INTRODUCTORY
OCEANOGRAPHYINTRODUCTORY
OCEANOGRAPHY
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In the first part of the lesson on ocean waves, we will discuss the various ways in waves are classified, why wave phase speed is a function of either the length of the wave or the depth of the water, and how a chaotic sea is dispersed into swell.
Ocean surface waves propagate horizontally along the air-sea boundary. They are described as being orbital progressive waves to distinguish them from transverse waves or standing waves. They are orbital because, as the wave form passes a certain point, the water particles under the wave move with orbital paths. They are progressive because the wave form moves (progresses) horizontally from one location to another. You can see this clearly in Fig. 10.1, where a wave moving from left to right causes the seagull to rotate in a complete circle with the passage of one complete wave. You also can observe it if you tie a ribbon to the middle of a rope, attach the rope to a door handle, and create a series of waves along the rope by moving your hand up and down. As you move the rope up and down and watch closely, you will see the wave progress along the rope and the ribbon moves in an orbital path. Like the water surface, the rope is the medium upon which the wave progresses. Note in Fig. 10.3, that these orbits extend below the surface of the water. We will learn later why the radius of the orbits decrease with depth.
The
ideal ocean surface wave, as can be seen in Fig. 10.2 to the right,
is sinusoidal (with crests and the troughs having identical shapes
and the wave having one fixed wavelength) and orbital progressive,
with water particles under the wave moving in orbital paths that make
one complete cycle with the passage of one complete wave. On a
spatial (or distance) scale (usually measured in meters), the
horizontal distance between two adjacent crests (or troughs, for that
matter) is defined as the wave length
(L) and the vertical distance from the top of the crest to
the bottom of the adjacent trough is defined as the
wave height (H). On a temporal
(or time) scale (usually measured in seconds), the time that it takes
for two consecutive crests to pass a fixed point is defined as the
wave period (T). The inverse of
the period is the wave frequency
(f), which is a measure of the number of times one
complete wave will occur per unit time [with dimensions of cycles
per second -- where 1 cycle per second is defined as 1 hertz
(Hz)]. Finally, the speed with which a wave crest moves
horizontally across the ocean surface is defined as
wave celerity (c) or phase speed,
and is usually measured in meters per second (not shown in the figure
above).
Actual ocean waves do not, of course, have a sinusoidal shape and rarely are found with a single wavelength or wave period. In fact, the ocean surface is quite chaotic and made up of many component waves of different periods and directions combining to produce what we know as "sea". And when they do appear more as individual waves, as in the case of ocean "swell", their crests are more "peaked" and troughs more "cantilevered" than the ideal wave (somewhat like the wave shown in Fig. 10.1). We will learn later how ocean waves change from "sea" to "swell".
Waves can be classified in at least four related ways (Water Depth; Method of Generation; Wave Period; Relationship to Generating Force) as described in more detail below:
In general, wave celerity (c) is directly proportional to both L (or T) and to water depth (d), or
and are called transitional waves or intermediate depth waves.
How can we say that c a T if c = L/T (doesn't this imply that c is inversely proportional to T)? Also, how do we show that c a d? To find out, link to celerity - the mathematical manipulation of the wave celerity equation also can be seen on p. 242 in the textbook, an addition to the text that I requested during my review of the manuscript. I will not hold you responsible for showing this on an exam, but many of you have asked the question and I though you would like to see the answer.
Often,
we simplify this intermediate depth wave equation by going to the two
extemes of depth and by showing that waves are either only a function
of L (or T) or only of depth (see Fig. 10.6 to the right).
This means that waves with longer wavelengths (wave periods) will travel faster across the ocean surface.
This means that as water depth decreases, waves slow down.
Waves also may be classified by the method of their generation. Wind waves are generated when wind blows across the water surface and momentum is transferred from the wind to the water. Impact waves (such as Tsunamis) may be generated on the water surface by earthquakes or any other forms of impact (even, on a small scale, by a rock thrown into a pond).
As shown in Fig.10.5 below, waves may be classified by wave period. Note in this plot of the cumulative energy distribution in ocean waves, that the principle generating forces and principle restoring forces change as the period of waves increase. The smallest waves ("ripples" or capillary waves) have periods < 0.1 sec and are generated by a small puff of wind and, because they are so small (are molecular waves), are restored by surface tension (see Fig. 10.8 for a picture of this wave and its rapid generation with small amount of wind -- you can create one in your coffee cup blowing to cool the liquid). The most common waves ("gravity waves") have periods between 1 sec and 30 secs (with the most energy centered around 10 secs), are generated by the wind and storms, and are restored by gravity. Waves with periods greater than 5 min periods are "long waves" which are generated by intense storms and by earthquakes, and restored by gravity and the coriolis force. The longest waves shown are the 12 hr and 24 hr tides, generated by the sun and moon and restored by bottom friction and the Coriolis force.
Waves that run independent of their generating force (such as impact waves) are called free waves, while waves that are dependent upon their generating force for their continued existence (such as the tides) are called forced waves. Some wind waves being actively generated (in an intense storm, for instance), as we will find out later, may be classified as free/forced waves.
Ocean
waves are very difficult to measure for several reasons. The sea is
very confused and irregular, and the wave gauges discussed in the
last section may only measure wave height or wave height and wave
direction. And, because these gauges are generally fixed in space, we
only obtain a time record of wave motion at one point. To measure
waves over a large area requires a satellite or a high flying
airplane, and now we have a very complicated data set to analyze
because it varies both in space and time.
Shown on the left is a pitch/roll wave buoy that I built to measure wind-wave height and direction. The buoy is being prepared for launching in the Gulf Stream from our research vessel (RV Cape Hatteras) for a study of the interaction between waves and currents.
As we learned above, the celerity (c) of a deep water wave is directly proportional to the length (L) or period (T) of the wave; therefore, longer waves travel faster than shorter waves. This has some interesting consequences. As a first example, suppose you tossed a large rock into a pond. The immediate result of this is a turbulent splash and the creation of many impact waves of various wavelengths all mixed up together. After just a few seconds, however, if you look closely you will see concentric rings of circular waves propagating away from the center and you will note that the longest waves are out in front of the next longest wave, which is out in front of the third longest wave, etc. In other words, the longest waves outrun the shorter waves and order is created out of chaos. This sorting of waves by wavelength is called wave dispersion.
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A real 'ocean' discussion of wave dispersion |
As
a second example, let me relate dispersion to an event with which you
all are probably familiar - - the New York Marathon. Many thousands
of runners enter this event and crowd at the starting line. In this
group are runners with a wide range of running abilities, but the
fastest runners are "seeded" and given positions at the front. When
the gun sounds the runners begin to move. The fastest runners take
the lead and begin moving away from the group, but it takes a long
time to get the whole group moving (in fact, those at the back do not
cross the starting line for 20-30 min). After an hour or so the group
has dispersed into a long string of runners, or groups of runners,
and this dispersion continues long after the first runners cross the
finish line in about 2.5 hrs.
It is by this process that ocean "swell" leaves behind the confused "sea" present in a storm's active wave generation area and outruns the storm that creates it (as shown above in Fig. 10.11). Therefore, the first swell to arrive at some distant point will be the longest, and as the storm gets closer, the wavelength and period of the arriving swell will decrease.
Do you understand how you could use the knowledge of wave dispersion to warn you of an approaching hurricane?
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