# Phase and group velocities in deep and shallow water

When Tor came to visit me in GFI’s basement lab a couple of days ago, he told me about an experiment he had seen in Gothenburg in the seventies. So Elin and I obviously had to recreate it on the spot. Therefore today, we are comparing phase- and group velocities in deep and shallow water!

Waves are excited by means of an oscillating, hand-helt beer can, curtesy of the beer brewing club at GFI. The experiments are filmed and wave lengths and phase velocities are determined from the videos, which is a lot easier than measuring them directly while the experiment is being run.

# Shallow water waves

For shallow water, we are using a water depth of 10 cm. Waves are very easy to see and phase velocities are equally easy to measure.

There is another experiment on (standing) shallow water waves being run at GFI the year before students attend GEOF213, which I described back in 2013.

# Deep water waves

For deep water waves, we use a water depth of 42.5 cm (the exact number only matters when the tank filling is also used to fiddle with the dead water experiment, as I had been when the idea for this experiment came up).

Typical wave lengths that are easy to do are between 10 and 25 cm (wave lengths obviously have to be short enough that the water is still “deep”, i.e. H>>wave length) — Elin’s instruction to me for the kind of waves she wanted was “Allegro!” :-D Elin, you are really the coolest and most fun person to play with tanks with!

In deep water, we now have the added difficulty that the phase speed is twice as fast as the group speed. This makes observing the whole thing a lot more difficult. Also amplitudes are a lot smaller now, since the tank was so full and we wanted to keep the water inside…

Here is t0 — Elin has just dipped the beer can into the water for the first time

t1 — can you see the wave signal has propagated up to where the red arrow is pointing to?

t2 — the signal has reached my thumb at the left edge of the picture.

From timing this, we can calculate the group speed. We can also measure the wave length on the video and then calculate a theoretical phase speed from that. For the experiments Elin and I did, the results were pretty good, as in phase speed was usually about twice as fast as group speed. And I am curious to hear how well this works out when the students run the experiment!

# Wave watching

This is an old picture from early spring, but I just love how the reflection of that pier shows up the different wave lengths so clearly. The longer swell wouldn’t have been visible just from reflections of the sky…

# The enormity of waves

It’s easy to forget the enormous size and power associated with waves in the ocean. