Waves Unit II: Waves in the Ocean (3.5 pts)

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1 T. James Noyes, El Camino College Waves Unit I: The Nature of Waves (Topic 5A-1) page 1 Name: Section: Waves Unit II: Waves in the Ocean (3.5 pts) Changes in Wave Height, Wavelength, and Wave Speed at the Shoreline As a wave moves into shallow water, its orbitals feel the bottom, causing it to slow down. The wave crests that are closer to the shore ( in front ) are in shallower water, so they are moving slower than the wave crests farther out in the ocean ( behind ). This allows the wave crests out in the ocean to get closer to the wave crests near the shore, reducing the wavelength (the distance between the crests). This squeezes the water in-between the two wave crests horizontally; the water cannot go down (the ocean is getting shallower as it approaches the shore!), so it goes in the only direction it can: up! This is why waves grow larger at a beach. I like to say that the reduction in wavelength at the shoreline is like a traffic jam. Imagine that you are driving north on the 405 towards the junction with the 105 by LAX. You begin with lots of distance between you and the car in front of you, but as you come around the bend near LAX, you ll see a sea of red tail lights in front of you: they re all slowing down. Both you and the car in front of you put on your brakes, but he saw the tail lights first, so he starts stopping first. While you re going faster, you get closer to the car in front of you, just like the wave crest behind gets closer to the wave crest in front of it. In other words, the wavelength (the distance between you) gets smaller. Here is another way to think about why waves grow at a beach: the front part of a wave crest is in slightly shallower water than the back part of the wave crest, so it is always going a little slower than the back part of the crest. As the back part of the crest catches up to the front part of the crest, more and more of the water that was spread out over a wide area gets concentrated in a narrower area. (See the

2 T. James Noyes, El Camino College Waves Unit I: The Nature of Waves (Topic 5A-1) page 2 picture above: 1 foot 120 feet becomes 30 feet 4 feet) I always hesitate to use this explanation because many students think that a wave crest that is behind another wave crest can actually catch up to the wave crest that is in front of it. This cannot happen, because the wave crest that is behind slows down more and more as it enters shallower water, so it can never actually catch up to the wave crest in front of it. Instead, it is always catching up, but never can quite do so. The key thing to remember to avoid confusion is that the back part of a wave crest is catching up to the front part of the same wave crest; two separate wave crests are not merging. In fact, one wave crest can catch up to another wave crest if two groups of waves from different places are arriving at the same time. In shallow water the orbitals of the waves with a shorter wavelength do not reach down as far as the waves with a longer wavelength and thus do not feel the bottom quite as much. So, on a beach the waves with a shorter wavelength waves move a little faster than the waves with a longer wavelength! This allows a wave crest of the waves with a shorter wavelength to catch up with a wave crest of the waves with a longer wavelength. Since their speeds are pretty close, the crests can stay together for quite some time, leading to a significant increase in wave height due to wave interference for much longer than a moment. This is why there are sets of waves with larger heights and why some surfers have rules of thumb like every seventh wave will be larger than the rest. Note: Waves do not grow at a beach because the bottom pushes them up (as if they are hitting the bottom and bouncing upwards). Also, they are not gaining energy as they grow. Wave growth as an example of the conservation of energy: the forward motion energy of the wave (kinetic energy) is being converted into gravitational potential energy (it goes upward, fighting gravity), like a ball being thrown upward loses speed ( motion ) as it goes upwards fighting gravity. However, as you know, what goes up, must come down: the wave eventually becomes too steep and it gets pulled down by gravity, causing it get all of its motion energy back. 1. As waves approach a beach, do the waves speed up (go faster) or slow down? 2. Why does the speed of waves change as they approach the beach? 3. As waves approach a beach, does their wavelength get longer (increase) or shorter (decrease)? 4. Why does the wavelength of waves change as they approach a beach? 5. Why do waves height grow when they approach a beach?

3 T. James Noyes, El Camino College Waves Unit I: The Nature of Waves (Topic 5A-1) page 3 Wave Refraction Most ocean waves are created by winds (often during storms). Winds can blow from any direction, so at any given spot in the ocean, waves are typically coming from and going in a wide variety of directions. However, if you think of waves at a beach, you know that they pretty much go right towards the shoreline. In other words, they go towards you when you are standing on the beach; they do not go up or down the coast. This means that as waves approach a shoreline, they turn or bend towards the shoreline, a process we call wave refraction. (Not reflection: reflection is when a wave bounces off something, like a wall.) The result is that wave crests tend to parallel or match the shape of the shoreline as they break. To understand why this happens, imagine a line of soldiers marching towards some mud at an angle. (Why march into the mud? Because Sarge told them to.) A soldier at one end of the line will reach the mud first, slowing him down, while the other soldiers continue moving forward. Each soldier spends a little more time on the grass than the soldier to his left, so he moves farther than his neighbor, getting ahead of him. The result is that by the time the last soldier steps into the mud, the line of soldiers has been stretched out and now makes a new angle: the line has turned or bent. The only difference between this example and waves is that they actually change direction, unlike the line of soldiers. A better example is to imagine pushing or driving a two-wheeled object like a hand truck ( dolly ) or Segway into the mud. The wheel in the mud would get stuck, but the wheel on the grass would keep moving and turn the object towards the mud. As a wave crest approaches the shoreline, typically one end of the line is closer to the shoreline than the other. This end is in shallower water, so it slows down while the other end, in deeper water, moves forward faster. This swings the wave crest towards the shore, since the end in deep water covers a larger distance towards the shore than the slower-moving end in shallow water. If the seafloor slope around an island is not too steep, wave refraction can actually cause waves to turn all the way around ( wrap around an island) and hit the opposite side. However, waves tends to be weaker on the side of the island facing

4 T. James Noyes, El Camino College Waves Unit I: The Nature of Waves (Topic 5A-1) page 4 away from the original waves, because the waves are getting stretched out over a larger area (as in the soldier example where the line got longer). This means that the energy in a wave is also spread over a larger area, which reduces the height of the waves. In other words, refraction often makes waves smaller. However, if waves bend towards one another and begin to come together, they interfere, creating a higher wave crest. Thus, wave refraction can also increase the height of waves. This typically happens near the shallow water of a point or headland (a place where the land sticks out into the ocean). The waves bend towards the headland, causing them to come together, increase in height, and pound the headland even more fiercely than the rest of the coast. If waves completely wrap around an island and come together on the other side, they will become larger as well. Typically, waves break before refracting completely (becoming parallel to the shore that is, perfectly matching the shape of the shoreline), which allows them to push sand down the coast, our next topic. 6. What is wave refraction? 7. Where are waves typically moving faster, in the shallower water closer to the shoreline, or deeper water farther from the shoreline? 8. Where does wave refraction make waves height smaller, where the wave crests bend together (as at a headland) or when the wave crests get stretched out (as happens along a ordinary straight shoreline)? 9. True or false? Wave refraction can cause waves to go around an island and meet another part of the same wave crest on the other side of the island.

5 T. James Noyes, El Camino College Waves Unit I: The Nature of Waves (Topic 5A-1) page 5 Longshore Transport of Sand by Waves Waves often do not refract completely, and come into the shoreline at a small angle, allowing them to push sand along the shoreline. We say that the waves are transporting sand down along the coast, and hence call it the longshore transport of sand. A breaking wave pushes sand up the slope of the beach at an angle. The water and sand then slide back down the beach slope into the ocean, pulled down by gravity, but they go straight downhill, taking the fastest route back into the ocean. Thus, they are not back where they started. (This motion is often called zig-zag motion.) Each breaking wave pushes sand a little bit down the coast. This may seem like a small effect, but waves endlessly pound the shore, day after day, year after year, slowly pushing sand down the coast: inch after inch eventually becomes mile after mile. As a non-breaking wave goes by, the water beneath the wave moves in a circle. In shallow water, though, the bottom gets in the way, distorting the circle into an ellipse (oval). At the very bottom, the ellipse is completely squished, so that the water hardly moves up and down at all: instead it goes side-to-side or back-and-forth as the wave goes by. This water motion pushes the sand beneath it, causing the sand to wiggle back-and-forth as well. Even though the sand moves, it does not go anywhere: like a child on a swing, it goes back-and-forth but does not actually travel from place to place. (Non-breaking waves moving sand back-and-forth does cause the sand migrate or drift a little bit, but this is very small and slow compared to longshore transport.) 10. What is longshore transport? 11. What causes longshore transport? 12. Why do waves have to break for longshore transport to occur? In other words, why don t non-breaking waves cause sand to move along the coast? 13. True or false? Waves that approach the coast at a steep angle push more sand down the coast than waves that come into the coast nearly parallel to the coast (match the shape of the shoreline).

6 T. James Noyes, El Camino College Waves Unit I: The Nature of Waves (Topic 5A-1) page 6 Wave Period and Wave Frequency Another way that scientists describe waves is to measure how quickly they cause the sea surface to bounce up and down. One strategy for measuring this feature of waves is to watch a single spot, and to count how long it takes for one wave crest to be replaced by the wave crest behind it. (For example, watch a surfer or a bird bob down and then back up again.) This is called the wave period, the period of time is takes for a wave crest to go by (travel the distance of 1 wavelength). Alternatively, you can measure the wave frequency, how often a wave comes by. (For example, 6 waves pass by in a minute.) They are inversely proportional to one another: frequency = 1/period, meaning that if one is high, the other is low; if waves pass often high frequency then small amount of time between them a short period of time. Note that if you measure one, you can calculate the other. Scientists measure wave period or frequency for several reasons. One reason is that wave period and frequency never change as waves travel, unlike wave height or wavelength. Secondly, they are much easier to estimate from a distance than wave height or wavelength. Finally, if you measure the wave period or frequency and know the depth of the water, then you can calculate the waves wavelength and speed. The relationship between wave period and wavelength is: the longer the period, the longer the wavelength. Think about it for a moment: the larger the distance between the crests, the longer the time it takes for one crest to replace the one in front of it. Since long-wavelength waves move faster than short-wavelength waves, long-period waves move faster than short-period waves. For those of you who are interested, this is the formula that relates wave characteristics to one another: ω 2 = gk tanh(kh), where ω is the angular frequency, g is gravitational acceleration, k is the angular wavenumber (wavelength), and h is the depth of the water. In deep water, it is simply ω 2 = gk. In shallow water, it is ω 2 = ghk 2. Wavelength changes as waves approach a beach, because the waves are slowing down. The period does not change at all; the wavelength does all the adjusting that is necessary. The period does change when the waves break, but by this point it no longer matters: once they break, they are no longer waves. In short, the waves height, wavelength, and speed change as they approach the beach but one wave characteristic does not change: wave period (and frequency).

7 T. James Noyes, El Camino College Waves Unit I: The Nature of Waves (Topic 5A-1) page What is the period of a wave? 15. What is the frequency of a wave? 16. If a wave has a long period, does that mean it will have a high frequency or a low frequency? 17. Which wave characteristic is easiest to measure, height, period, speed, or wavelength? 18. True or false? If you know the period of a wave and the depth of the water, then you also can calculate the waves wavelength and speed. 19. If a wave has a long period, does that mean it will have a long wavelength or a short wavelength? 20. Which move faster, waves with a long period or waves with a short period? 21. Which waves created by a storm will reach the coast first, the waves with a long wavelength or the waves with a short wavelength? 22. Which wave characteristic does not change as waves approach a beach, the waves height, period, speed, or wavelength?

8 T. James Noyes, El Camino College Waves Unit I: The Nature of Waves (Topic 5A-1) page 8 Making Waves Most ocean waves are created by the wind blowing over the surface of the ocean. The largest waves are created by the strong winds of storms. The wind enhances small differences in the surface of the ocean by pushing the top of the waves forward and making the waves grow via the Bernoulli Effect. Have you ever been standing by the side of the road when a fast-moving truck goes by and felt pulled towards the truck? This is owing to the Bernoulli Effect. The truck pushes air out of the way quickly, and you get sucked in with the air moving in to replace it. In the same way, a fast wind sucks the surface of the ocean upward. Bernolli Effect Experiment: Take a piece of paper (lighter is better), and hold one end with both hands just beneath your mouth. Now, blow across the top of the paper. Notice how the paper rises, pushed upwards by the air beneath. The wind causes waves to grow in the same way. Waves must go through a cycle of growth and breaking many times to become large (tall height and long wavelength). As a small wave grows higher, it becomes too steep and breaks, causing it to lose the height it gained. However, the breaking causes its wavelength to stretch out (gets longer), so when it grows again, it can get taller before becoming too steep and breaking again. The wavelength gets stretched again and again, and the wave grows again and again. Remember: the wavelength of a wave affects its speed: the longer the wavelength, the faster the speed. Eventually, the wave moves as fast as the wind, so the wind can no longer push it, and the wave stops growing. The largest waves are created by strong, steady winds that blow over a large area called the fetch. Since waves grow until they match the speed of the wind, strong (fast) winds make the biggest waves. If the strong winds keep shifting first making waves going one direction, then another then the wind will create small waves going in many directions, not large waves going in one direction. It takes time for large waves to grow, so the longer the winds blow in one direction, the bigger the waves can become. Waves stop growing if there is no wind, so once they leave the area where the wind is blowing (the fetch), they cannot grow any more. Winds with a large fetch can help the waves grow for a long time before they leave the wind behind. Winds over the ocean are strongest near the Poles, and waves are also largest where the winds are strongest. Storms are common at these latitudes, especially in the winter, though storms are more common in subtropics during the winter as well. During the summertime, tropical storms are common near the Equator, and tropical storms that grow into hurricanes can create huge waves. Tropical oceans are much calmer than polar oceans most of the time. Thus, most of the large waves that strike the coast come from the Poles.

9 T. James Noyes, El Camino College Waves Unit I: The Nature of Waves (Topic 5A-1) page What create most of the waves in the ocean? 24. Which produces waves with a larger height, a strong (fast) wind or a weak wind? 25. Which produces waves with a longer wavelength, a strong (fast) wind or a weak wind? 26. Which produces waves with a larger height, a steady wind or a wind that changes direction over time? 27. Which produces waves with a larger height, a wind the blows over a large area or a wind the blows over a small area? 28. True or false? Waves grow until their speed matches the speed of the wind. 29. Where are most of the big waves created, closer to the Poles or closer to the Equator? 30. During which season are waves especially large near the Poles, summer or winter?

10 T. James Noyes, El Camino College Waves Unit I: The Nature of Waves (Topic 5A-1) page 10 Waves across the Ocean Once waves leave the fetch, waves lose very little energy as they travel across the ocean. Like a row of dominos, water molecules bump into one another, passing the disturbance and its energy from one to the next quite efficiently. Waves may lose energy if wave interference makes them large enough to break, or winds encountered in their journey add or remove energy and of course they lose all their energy once they finally break along a shoreline. As a wave moves away from the storm that created it, the wave is spreading out (like ripples on a pond), so the wave height do decreases. The reduced wave height does not mean that the waves are losing energy, though. They have the same total amount of energy, but it is spread over a larger area. Thus waves from a nearby storm are larger (as you might have guessed) but affect a smaller section of the coast than waves from a far-away storm. The winds of a storm create waves with a variety of wavelengths and heights, but as they travel across the ocean, they begin to sort themselves out by wavelength. The longer-wavelength waves are faster, so they leave the shorter-wavelength waves behind. We call this wave dispersion (disperse = too go apart, like the police telling a crowd to disperse ). When all the waves of different wavelength are all jumbled together, it can produce a very complex sea surface (see the section on wave interference ). Once waves separate (disperse), the sea surface becomes more regular, resembling the nice smooth patterns in my side-view sketches of waves. We call such nice, regular waves swell. When jumbled together, we say that they are sea waves. 31. True or false? Wave typically lose little or no energy as they travel across the ocean. 32. Does waves height increase, decrease, or stay about the same as they travel across the ocean? 33. How are swell different from sea waves?

