Waves-Lecture Notes

Ocean waves are on one hand infinitely complex in their behavior and form, and on the other hand, follow simple rules of physics. For this lecture, we will first summarize the physical attributes of ocean waves and then focus in on the various types.

General wave terminology

The height of a wave is the vertical measurement from its crest (highest peak) to its trough (lowest valley). The wavelength is the horizontal measurement between successive crests or troughs. The frequency is a measure of the number of waves that pass a stationary point in a given amount of time, usually one second. The period is the amount of time it takes successive waves to pass the same point, such as a stationary pier piling. In other words, if a wave passes a particular pier piling and you start your stopwatch, you would stop it when the next wave passes the same spot.

Motion of surface ocean waves

Common ocean waves form from wind blowing across the surface, disturbing the atmosphere-ocean interface. For wind waves to form, the wind has to be strong, and blow form a long length of time, known as the "duration." The distance that the wind steadily blows is called the "fetch." As the wave is being propelled, it is referred to as a "forced wave." Once the wave gets momentum and moves on its own, it is called a "free wave." It is important to realize that although it looks like waves are "moving" across the surface, the individual water molecules actually only move in circles, or orbits. Out on the ocean, the wind pushes the water up and then either the surface tension (for small waves) or gravity, pulls the water back down. Because the molecules slide into the trough and are pushed a bit by the crest, the actual motion is an enclosed circle. As you look down in the water column below the surface, the circular path that a water molecule moves becomes more squashed in the vertical direction. Eventually, the water molecules only move in a horizontal, back and forth motion. The lowest point in which the water molecules moves is called the "wave base." Interestingly, the wave base is determined by the wavelength, not the height, and is ½ of the wavelength. If the depth to the seafloor is less than 1/20 of the wavelength, all of the water motion is horizontal.

Now for some fun stuff! The longer the wavelength, the faster the wave moves through water. We measure the speed of waves by the following formula: S=L/P where S=speed in meters per second, L=wavelength in meters, and P=period in seconds. In the open ocean, where the depth is greater than ½ of the wavelength, the speed can be calculated from the period by this formula: S=gP/2B where g=acceleration from gravity, or 9.8 meters per second2, and B=3.14. If you merge the constants, you can rewrite the equation as S=1.56P.

Another major motion of waves is "refraction" or bending of waves. Simply, the energy of the wave may drag along the bottom as it approaches shallow water, slowing the forward motion and causing a bending of the overall wave front. Similarly, waves refract around islands because they feel the drag. Remember, the drag is felt when the water depth is ½ of the wavelength. As the wave continues into shallower water, the slowing causes the wavelength to decrease, while the height is unchanged (or even pushed upward). When the height to length ration reaches 1/7, the wave is too steep, and breaks, forming "surf."

In addition to refraction, waves can also be "reflected". That is, waves can be "bounced" off of an object, such as an island or sea cliff, much like light is reflected off of a mirror. As two (or more) waves moving in different directions meet each other, the troughs and crests are added together. If the trough of one wave meets the trough of another wave, if forms a very deep trough. Likewise, if the crest of one wave meets the crest of another wave, if forms a very high crest. If the trough of one wave meets the crest of another, they cancel out.

Types of waves

Capillary waves-the smallest of wind-driven waves with wavelengths less than 1.73 centimeters.

Wind waves-described above, driven by winds. If they pass over water greater than ½ of the wavelength they are called "deep-water waves", otherwise they are "shallow-water waves."

Seismic sea waves or Tsunamis-driven by large displacements of water, such as by underwater avalanches, breaking off of icebergs, or vertical seafloor movements along faults.

Seiches-a wave that sloshes back and forth across an entire basin, such as in a bathtub. This is a fair analogy for tides (see tides below).

Rogue wave-anomalously large wave made by adding together the heights of several waves which meet simultaneously (constructive interference).

Internal waves-formed at the contact between watermasses of different densities, such as at the base of the pycnocline. We know they exist, but don't know why…the truth is out there!

Sea-the term for when the surface of the ocean is riddled with wind waves forming. As wind waves move away from the "sea," they regulate, forming linear swells.

Tidal wave-TRUE tidal waves form when the incoming or outgoing tide is forced into a narrow area forming a wave front. True tidal waves are also called tidal bores.

Additionally, you should note that the various waves have distinctly different wavelengths.

