High School Ocean Lesson Plans: Tsunami Waves

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Wave References:
Tsunamis Remembered by Survivors
Ocean Wave Theory
Tsunami Photos
USC Tsunami Research Group
Tsunami at Pacific
U of Wash Tsunami Page

Waves

Topics Covered in this Lecture:

Overview

The summer of 1997 brought some of the most spectacular waves in a decade to southern California shores, just in time for the U.S Open Surfing Championships in Huntington Beach. Whether you have any interest in surfing or not, the sight of those big waves and the daring feats of those that ride them evoke thrill and wonder. But just where do those big waves (or any waves for that matter) come from? Why do some waves tower like monsters from some Japanese animé while others merely caress the shore with their gentle lapping? And how is it that anyone can stand on a fiberglass board and catch a ride on these walls of water? The answers to these questions and more as we wax our minds and explore what's up when the surf's up.

Anatomy of a Wave

Waves have frightened and inspired man for millenia. While it's the large waves that often get the most attention, waves of all sizes play an important function in the way the ocean works. And all waves, no matter how large or small, have a few fundamental characteristics in common. Let's familiarize ourselves with them.

All waves are the movement of energy through a medium (like air, rock, water...not psychics.) The term wave refers to a series of vibrations, pulses or undulations in a medium, such as water, air, or radiation. Think about all the different kinds of waves you have encountered: ocean waves, a waving flag, amber waves of grain, sound waves, even light waves. All of these waves are a manifestation of energy moving through a medium.

A water wave is the movement of energy through water. The kinds of water waves we are talking about are the rises and falls, hills and valleys, ups and downs of water (a lake, the sea, your coffee cup) that occur through the entire medium. The foamy breaky things that you see on the shore are the last gasp of waves that have traveled thousands of miles to spend their energy on the beach where you stand.

We are not talking about those kinds of waves right now. We are talking about the waves that travel through water before they break.

A wave has two parts: a top, known as the CREST, and a bottom, known as the TROUGH. The horizontal distance between two successive crests is defined as the WAVELENGTH. The vertical distance between the crest and the trough is defined as the WAVE HEIGHT.

The snake-like, sinusoidal pattern of a wave is the form that all waves take. When you look at the surface of the ocean or a lake, you are seeing the net result of all the different waves that are traveling through the water at any given moment. The sea surface is a composite of all the different waves. If we were to take apart the sea surface we would find a series of sinusoidal wave patterns all with different wave lengths and wave heights. In other words, all these simple waves add up to make one big complex wave.

When waves travel through each other, they made add to each other's height or they may cancel each other out. When two waves add together making one wave that is bigger, it is called CONSTRUCTIVE INTERFERENCE. When two waves cancel each other out, making a flatter wave than the two individual waves, it is called DESTRUCTIVE INTERFERENCE. Refer to your book for more details.

Now this definition of wave height is the scientific definition. Ask a surfer in southern California to define wave height and he/she will give you some measure in terms of their body length. For example, 4-5 foot waves might be described as shoulder high, 7-8 foot waves as overhead, 10-12 foot waves as double-overhead. In Hawaii, waves are measured from the back of the wave and so Hawaiian surfers tend to underestimate the true size of a wave.

The surfer definition of wave height becomes necessary to describe breaking waves, which do not follow the rules for our "ideal" sinusoidal wave. Thus, it is often practical to judge wave height using the average height of a surfer as the yard stick of measurement. In California, wave heights may be chest high (~3-4 ft), head-high (~5-6 ft.), overhead (~7-9 ft.) or double overhead (~10-12 ft.). With this scheme, anybody standing on shore can easily determine wave height, as long as there are surfers in the water.

Wave height and wavelength are static measurements of a wave. As we all know, waves move through water. Consequently, we can define the speed of a wave and two other characteristics: frequency and period.

The speed of a wave is simply how far it moves in a given amount of time. However, as it turns out, there is a close relationship between wavelength and speed,as we'll see below. Small waves tend to move slowly at a few knots (1 knot equals 1 nautical mile per hour). Medium-size waves may move at tens of knots; large waves move 30 - 50 knots and more. Tsunamis, which are the largest waves of all, can reach speeds up to 450 knots.

The period of a wave provides many important clues about surf conditions. The wave period is defined as the time between successive crests. For example, if you stand on the end of a pier, start your stopwatch when a wave hits a fixed spot, and stop your stopwatch when the next wave hits that point, you will have measured the wave period. Long-period waves tend to be larger and stronger, while short-period waves are smaller and less energetic. By measuring the period of waves, surfers can get an idea of the swell to come within the next several hours, and determine whether different swells (waves that originated in different locations out at sea) are hitting the beach at the same time. Generally, longer period waves contain travel longer distances, have more energy, and create higher breakers on the shore.

Wave frequency is important to ocean engineers and architects who contruct jetties, piers, and other man-made obejcts in or near the ocean. The wave frequency is defined as the number of waves passing a fixed point in a given amount of time. Again, taking a stopwatch, count the number of waves that pass a fixed point over a 30-second interval. Divide by 30 and you have the wave frequency, the number of waves that pass a point every second.

All of these quantities are related to each other and can be expressed as simple mathematical equations. For example, the speed of a wave (assuming the wave is not influenced by the bottom) can be expressed as V=L/T, or speed equals the wavelength divided by the period. Note what happens to the speed of a wave as the wavelength increases. Of course, longer waves also have longer periods; it's the relationship between the wavelength and period that determine the speed of the wave, as expressed in this equation. Just thought you should know that.

Formation of Waves

So, we have different waves, but where do they come from?

If you guessed the wind, you are correct. But where does the wind come from?

If you guessed storms or the atmosphere or the sky, you are close, but really, the wind comes from an "imbalance" in air pressure. What the heck does that mean?

Consider what happens to air when you heat it. It rises. It will continue to rise until it reaches an elevation where the surrounding air has the same density (or pressure). If it cools, it will sink, again, until the surrounding air has the same density (or pressure).

Why does air rise and sink? Changes in air temperature cause changes in the density of air. Density is defined as mass per unit volume. The simplest way to think of it is as the number of air molecules in a given volume (like the amount of air in an empty 2-liter Surge Soda bottle). As you add heat to the air, the air expands, and now we have fewer air molecules in the same volume, In other words, its density decreases. The opposite happens when you cool air. Colder air is more dense than warmer air.

 Increases in density also bring about increases in air pressure; decreases in density cause air pressure to be lower. When there is a difference in air pressure, the air will move and continue to move until air pressure is the same everywhere. This moving air is known as WIND.

Here's another way to think about the relationship between density and air temperature. If you were in a room with 100 people and the doors were locked to prevent your escape and suddenly the room was cooled to 100 degrees below zero, everyone would quickly lose their inhibitions and start to huddle together. The same thing is true about air (and water and lots of other things). The colder it gets, the more dense it becomes, the closer its molecules get. On the other hand, if we heat up the room to 100 degrees above zero, everyone would want their space and put as much distance between themselves as they possibly could. Again, the same is true about air (and water.)

This concept of the relationship between temperature and density is very important. We will return to these ideas when we talk about deep-sea circulation and the physical structure of the water column. Understanding this concept will help us to understand physical changes in the ocean that affect organisms, including humans.

Now, how do we create these areas of high pressure and low pressure across our planet. Simple, the sun heats the equators more than the poles and we have DIFFERENTIAL HEATING of the planet. Cold dense air descends from the poles, warm light air rises from the equator.

On a perfectly round, non-rotating planet made up of a single material, like asphalt, for instance, the rising air at the equator and the sinking air at the poles would give rise to two giant CONVECTION CELLS, one in each hemisphere. But, because the Earth spins on its axis and because the surface is composed of continents and oceans, there are actually three convection cells in each hemisphere. Regardless, it is the creation of high pressure cells and low pressure cells from differential heating of the planet that give rise to the winds.

And so, what is the ultimate source of the energy that travels in water waves? THE SUN!!!! So, all waves are solar-powered, really.

If you are interested in more details about heating of the planet and creation of weather patterns, check out the chapter on the Atmosphere in your book. The chapter on ocean physics also has some of this info.

When the wind blows across the surface of the water, the water begins to ripple. These tiny ripples are called capillary waves. Presumably they are called capillary waves because they are about the thickness of hair, which is where the word capillary comes from. As capillary waves form, the create tiny walls and depressions against which the wind can push even more. The net result is a transfer of energy from the wind into the water. The harder the wind blows or the longer the wind blows, the more energy that will be transferred from the wind to the water.

Okay, after all that, we have a better understanding of the winds that cause the waves, but how does the wind affect waves? How do we make bigger waves?

Simply put, we can blow harder, longer, and over a greater area to get bigger waves. Thus, the primary factors that affect wave formation are:

1) wind speed; 2) wind duration, and 3) the fetch, which is defined as the area over which the wind blows.

The importance of the fetch can be realized when you consider that the biggest waves don't come from hurricanes, which have the fastest winds, but from large storm systems that blow over hundreds, possibly thousands of miles. Hurricanes are a local wave generator and will make waves over a small area, but for the most part, the really big waves that hit our beaches come from big storms in the Antarctic or the North Pacific Ocean.

