Ocean Waves and Tides (Chapters 10&11)

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Lecture Material for 10/24/00


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.
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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.

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