Tides

One of the most peculiar types of waves is the common tide. Unfortunately, like most subjects in this class, we can only skim the surface of tides. Tides are ultimately driven by the gravitational pull of the moon, and to a lesser degree, the pull of the sun. If the Earth was a simple ball of water, we would see two bulges, or wave crests, aligned with the position of the moon. As the Earth rotates, the bulges do not move with respect to the moon, but pass by stationary points on the Earth. In this ideal model, each spot on the Earth (except the poles) would receive two high tides (crests) and two low tides (troughs) each day. But, we are not on an ideal Earth…Many complications such as the Coriolis Effect, shape of the ocean basins and shoreline, differences in the distance between the Earth and moon, etc., affect the timing and heights of the tides.
With this said, there are three basic types of tides. If only one high tide and one low tide occur, the tides are "diurnal." If an area receives two similar high tides and two similar low tides in one day, the tides are "semidiurnal." In California, we have two high tides and two low tides, but there are big differences between them. This situation is called "mixed tides." Two final terms are "spring" and "neap" tides. Spring tides are when the moon is closest to the Earth and the tides are high HIGH and low LOW. Neap tides are when the difference between the high and low tides is not so great.

Key Points:

1. The height of a wave is the vertical measurement from its crest (highest peak) to its trough (lowest valley). The wavelength is the horizontal measurement between successive crests or troughs. The frequency is a measure of the number of waves that pass a stationary point in a given amount of time and the period is the amount of time it takes successive waves to pass the same point

2. Wind wave height is determined by the strength and duration of the wind source. Initially, the waves are "forced," later they move as "free waves."

3. Water molecules within a passing wave move in enclosed orbits.

4. The orbits become more squashed vertically with increasing depth. Wave base is the depth in the ocean equal to ½ of the wavelength. If the water depth is less than 1/20th of the wavelength, all the motion is entirely horizontal.

5. Waves refract or bend because of friction due to drag. In addition to bending, the drag causes the wavelength to decrease. When the height to length ration reaches 1/7, the wave is too steep, and breaks, forming "surf."

6. In addition to refraction, waves can also be "reflected."

7. Waves originating from different sources can cross each other. The energy reflected in the crests and troughs is added (crest and crest or trough and trough) or subtracted (crest and trough).

8. Capillary waves are the smallest of wind-driven waves with wavelengths less than 1.73 centimeters.

9. Wind waves are driven by winds. If they pass over water greater than ½ of the wavelength they are called "deep-water waves", otherwise they are "shallow-water waves."

10. Seismic sea waves or Tsunamis are driven by large displacements of water (e.g., underwater avalanches, breaking off of icebergs, or vertical seafloor movements along faults).

11. Seiches are waves that sloshes back and forth across an enclosed basin.

12. Rogue waves are anomalously large waves made by adding together the heights of several waves which meet simultaneously (constructive interference).

13. Internal waves form at the contact between watermasses of different densities.

14. The term sea refers to the area of the ocean riddled with forming wind waves.

15. TRUE tidal waves form when the incoming or outgoing tide is forced into a narrow area forming a wave front. True tidal waves are also called tidal bores.

16. Tides are driven by the gravitational pull of the moon, and to a lesser degree, the pull of the sun.

17. Many complications such as the Coriolis Effect, shape of the ocean basins and shoreline, differences in the distance between the Earth and moon, etc., affect the timing and heights of the tides.

18. Diurnal tides are one high tide and one low tide in a day.

19. Semidiurnal tides are two high tides and two low tides in a day, with the highs being roughly similar and the lows also being roughly similar.

20. Mixed tides refer to two high tides and two low tides in a day, but there are big differences between them.

21. Spring tides occur when the moon is closest to the Earth and the tides are high HIGH and low LOW. Spring tides occur year round (twice a month), not just in the spring

22. Neap tides are when the difference between the high and low tides is not so great.

WWW Sites:

http://www.humguide.com/weather.shtml

Site to get lots of links to Humboldt County marine (and weather) conditions.

http://www.nws.fsu.edu/B/buoy?station=46022

Bouy off of the Eel River

http://www.opsd.nos.noaa.gov/tides/westHB.html

Tides for Humbodt Bay, in month by month listings.

http://tbone.biol.sc.edu/tide/tideshow.cgi?site=Humboldt+Bay%2C+California

Another good site for tides in Humboldt Bay.

http://www.geophys.washington.edu/tsunami/intro.html

Site for lots of Tsunami information.

http://cwis.usc.edu/dept/tsunamis/

More tsunamis, including MOVIES!!

http://www.jodc.jhd.go.jp/online.html

Site for data from the Japanese Oceanographic folks.

http://www.amsci.org/amsci/articles/95articles/bjkorgen.html

Good site for an informative article on seiches.

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