Waves

I. Introduction

A. By far the most important cause of waves on the ocean is the wind.

B. We will only briefly mention tsunami(seismic sea waves) episodic or rogue waves, and internal waves.

 

II. Terminology of wave forms 

A. Still water level = the undisturbed water level

B. Crest = the top of the wave

C. Trough = the low spots between crests

D. Wavelength (L) = the distance between successive crests, troughs or other equivalent spots on a wave

E. Wave height =  vertical distance from the bottom of the trough to the top of the crest

1. Wave height is determined by fetch, wind duration and wind speed.

F. Wave amplitude = vertical distance from the still water level to the top of the crest

G. Period  (T) =  time required for two successive crests or troughs to pass a fixed point

 

III. Types of wind-driven waves

A. Capillary waves = small amplitude waves (<2 cm) whose motion is modified by surface tension which provides the restoring force to bring the sea surface back to still water level after capillary waves have raised it. (Surface tension is the tendency for H2O molecules to arrange themselves so they present the smallest surface area to the air.)

1. These are the first stage in the development of the larger gravity waves.

B. Gravity waves  =  wind-generated waves for which gravity provides the restoring force.

1. Gravity pulls elevated wave form back down and water gets forced out from under it causing the next crest to form.

2. Each successive crest and trough overshoots the equilibrium  (still water level) and the cycle of ups and downs continues.

 

IV. Wave motion and speed

A. Waves of oscillation  =  within the wave the water molecules follow a circular to elliptical orbit and don't actually move along with the wave form.  Mainly deep water waves.

B. Waves of translation  =  within the wave the water molecules move forward along with the wave form.  Form at the beach where waves begin to break.

C. The magnitude of the orbit of the individual water molecules decreases with depth and orbital motion ceases entirely at a depth equal to 1/2 of the wavelength. This depth is called the wave base.

 

1. The nature of the ocean bottom has no effect on a wave unless the water is shallower than 1/2 a wavelength.

2. In shallow water, friction along the sea bottom slows waves and changes their circular orbits to elliptical ones.

D. Velocity or speed of a wave

 

           distance traveled     wavelength      L

Speed (C)=------------------- = ------------ =   --

           time to travel it       period        T

 

1. Once a wave has been generated its speed may change, but its period does not as this characteristic is determined by the generating force.

2. Deep-water waves (waves of oscillation)

a.  Deep-water waves occur where the water is deeper than 1/2 the wavelength of the waves.

b. In deep water the velocity of a wave is a function of wavelength

c. Waves are created in storm centers or by the steady winds of the westerlies and trades. Near the storm center or in the region where waves are being generated, the sea appears chaotic and jumbled with lots of different sizes of waves all occurring in the same place.  As waves move out away from this area they experience sorting or dispersion  because the longer wavelength waves travel faster than those with shorter wavelengths.

1) The faster, longer waves gradually move through and ahead of the slower, shorter waves and the sea becomes calmer and more homogeneous.  The longer they travel, the more distinct becomes the separation.

2) SWELL is the term used to describe well-sorted, uniform, long  waves.

d. Observation of groups of waves or wave trains shows that the leading wave soon dissipates because it must initiate the orbital motion in "untouched" water so it soon runs out of energy.  At the same time a new wave is continuously generated at the back of the wave train where orbital motion stops and where extra energy is released.

e. Obviously this indicates that the individual waves travel faster than the wave train or a wave could never make its way up through the pack.

1) Individual waves move at twice the velocity of the train.

3. Shallow-water waves (waves of translation)

a. As deep-water waves move into shallow water the water particle orbits become flattened into ellipses as the waves begin to "feel bottom". Therefore, the longer waves feel bottom sooner and are slowed down the most.

b. Waves travelling in water shallower than 1/20 the wavelength are considered to be shallow-water waves and their speed is determined only by water depth.

1) The shallower the water, the slower the speed

                        C  =  3.13 √ D

 

V. Other important properties of waves

A. Superposition of waves

1. When waves moving out from one storm center meet up with waves generated by another source  the energy carried by these waves interacts to produce a net change in the elevation of the sea surface.

2. It is an interesting characteristic of waves that the movement of two such individual wave trains is completely independent of and unaffected by that of the other wave train. Even when passing through the same area at the same time, they behave as if the other one weren't there.

3. As a result, the change in the elevation of any region of the sea surface is a result of the combined effects of all the wave trains passing through that region at a given time.

4. In other words, the resultant displacement  =  the sum of all the individual displacements.

5. This phenomenon is called superposition of waves.

6. The effects of the interfering wave trains are said to be constructive or additive if the crests and troughs generally coincide and the amplitudes of the crests and troughs increase.

7. If the crests of one set of waves coincide with the troughs of the other set the interference is said to be destructive and the amplitudes of the crests and troughs are decreased.

8. When two sets of waves with slightly different wavelengths and approximately the same direction enter an area at the same time they produce alternating patterns of small and large waves and they sometimes interfere constructively and sometimes destructively. This effect is called surf beat . 

B. When waves approach the coast and enter shallow water  they are refracted and their energy is concentrated on headlands and dispersed in embayments.  The longshore current is also generated.

C. Diffraction is also associated with waves as they enter shallow water.

1. All points on a wave serve as point sources for the generation of new smaller waves that radiate out in all directions away from the wave. Diffraction is caused by the spread of wave energy sideways to the direction of wave travel.

2. So when a wave enters a harbor through a breakwater or a narrow channel, the new waves fan out in all possible directions.  Part of the wave is stopped by the obstacle so the part of the wave that passes through now has no elevated sections at its ends, so when it falls back down new waves form going out in all directions.

D. In shallow water when waves impact on a vertical barrier their normal orbital motion is disrupted and the wave is reflected back out the way it came in.  The resultant interference between incoming and outgoing waves yields water motion that is up and down.

E. When wave enter shallow enough water they break because the motion of water in the lower part of the wave nearest the bottom is slowed by friction so that the motion of water molecules in their orbits in the crest of the wave is faster than its supporting portion at the bottom. Therefore, the wave collapses forward and breaks. The nature of the underlying beach slope  determines which type of breaking wave forms in the surf zone.

1. Plunging breakers =  narrow, steep beach slopes

a. Breaking crest plunges down towards the base rather than spilling slowly down the face.

2. Spilling breakers  =  wider, flatter beaches where the wave energy is extracted more gradually from the wave.

a. Breaking crest spills down the face a bit at a time.

3. Surging breakers  =  very narrow steep beach

a. Waves build up and break right at the shore.

 

VI. Episodic or Rogue Waves

A. Large waves can suddenly appear at sea unrelated to local conditions. These are called episodic or rogue waves. These are abnormally high waves that occur due to a combination of intersecting wave trains, changing depths, and currents. We don't know much about these and they don't exist for long and they can and do swamp ships, thereby removing any witnesses.

1. Occur most frequently near the edge of the continental shelf in water about 200 meters deep.

a. The Agulhas Current, sweeping down the east coast of South Africa, is noted for such waves.

B. Heights of 20-30 meters and have been recorded up to 35 meters.

1. In 1995 the Queen Elizabeth II was struck by a 29-meter (95 foot) rogue wave.

2. In 1995 an oil rig in the North Sea was hit by an 85-foot tall wave. The waves around it were less than half as tall.

C. These waves are now suspected to be the cause of many unexplained disappearances of vessels and are much more common than originally thought. Research in early 2001 revealed that in a three week period during which satellite data were collected, 10 rogue waves occurred in various parts of the world (all more than 25 meters).

 

VII. Tsunami -  Caused by displacement of the seafloor due to earthquakes or explosions.

A. Also called seismic sea waves.

1. Formerly called tidal waves, but these waves have nothing to do with tides.

B. Have extremely long wavelengths (100-200 km),long periods (10-20 minutes) and rapid velocities (700-800 km/hr).

1. Since the average depth of the oceans is about 4000 m, this depth is less than  1/20  the wavelength of these waves so they behave like shallow water waves. Therefore, their speed is determined by the ocean's depth. They may be refracted, diffracted, or reflected in mid-ocean just like all shallow water waves.

C. Wave height is usually only a few meters in the deep ocean.

         

VIII. Internal Waves

A. Waves on the ocean surface occur at the boundary between the air and the water.  Both air and water are fluids, but they vary greatly in their density.  Therefore, it can be said that surface waves form along a boundary between two fluids of different density.  Beneath the surface of the ocean there are also fluid layers of varying density.  The density differences are small, but waves form along this boundary, also.  such waves are called internal waves. 

B. These internal waves have large amplitudes, long wavelengths, and low velocities.

C. Believed to be triggered by :

1. Passage of the surface layer over a more static lower layer in the same way the wind produces surface waves.

2. seismic disturbances

3. long-term wind changes

4. tidal forces.

D. Dangerous for submarines because they can push them down

to great depths very rapidly and perhaps overwhelm their ability to cope with pressure changes.