Tag Archives: waves

Velocity of shallow water waves.

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The experiment we run to discuss the velocity of shallow water waves.

In this post, I discussed how it took us several years to modify an experiment to make it both student and teacher-friendly. But what can you actually see in that experiment?

The movies below show the type of standing waves that are excited in the tank. This movie for 24 cm water depth (Ha – this is going to come back and haunt me! I’m not actually sure what the water depth in this experiment is. It looks like this is the case with the highest water level we have run. But if you want to know for sure go ahead, measure the period, calculate the phase velocity (the tank is 175 cm long) and then calculate the water depth. Good practice! ;-))

And then this movie shows the experiment with a lower water level (12 cm? 8? I don’t remember).

It’s interesting to see how much more difficult it is to excite a nice standing wave if you have less water in the tank. Intuitively that makes sense, but does anyone have a good, not-too-theoretical explanation?

Seesawing of standing waves.

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Improving one of the experiments run in the GEOF130 lab.

One experiment that has been run in GEOF130 forever is the “standing wave”, where a wave is excited in a long and narrow tank and then, for different water depths, the period is measured and the velocity calculated in order to compare it to the one calculated from the shallow water wave equation.

Traditionally, the standing wave is excited by lifting one end of the tank, letting the water settle down, and carefully putting the tank back down. This, however, means that someone has to lift a pretty heavy weight. So Pierre and I were quite proud of ourselves when we constructed a pulley system last year and now instead of lifting the weight up, someone could hang on a rope instead.

However, this was still hard work, and even though the picture shows a student doing the lifting, for most lab groups it was actually Pierre who did it.

But then this year, we came up with a much simpler solution and I don’t know how we didn’t see this before now. As Pierre remarked: We talk about seesawing standing waves ALL THE TIME. How did it not occur to us that the simplest setup would be a seesaw? So now we have two wooden blocks underneath the tank, one supporting it in the middle and one underneath the end where the operator is standing. So all that needs to happen now is a slight lift of the tank and then a slight downward push to bring it back in the horizontal.

So much easier!

Waves being deflected towards regions of lower phase velocity

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Movie of waves being deflected towards regions of lower phase velocity.

We are so used to seeing waves behave in a certain way that we usually don’t stop and think about why waves behave the way they behave.

Imagine a headland with not-very-steep slopes, and wave crests approaching it. Consider now two possible scenarios. In the first one, the wave crests bend around the headland almost as to embrace it. In the second one, wave crests bend away to channel the energy through the deeper waters around it. Which one will it be?

The only difference between those scenarios is that in one case waves are being refracted towards regions of lower velocities and in the other towards regions of higher velocities.

[https://vimeo.com/ 76805199]

Types of breaking waves depending on steepness of slope – small scale

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Video of different types of breakers – small scale.

In this recent post we talked about types of breakers depending on the steepness of the slope. But even on a single stretch of coast line you can easily observe several kinds of breakers. My friend E lend her cabin on an island just outside of Bergen to me and another friend E for the weekend, and just sitting on the rocks we could observe at least two types of breakers.

Different types of “breakers” depending on the slope of the beach. Also see video below where it might become more clear…

In the movie below, you see surging breakers on the first little headland – the water level just raises and falls and no breaking occurs – whereas in the small bay behind the headland and on the next headland the slope is much less steep and here spilling breakers develop. Spilling breakers can also be seen about halfway through the movie on the right hand side beach. Isn’t it awesome how you can see so many concepts on the smallest scales once you start looking for them?

Waves breaking depending on steepness of the slope

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Waves breaking on slopes of different steepnesses.

Depending on a slope’s steepness, waves can break in very different ways. On nearly horizontal beaches, spilling breakers develop. On steeper beaches, plunging breakers, the kind of breakers that form the tunnels that people surf in, form. And on very steep beaches, the breakers don’t actually break, but surge up and down.

Types of breakers developing on beaches depending on the beach’s slope.

This can be seen on  the large scale when different beaches are known for different kinds of breakers, and one impressive example are Oahu’s North Shore plunging breakers that my friend Tobi took me and a couple of friends to see in 2010.

Plunging breakers on Oahu’s North Shore in September 2010.

 

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Another plunging breaker on Oahu’s North Shore. See surfer for scale.