Let's take a look at how waves might be generated far out at sea. Prevaling meteorological conditions during the winter in the northern hemisphere give rise to vast low pressure systems that generate lots of wind over vast areas of the ocean. Typically, these weather systems travel northwest to southeast, generating ocean swell, sometimes called groundswell, all along the away. These winter storms may generate waves thousands of miles from your local beach. However, waves from these storms, say, with a 20-sec period, might travel at 30 knots. Over a 24 hour day, that wave would cover 720 miles. Given a distance of roughly 3000 miles (for the sake of argument) between the North Pacific Ocean and Huntington Beach, these newly generated waves might be crashing on our shores in just over four days. More times than not, the best surfing in winter comes from that northwest swell.

What about summer surfing? Remember the big waves mentioned above? In our summer, winter storms brew in the southern hemisphere (because our summer is their winter). Storm systems traveling from southwest to northeast pack a mighty punch as they wreak havoc over a much larger ocean area than is even possible in our paltry northern Pacific Ocean. Take a look at a world map. More than 60% of the oceans reside in the southern hemisphere. The greater extent of the South Pacific Ocean allows larger fetch and creates even bigger swell than we find in the nothern hemisphere. Thus, south swell tends to really get things rolling around here (i.e. the waves tend to be bigger when they come from the south).

And what about hurricanes and typhoons? Don't they generate the largest waves? Not necessarily. Although wind speeds in excess of 100 knots are possible in a hurricane or typhoon, the wind energy tends to be concentrated in a much smaller area than a typical weather system. In other words, the fetch for hurricanes and typhoons is smaller. While these powerhouses create incredible wind speeds, their action is limited to the specific areas in which they occur. Waves may be larger in the region of the storm for a limited time, but the large and consistent swell generated by long-fetch winds just doesn't occur.

One other feature in the formation of wave swell is worth noting. A given wind speed can only generate waves of a certain size. After a period of time, the waves get no bigger. In this case, the seas are said to be fully formed, the largest waves that can be created for a given wind speed are being created. Once formed, the swell is free to travel as far as it can, altered only by friction with the bottom or obstacles, such as islands or continents.

The generation of waves from the time the wind starts blowing to the time that fully-formed seas developed gives rise to a series of waves with different wave periods and speeds. Since the longer period waves tend to be faster, these waves move out ahead of the rest of the waves. For this reason, groups of wave trains develop. A wave train is a group of waves traveling at the same speed across the ocean. These waves, obviously, hit the beach at the same time and, hence, create the well-known phenomenon of wave sets.

Breaking Waves

Waves travel out from these storms for thousands of miles before they hit our beaches. So what happens to a wave as it moves through the ocean and why do waves break when they reach the shore?

To understand waves, it is important to realize what is happening to water particles within the wave as the energy moves through the water. As illustrated in your book, water particles move in a kind of circular fashion as the wave energy passes through. The water in a wave has no net forward or backward motion. The particles simply move in a circle. Water particles near the surface of the wave move in larger circular orbits than water particles deeper in the water column. At some depth, the water particles don't move at all. This depth is known as the DEPTH OF NO MOTION.

As it turns out, for reasons that are only clear to physical oceanographers and a small band of space aliens living in a remote region north of Bellatrix in the constellation Orion, the depth of no motion occurs at a distance from the sea surface that is equal to one-half the wavelength. What this means for the wave is that if it travels through water that is deeper than one-half its wavelength, then the wave can travel unimpeded by the bottom. But if the wave gets into water where the bottom depth is less than one-half the wavelength, the wave is said to "feel bottom," The wave begins to encounter friction along the bottom and this will change the wave in two fundamental ways.

As a wave "feels bottom' (again, at depths less than one-half the wavelength), the energy that was once distributed throughout the entire 1/2-wavelength region gets "compressed" and needs to go somewhere. Taking the path of least resistance, it goes upwards causing the crest of the wave to grow taller. This is one result of a wave feeling bottom

The second result is that as a wave feels bottom, it begins to slow down. And since the bottom of the wave is feeling bottom first, it is the bottom of the wave that slows down first. The water particles at the bottom of the wave can no longer complete their circular orbits, so the orbits become more elongated and elliptical. However, the water particles at the top of the wave are still going like gang-busters and are moving faster than the water particles at the bottom.

The net result is that the wave starts to peak and get stretched out at the same time. Eventually, the wave peaks so high that it can no longer keep its shape and the stretching surface water particles orbit faster at the top than the wave is moving forward at the bottom, and the entire wave pitches forward and breaks. After a journey of thousands of miles, the wave meets its final destiny on the shore and spills its energy onto the beach. If it's lucky, it's short 5-6 day life span will be remembered as a short 2-3 second burst of exhilaration in the mind of some passing surfer who happened to hitch a ride.

As many of us have experienced firsthand or through re-runs of Hawaii Five-O, there are many different kinds of breaking waves. On the east coast of the US, most waves are rather gentle and spill lightly on the shore. Contrast that with a place like Pipeline on Oahu, where beautifully shaped tubes of water are the norm. What causes these differences in the size and shape of waves that we see on different shores?

It all has to do with the bottom. If the bottom slopes gently such that a wave has to travel a great distance before it reaches the shore, the wave will lose most of its energy to friction as it approaches the shore. The wave has a good distance over which it travels and slows down before it breaks. On the other hand, if the bottom rises very steeply, such that the wave only encounters the bottom at the last minute, the wave doesn't have time to slow down, and it hits the shore at a greater speed and all that energy is pitched upwards and forwards in one great burst, creating the types of BIG waves that we see at places like Jaws and Mavericks.

Besides this general effect, the shape of the bottom also has an effect on how waves break. Consider the drawing below. The dashed line represents a wave approaching shore.

The solid lines represent lines of equal depth, called isobaths. The entire plot is called a contour plot. In this type of plot we can get some idea of the three-dimensional structure of some parameter, in this case, the depth of the sea bottom. You are probably familiar with other contour plots, such as weather maps, as seen in the USA Today or on the Weather Channel, or topographic maps, such as you use for hiking.

Contour plots are very important in oceanography. They help us visualize the ocean. You should get used to reading them. Take a look at the line marked 5 feet. Everywhere on this line the water depth is 5 feet deep. Above the line, water depths are between 5 and 10 feet. Below the line, water depths are between 0 (sea level) and 5 feet.

 

Now, consider the wave approaching shore. As it approaches the "canyon", the wave slows down, but only where water depths are shallow, say 20 feet. In the middle of the wave, as shown in the figure, the wave maintains its speed. The wave bends because part of it is slowing down while other parts are maintaining their speed. The bending of waves is called wave refraction.

Wave refraction tells us that waves will take on the shape of the bottom. As waves begin to feel bottom, the will begin to follow the contours of the bottom. Thus, as shown in the figure, the wave bends to fit the shape of the bottom.

Try making a drawing similar to the one above, only this time, create a little hill or elevation instead of a depression or canyon. (Flip the lines up.) Draw a wave as it approaches and then draw it as it feels bottom. It should be intuitively obvious to you that the wave will slow down where depths are shallow and continue on its way where depths are deep.

Now that you know how waves bend to fit the contour of the beach, think about where the waves would break first. Of course, they are going to break in the shallower water first. If you go to the beach and watch waves, you will see that they are not all breaking in the same place. That's because some parts of the beach are deeper than others. Any lifeguard worth his salt can point out to you the presence of sand bars, breaks in the sand bars, depressions and elevations in the sea bottom in front of his lifeguard stand. Experienced surfers will also be able to tell you something about the shape of the bottom based on how the waves are breaking. Try it for yourself next time you are at the beach.

One last little item on this topic: If you are still having trouble understanding contour plots, try this simple exercise. It involves something all of you have done at one point in your life, probably when you were a little kid, maybe you are still doing it. This is an exercise in connect-the-dots.

Check it out. Connect the lines of equal depth in the drawing below. What is the feature that is revealed by the isobaths that you have drawn? If you can't figure it out then e-mail me.

 20-----20----15----15----20----20

15-----15----10----10----15-----15

10-----10-----5-----5------10----10

5-------5------3-----3--------5------5

0-------0------0-----0-------0-------0

Here's a few other things to think about. What if the waves are approaching at an angle? What is the effect of a submarine canyon on surfing? How does the shape of the bottom change on a daily basis?

Concluding Remarks

A story is told how the South Pacific Islanders could predict the weather, locate islands and navigate across the open sea just by watching the waves. Their understanding of waves, far beyond anything we are capable of, has slowly been lost as their culture merges with modern times. Nonetheless, there is a powerful lot of information in waves and even your brief study of waves here has given you plenty to think about next time you go to the beach.

For those of you who surf or anyone else who wants to know more about waves, check out the December '98 issue of Surfer. There are also a few good web sites that will help you better understand when and where those fine waves are going to be. Check them out in OtherWorlds on our web site.


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