1998 is the Year of the Oceans

3 March  1998 Class Notes

Date these notes last updated: 05/21/01

Announcements

Second Mid-Term Examination: Thursday, 19 March, Material covering Chapters 6-10 and class lecture notes.

Homework No.7 Critical Thinking Question No. 9-1 on page 250; due on 19 March.

Homework No 6  Critical Thinking Question No. 8-5 on page 229.   is due this coming Thursday,  March 5th.

Chapter Reading: Chapter 9

Critical Concepts: Critical Concept 11

Lecture Notes

Waves

The presence of ocean waves pounding the shoreline is the first “dynamic” process a person usually sees when he or she goes to the beach. The definition of “wave”, in my dictionary, is “To move back and forth or up and down in the air: branches waving in the wind”. Farther down in the list of definitions is the one pertaining to the ocean: “A ridge or swell moving along the surface of a large body of water and generated by the action of gravity or the wind”.

But lets be sensible: who really needs to go to a dictionary to find the definition of an ocean wave! We have all been on a beach, we have all seen waves, we have all been in waves, and some of us  have ridden, or tried to ride, a wave (surfing!). We know about waves at least qualitatively.

The scientific study of waves can begin with a very simple conceptual picture
of what a wave looks like. Your book, page 244 (Figure 9-1), shows profiles of ideal waves. If you look at these profiles you should recall (immediately, I hope) that an ocean wave looks just like a familiar wave you use in trigonometry: the sine wave (or cosine wave). Even now in calculus you will be revisiting the properties of sine/cosine waves. Later if you are in ocean engineering you will use sine wave functions to describe periodic events quite unrelated to ocean waves.

The “first order ” terms we use to describe a wave are wave length, period and height. Surfers in class will be very interested in these wave properties.

Before I move ahead on this subject, I want to put in a plug for a wonderful little paperback book on ocean waves called: "Waves and Beaches", by Willard Bascom, published by Doubleday in 1980. I also bought an earlier edition in about 1963 and have used it many times. Mr. Bascom's book is unique because of its very easy writing style and its hand-drawn illustrations (by Willard Bascom) . Mr. Bascom, an engineering by training, is an acknowledged expert in waves and you can see him personally describe waves in the Oceanus video series (go to reference desk, library, under my name to get the tape on Waves. During the lectures, I will be drawing a lot of material from Mr. Bascom’s book.

What causes ocean waves? Winds of course because they “touch” the ocean. This touching is also called air-sea interaction (oxygen exchange with the atmosphere is another kind of air-sea interaction). As soon as the wind makes physical contact with   the ocean, the water will move; advection (we learned earlier) is another word for the movement of the water.

As the wind gets stronger it will cause a miniature “ripple”in the wave: the wind pushes water to create a little high side on the face of the wave; this high side creates more area for the wind to "attack" the water.  Eventually the ripple spills over: you now have a wave, a miniature one, but a wave.

These small, miniature waves are called capillary waves by oceanographers. They are the “first” waves. They may get their start 1000s of kilometers out to sea where wind or a beginning storm begins to act (again, another form of air-sea interaction) on a smooth ocean. The ripples occur in a periodic way because when the ripple breaks the wind acts on the next parcel of water and so on.

Soon you have thousands to millions (or even billions) of small waves. If you are out on a ship or on a dock and see a group of capillary waves you would probably not really recognize them as waves because they would be only a few millimeters in height.

How fast does a wave “grow up”? The next time you are surfing on that
“really great one” or you go to the beach and see breaking waves, just remember that the wave started as a group of capillary waves way out in the ocean.

The process of creating what will eventually be a beach wave is a complicated. First, the wave needs time to grow; then different waves come together “interact” to generally reinforce each other, resulting in perhaps bigger and longer waves. If the winds stop, the waves don’t immediately stop, but may continue growing. Then, if the winds pick up, waves begin to grow faster again, with the little capillary waves being part of the “older” waves. As the waves move into shallow
water, other effects occur, such as the creation of “breaking” waves.

Then, finally, right at the beach, all the energy in the wave is dissipated as the wave rest peaks and then breaks followed by water rushing up the face of the beach. The last remnants of a wave on a beach is the foam or bubbly seawater you wade through on the beach.

Let’s look in more detail at the beach wave; then we will go to the open
ocean to examine  deep-water waves.

Shallow-water waves.

If you could “slice” the ocean with a gigantic kitchen knife and push one side away and look into the other side while the water was still moving you would see that the “moving” water is not all  moving in the same direction from surface of the ocean to the bottom. What you would see would be a series of circular (called orbital motion) paths being taken by the water. The first circle (or orbit) is the largest and its diameter is the height of the wave (from trough to crest). So, if you are a surfer and you see a 10 foot wave approaching, the diameter of the “circle” we have been talking about is 10 feet.

What’s below the first circle? More circles, but smaller ones. This is nicely
shown on page 252 (Figure 9-9) of your textbook. However, as you go from the surface to depth, the circles get smaller and smaller, until you reach a depth where there are no more circles. This depth (where the circles of moving water disappear) can be calculated by dividing the length of the wave (or wavelength,
from crest to crest or from trough to trough) by two. Thus, if you are out at Melbourne Beach surfing and you estimate  that the distance between crests (or troughs, the low points) is about 50 ft, then the depth where the orbitals of moving water completely disappear is 25 feet.

