Today's lecture is going to be on waves and wave phenomena. Lots of people out there have yachts, wealthy people, race. This was a race in 1998, Sydney to Hobart.
They ran into the storm weather, they ran into 100 mile an hour winds and 66 foot waves. It's just killer. A lot of people died. sometimes you get stormy conditions you know this is another race in the england channel race of the 50-foot waves you know in 1979 and most people can't uh most people have big ships can't even deal with that you know so waves here most waves are generated by winds blowing across the ocean on the surface but you know there are sometimes you get huge storms and with storms and high high uh high velocity winds you get higher and higher waves eventually can become very very dangerous. Now if you sit at the shoreline you're going to see that you know different you know as you sit at the shore you'll see big waves small waves again because wave trains cross each other sometimes you get constructive interference uh sometimes destructive interference the constructive is when you get a rogue wave.
uh in terms of amplitude but most times you're getting mixed interference where wave wave trains are just crossing paths this is another huge wave it was a basically a 1958 in alaska there's a huge landslide that's from caused by an earthquake and and this huge amount of debris fell into the cove there sent up a water wave 1700 feet high and some of the ships that were lifted out you know the water over over the over the this you know over over the into the main past the channel amazingly survived i mean you can't even imagine a ride like that i think that's the largest recorded wave you know this splash wave at that height Some people survived it, but it's hard to believe. You can also get internal waves because of thermoclines in the ocean, so you can get lower density separated from higher density water. and some waves propagate internally along the interface.
But most waves that occur on the surface of the ocean are generated by the winds and there are and they'll have you know period is the amount of time it takes for one wavelength to pass a set point. And so they're relatively short for wind generated waves, but they can be pretty long. When you start talking about waves, we'll see generated by tsunamis, earthquakes on the ocean floor can have much longer periods.
And of course, the ultimate waves are the ones generated by the gravitational attraction of the Moon and the Sun and the Earth that we know as tides. and we'll see you know we'll talk about tides separately these are very long long wavelength waves um with very very extended periods of course at 12 and 24 hours okay so waves you know we measure waves uh in terms of the wavelength we measure from crest to crest or trough to trough and the amplitude, that's the wavelength, the amplitude or the wave height is from distance from trough to crest. And we define deep water waves as waterways where the wavelength, where the water depth is greater than one half the wavelength.
So out in the open ocean, most wind generated waves start out as deep water waves just by definition because all water depth, you know, going down to 12,000 feet is always greater than one half the wavelength. for these types of wind generated waves out in the open ocean. Okay, these are orbital waves, but the net motion is in the direction of the winds.
So even though we have this orbital wave, this interface between the atmosphere and the surface, okay uh the in the waves are going in orbits the net effect is because it slows down in the deeper part of the orbit so the net effect is moving in the direction of the wind generating the waveform again deep wear waves where depth is greater than one half the wavelength again you get below that depth and you don't feel any water movement the transfer of energy so a little cartoon here again the steepness of a wave is measured by by the wave height divided by the wavelength i want you to approach a value of 1 7 white caps form because the waveform can no longer be maintained So t is the period of the wave, which again the amount of time it takes to pass a set point in a given amount of time. And wavelength is the way it is from crest to crest. The frequency is equal to the reciprocal of the period. Again, speed, if you want to know the speed of the wave, if you know the wavelength, you measure the wavelength divided by the period distance per unit time, which is also equal to the wavelength times the frequency. But the problem is, for all practical purposes, it's not easy to measure wavelength.
You can be out in the ocean, in the water, trying to, with a ruler, you know, whatever, trying to measure wavelength is not easy. So we have a different way of calculating the speed of, a fairly easy way of calculating the speed of a deep water wave. It's equal to basically, the speed of a deep water wave is equal to basically gravitational acceleration times the period divided by two pi. Okay, so in meters that would be 9.8 meters per second squared times the period or the time elapsed divided by 2 pi. And that basically works out to be the speed of a deep water wave is equal to 1.56 t as the period.
Because 1.56 t is the speed of a deep water wave in meters per second. It's 5.1 t in feet per second. So once we know the period, we can measure the speed of the wave. and we can calculate the period fairly easily unlike calculating the wavelength.
And so the speed is equal to 1.56 t then is equal to L over t that's the above the other equation for speed. So basically you know when we do that then we can we can calculate the wavelength and it's going to be equal to 1.56 t squared. So that's how we get to the wavelength basically for a deep water wave. Shallower waves, waves where again, well, as wind generated waves approach the shore, they, you know, the water depth decreases, the waves touch bottom, instead of a spherical motion you get more of an elliptical motion, and so frictional drag, you know, occurs, and so we define shallow water waves where water depth is less than one-half, less than or equal to one-twentieth, I'm sorry, one-twentieth the wavelength. okay this is the definition for shallow waterways so their their speed is impeded by touching bottom it's all wind generated waves in the open ocean eventually become shallow water waves as they approach the shoreline okay and again it's not that easy to measure wavelength but again wind generated waves i mean shallow water waves generated by winds their speed is controlled by water depth and so the speed of a shallow water wave is equal to the square root of gravitation acceleration times the water depth meters so that would be a 9.8 meters per second squared times uh water depth in meters and that's going to work out to approximately 3.1 times the square root of the water depth so that's the equation that we use to calculate the speed of a shallow waterway and the speed of a deep water wave again is equal to 1.56 t And of course there are intermediates that can you know there are waves that are sort of transitioning from being deep water waves to shallow water waves which of course all wind generated waves as they approach the shoreline eventually become shallow water waves.
Now some waves because of their extreme wavelengths are always shallow water waves because they're always impeded by the bottom. Waves generated by tsunamis, huge wavelengths, so these waves are always going to be by definition shallow water waves. okay so you have you know situations where that's going to be the other of course the waves generated by the tides by definition are also going to always be shallow water waves because they're extreme wavelengths but you never have water depth greater than one half this diagram good image or shows the relationship between wavelength, period, and speed.
As the wavelength increases, the period increases, and the speed increases. So as an example for a wavelength of 100 meters, the period is 8 seconds and 1.56 times 8, so you end up with a speed of 12.5, approximately 12.5 meters per second. Okay, so when wind generated waves begin, they're very small and they may be, you know, restoring force, maybe capillary action. Eventually, you know, you start getting larger, you know, as wavelengths increase, you know, the restoring force becomes gravity.
Eventually you reach that critical ratio of 1 7th for the wave height to the wavelength and the waveform can no longer be maintained and you start getting white caps waves. They define the area of the surface of the ocean that's under the direct influence of the force generating the waves as the fetch. So the area that's influenced by the winds directly is called the fetch.
But waves propagate once the winds die down, waves continue to propagate and transfer the energy eventually transferring it to the shore where they break. And so the area where the waves are propagating they're no longer under the direct influence of the force generating them is called the swell. Waves generated by the tides we'll see are always forced waves because gravity is always there.
Wave height, and you can see different parts of the world experience more extreme wave heights. basically you'll get rogue waves that can be damaging ships cruise ships damage you if you get caught underneath a road wave. When I was 10, my father and my sister and I were coming back to port from outside, we were about 12 miles out of the Atlantic overnight. Everything was calm and nice and as we entered the harbor we got picked up by a road wave and thrown into a bridge.
The boat shattered. We were rescued by another boat that actually a sailboat that ripped its mast off to get to us in time. and my sister never went on the water again. Unfortunately I'm old and back in those days there wasn't anybody taking video image or anything else on the phone but you lived through it once you never forget it.
propagating against most of the, you know, you can get, you know, when you have a rogue wave, you're getting perfect constructive interference. So you're getting a higher amplitude wave. If you had perfectly destructive interference, you get no wave at all. But most of the time, wave trains generate crossing paths, so you get mixed interference patterns, a little higher wave, a little smaller wave, and any time you've been to the beach, you've seen that. and rogue waves being the most you know very dangerous when they again waves as they approach you know wind generated waves as they approach the shore transition from deep water waves to shallow water waves because of frictional drag okay and eventually by the way it's touch bottom and they pull back and then they play and you go surf The type of sediment we get depends a lot on the incline of the beach itself.
If you touch the bottom, we'll see that a lot of the sediment is continually moving north to south along the east coast and west coast of the United States by a longshore current. The waves tend to break along the coastlines. They tend to cause erosion. The waves are not very strong. to reflect ways or track them to get for surfers and things.
Sometimes to protect harbors, it doesn't always work out so well. Tsunamis again are caused by displacement of water on the ocean floor, by earthquakes on the ocean floor. Once the wave is generated, it can be moving really, really fast. It can have an ultra-long wavelength.
They're very dangerous. These waves in the open ocean, you don't even notice they're there because of the ultra-long wavelength, but as they approach the shoreline, the water piles up. If the trough arrives first, you'll see a pullback from the shoreline. If you're ever along a shoreline and you see a rapid pullback, run.
Run as fast as you can. Most people that sit there with their mouths up and gawking when that wall comes in following that drawback is when trouble happens and people die. Obviously, there have been tremendous, terrible tsunamis in the last few decades in the Indian Ocean.
hundreds of thousands of people killed. More recently in Japan, again, thousands of people killed. It can be extremely dangerous if you're not careful enough or if you don't have enough time to get out of the area. to watch if they're, you know, minor, minor.
There are warning systems set up along the Pacific for tsunamis. In Hawaii, they know if a tsunami might be approaching from an earthquake on the ocean floor, the military moves all the ships out to sea. Okay, because out in the open ocean there's no effect at all, all the damage comes when they make land.
This table tells you a little bit about what to expect for average wave height, average wavelength, period. You can see with increasing wind speed they all increase. All right, so next time we'll be talking more specifically about the tides.