cases, a standing wave will form.
MONSTER WAVES (CHAPTER 11)
Storm Surges
As a tropical storm approaches land, the low atmospheric pressure tends
to draw water up into a mound near the center of the storm. As the mound
approaches the shore, its height increases (like deep water waves) until
it ultimately breaks on shore. The damage associated with storm surges
generally outweighs that resulting from the high wind velocities.
Tsunami
A Tsunami (word originates from the Japanese words for a harbor and
wave) results from a vertical displacement of earth in the ocean. The most
common form of displacement is along faults and generally accompanies some
severe earthquakes accounting for the label of a seismic sea wave = Tsunami.
These waves have extremely long wavelengths (<200km) and are therefore
shallow water waves (average depth of ocean = 5km which is much less than
200km/2 = 100km). They travel at speeds approaching 200 meters per second.
These waves are nearly imperceptible in open ocean as their heights are
only 60cm. However, as the Tsunami approaches land, the height can grow
to about 30m. The waves are extremely destructive. Fortunately, a warning
system was put into place in 1948 to alert countries which are about to
be hit by a tsunami.
Tides (Chapter 11)
Tides are very long waves which are set up by a combination of gravitational
and centripetal forces acting on the ocean. Tidal forcing between two celestial
bodies on objects on the surface of the earth:
Tidal Forcing = K(m1m2/r3)
All bodies on the surface of the Earth experience the inward attraction
associated with gravity. When you consider Earth+moon as a single rotating
entity, all objects at surface of Earth experience an inertial force directed
away from the moon. In addition to the inertial force, there is the straight
gravitational force associated with the moon on all Earthbound objects.
Because objects on the far side of the Earth are further away from the
moon, they experience a slightly smaller gravitational pull than those
situated on the side of the Earth which faces the moon. When you combine
both the inertial and gravitational components acting on the ocean, you
see that ocean will form two water bulges; one facing the moon and one
directly opposite the moon. The tides associated with the moon are called
the lunar tides. We need to remember that the moon is not in a stationary
orbit around the earth. The lunar cycle is 29.5 days.
To further complicate the tidal cycle, we need to
consider the solar influence. Similar inertial/gravitational forces exist
between the sun and the Earth but because the sun is so far away, the effects
are only about 50% of the lunar effects. Never-the-less, the solar tidal
cycle is important. The net result of the solar cycle is to modulate the
amplitude of the lunar cycle. The alignment of the three celestial bodies
(Earth, sun and moon) dictate the amplitude and timing of the tides. When
all three bodies are aligned, the tidal variations are largest and are
called SPRING tides. When the three bodies form a 90 degree angle,
tides are minimal and called NEAP tides. There are three types of
tidal variations at any specific point in the ocean:
1) Diurnal tides have one high and one low in a
given 24 hour period.
2) Semi-diurnal tides have two highs and two lows
for a 24 hour period
3) Mixed tides have one high and a low which have
amplitudes which are midway between neighboring highs or lows.