An interesting feature of the orbitals of water is the direction they move. The first orbit, the biggest one, will move water at the crest of the wave towards the beach. However, at the bottom of the same orbit, the water is going “out to sea”. By the same token, water at the trough of the wave (lowest part, but now at the surface water) is moving out to sea. Surfers, “has this been your experience”; it would appear that when you are on your surfboard and as the crests and troughs
pass you are not going anywhere! The crest will move you towards the beach, but in the trough you will be moved back out to sea. Result: no net motion; you are not going anywhere. Non surfers go to the boardwalk at Indialantic and note the “line” of surfers waiting for the big one; they are not moving (not much). But we do know that surfers frequently ride the "big ones" all the way to the shore; how is this possible because the orbit of water provide no net movement? I will be calling on you (surfers) to give your experiences to the class, so be ready. For any students (surfers) from California, I am especially interested in your
experiences or comparisons of California waves with Florida waves; what are the differences?? Share your experience and knowledge with the rest of the class.

What causes a beach wave to break and why does the surfer eventually “ride
his/her wave” to the shore.

I believe you will now be able to describe or understand why the crest of a wave crashes along a beach. The process is very much connected with the circles (or orbital motion of water) of moving water described above. As the wave moves into shallower water, the first orbit (the biggest one) begins to “feel” the bottom; additionally, the orbit begin to take on an elliptical shape with depth, and flatten
right at the bottom. When the orbit feels the bottom, the movement (water of course) at the bottom of the orbit is slowed down owing the friction between the bottom (the sand, rock or whatever) and the water. As water is a fluid, the friction is not great just above the bottom, but it is sufficient enough to slow down the moving water at the bottom of the orbit. But what about the movement of water at the top of the orbit. There is no friction at the top of the wave; it just keeps on "trucking" (moving) forward.

Thus water at the top of the orbit is moving faster than the opposite moving water at the bottom of the orbit. This can’t last very long at all. The result of course is rushing , breaking water (at the crest) called a breaking wave, or what you see at the beach. Actually, the breaking process is quite simple.

For the benefit of the surfers, Willard Bascom provides some tips. I will paraphrase a few of his statements: when you surf you use the energy of the wave. The more energy you use the better surfer you are; likewise, the more energy in the wave the better the surfing (this makes sense; surfing would be pretty poor (an not practical!) on capillary waves). Your movement on the surfboard is the result of two things. The gravity force as you are “sliding” down a hill (the wave is the hill, it has a slope). The movement of the wave is the orbital movement of the water which at the crest and along the face (as it faces the beach) as it moves towards the beach. Thus you ride the wave because the water is moving (from orbital motion) and also because gravity (your weight, bigger
people surf better??) is moving you down the slope. Somewhere on the slope you will find the optimum situation or spot on the wave: moving a little faster than the wave so it does not catch up with you. This has to be done by trial and error. Mr. Bascom also mentions that surfers moving sidewise across a wave may be able to move at speeds considerably greater than the advancing wave, especially if the sideways has a large slope.

As Mr. Bascom points out bow waves from moving vessels offer a “free ride” for those who can ride them; would you like to try it some time? Don’t, it is life threatening if you get caught under the boat.) How many times have you seen a porpoise ride the bow wave of a vessel. This can be seen in the Indian River Lagoon. The porpoise rides the wave just like the surfer. He/she finds the slope of the moving wave and “rides down it” thus using the energy (which created the wave in the first place) of the ship to propel it.

Waves, Energy, and Beaches

On the practical side waves have a tremendous effect or impact on beaches. Beach erosion is a serious, economic impact of wave action.  It is serious because some of us (not me) decided along time ago to live or have a business right on the beach, or at least have a residence or business a few meters from the breaking waves. Why would someone want to live on or very near the beach? Several reasons: Beaches are pleasing to be on, dynamic, full of bird life, great for fishing, habitat for turtles and so on.

There are many reasons why one would want to build a home on or near the beach. But one must be ready to suffer the potential adverse (from the human point of view) consequences. Besides why not leave the beaches alone so we could all enjoy them, kind of like a park, even some areas completely off limits.

Beaches are continually changing by natural processes: sand is added; sand is
taken away, for example by storms and seasonal processes. There is considerable energy in waves; a 3 meter (about 10 ft) wave has about 10000 joules/m2. What’s a joule? Its a unit of energy. You learned about energy earlier. The specific heat
of water is 1 cal/deg/g: The heat required to raise 1 gram of water 1 deg C from 15 to 16 deg C. There are 4.18 joules of energy per calorie. Thus 1 m2 of wave energy (above example) is equivalent to 2400 calories of heat. Or, 2.4 kg of water (or 2.4 liter) of water warmed 1 deg C. But we have more than just 1 m2 of wave area. The entire coastline of Florida has waves. Consider the distance between Melbourne Beach and Daytona Beach. A reasonable guess is 80 km (50 miles), or 80,000 m. Thus 80,000 packets of 1 m wave units would be equivalent 800 million joules. If the waves produce this energy every 10 seconds, then the power produced is 80 million joules per sec or 80 million watts, or 80 megawatts. This is a sizable power plant.