11 T. James Noyes, El Camino College Waves Unit I: The Nature of Waves (Topic 5A-1) page 11 Wave Groups As waves move outward away from the storm that created them, a curious phenomenon can be observed in the wave groups. A crest will emerge from the back of the group, move all the way to the front, and disappear. This keeps happening again and again, with wave crests emerging at the back of the group and disappearing at the front. Overall, this leads to a reduction in the group s speed (the group speed is ½ of the wave speed). The best though confusing way to understand this is that a wave group is composed of several waves of slightly different wavelengths all mutually interfering. New wave crests appear because the longer-wavelength waves are moving faster: instead of crests overlapping with troughs (canceling both), the crests begin to overlap with crests and troughs with troughs. The longer wavelength waves are moving slightly faster, leading to a wave crest moving forward through the group. However, the interference at the front of the group causes the waves to cancel out again as crests again line up with troughs, so the group does not move forward as much an individual wave crest. Note that the largest wave crest is in the center of the group. This is one reason surfers observe that every 3rd wave crest of a set (or every 7th wave crest, or other rules I ve heard them speak of) tends to be larger than the rest: two or more waves are coming into the beach at the same time and interfering, growing, and breaking together. The Importance of Waves in the Ocean Waves have several important effects on the ocean, particularly breaking waves. Once a wave breaks, the wave motion of the orbitals breaks down. Instead of moving in a circle, water surges forward (just like water surges up the slope of a beach). Thus, a breaking wave becomes a current. In addition, as water falls down the front of a breaking wave, it captures air. (In other words, bubbles form: the white foam that you see on a wave crest and is left behind as it moves onward towards the shore.) If these bubbles break underneath the surface of the water, then the ocean water captures gases from the atmosphere (they become dissolved gases). Thus, breaking waves help the ocean absorb carbon dioxide from the atmosphere which reduces the strength of the greenhouse effect and slows global warming. Similarly, breaking waves disturb the surface of the ocean, sending a spray of water droplets into the air. The water molecules, salts, and gases in the droplets now have a much easier time evaporating (there are more directions in which to fly away), allowing them to enter the atmosphere. Salts, of course, tend to settle back into the ocean or on land over time, but this is a major way in which the oxygen made by ocean algae (like phytoplankton) enters the atmosphere for us to breathe! (Thank you, waves!) Of course, air molecules can also strike the surface of the ocean, or break free from the ocean surface, but this process is much less likely (and thus slower) than the exchange of air molecules mediated by ocean waves.

12 T. James Noyes, El Camino College Waves Unit I: The Nature of Waves (Topic 5A-1) page 12 Finally, breaking waves and wave orbitals stir up the surface of the ocean (appropriately called the mixed layer), making it fairly uniform in temperature, salinity, and other characteristics. Their mixing brings up both sinking phytoplankton and unused nutrients from down deep, and sends down abundant oxygen from the surface. Since waves make the water move in circles, waves also push some phytoplankton floating at the surface down, but because phytoplankton tend to sink, there are more phytoplankton who need to be brought up than there are floating near the surface. Thus, overall waves tend to bring up more phytoplankton than they push down and bring up more nutrients than they push down as well. It should be noted that other phenomena help mix the mixed layer: for example, when surface water cools and sinks (higher density) and is replaced by the somewhat warmer water from below, similar to the effect of wave orbitals. 34. True or false? Breaking waves help create ocean currents. 35. True or false? Breaking waves help the ocean absorb carbon dioxide from the atmosphere. 36. True or false? Breaking waves help the ocean release oxygen made by phytoplankton into the atmosphere. 37. True or false? Waves tend to harm phytoplankton, making it more difficult for them to get sunlight and nutrients needed for photosynthesis.