More awesome breakers were to be seen on the Big Island a couple of days later:

Plunging breakers on Big Island in September 2010.

And of course I have movies of those breakers for you, too, first Oahu and then Big Island:

 

Interference of waves.

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Movie on wave interference – two wave fields arriving perpendicular to each other, interacting and leaving.

When talking about waves, it is often difficult to explain that wave heights of different components of a wave field can be added to each other to give a resulting wave field, but that each of those components continues to travel with its own direction and speed and comes out of the wave field basically unaltered. Students learn about constructive, destructive and complex interference (see image below), but it is hard to realize that those interactions are only momentary.

Constructive, destructive and complex interference of waves.

When I was on my way up to Isafjördur to teach CMM31, my friend Astrid and I happened to find the perfect example for the phenomenon described above. We were in Gardur in southwest Iceland and took a sunset walk to the lighthouse.

Old lighthouse in Gardur, southwest Iceland.

The lighthouse is located at the end of a pier and we observed a spectacular wave field. Two distinct fields were meeting each other at an almost 90 degree angle, interacted and left on the other side still clearly recognizable.

Two wave crests meeting at approximately 90 degree angle.

The waves met, interacted, and left the area of interaction. Watch the movie below to get an impression!

Standing waves.

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A seesaw to visualize how standing waves move in an enclosed basin.

In enclosed basins, standing waves can occur. In the simplest case, they have a node in the middle and the largest amplitudes at the edges of the basin. The movement of the water’s surface then closely resembles that of a seesaw.

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A seesaw. Largest amplitudes at the ends, node in the middle.

Extremely simple but extremely effective visualization!

Progressive waves on a rope

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Visualization of progressive waves: wave form and energy move forward while the rope itself stays in place.

When I talked about waves in GEOF130 recently, in order to explain the concept of progressive waves, I showed a drawing from one of the textbooks, where someone was moving a rope such that waves traveled on the rope. The idea was to show that for progressive waves the wave form and energy travel, while the matter itself stays more or less in place, only moving up and down or in circular orbital motions.

The look I got from one of the students for showing that drawing confused me a bit and I am still not sure whether it was a “I have no idea what you are trying to tell me!” or a “Duh! Are we in kindergarden?”, but I think it was probably closer to the former. So from now on I will carry a piece of rope on me to show this in lectures and to have students try themselves.

A wave shape traveling forward on a rope, while the rope itself stays in place.

I filmed a quick video because it was difficult to watch the wave while exciting it myself, but it turns out it is even more difficult to hold a camera more or less steady while exciting waves at the same time, plus the movement is pretty quick even for a camera as awesome as mine. Anyway, if you want to procrastinate learn more about waves, watch this!

Internal waves in the atmosphere

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A photo of internal waves in the atmosphere.

Internal waves exist on the interface between fluids of different densities. In the ocean they are mostly observed through their surface imprint. In the tank, we could also observe them by looking in from the side, but this is hardly feasible in the ocean. But luckily vision is easier in the atmosphere than in the ocean.

On our research cruise on the RRS James Clark Ross in August 2012, we were lucky enough to observe atmospheric internal waves, and even breaking ones (see image above). This is quite a rare sight, and a very spectacular one, especially since, due to the low density contrast between the two layers, the waves break extremely slowly.

It is really hard to imagine what it looked like for real. This movie shows the view of Jan Mayen – the volcano, the rest of the island and then the atmospheric waves. Please excuse the wobbly camera – we were after all on a ship and I was too excited to stabilize properly.

Details of lee waves in the tank.

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A movie focusing on details of the lee waves in the tank.

In this post, we investigated lee waves in a tank in a general way. Here, I want to show a detail of those lee waves:

In this movie, the concept of hydraulic control becomes visible. On the upstream side of the mountain, the dense water layer forms a reservoir which is slightly higher than the mountain. On top of the mountain and towards its lee side, the layer of denser water is stretched thin and has a smooth surface until about half way down the mountain, where waves start to form. In this thin, smooth layer, flow speeds are higher than the wave speeds, hence disturbances of the interface are flushed downstream and cannot deform the interface. Only about halfway down the mountain, the phase speed becomes equal to the flow speed, hence waves can both form and stay locked in place relative to the mountain.

For more information on internal waves, check out these posts [which are scheduled to go online over the next couple of days]: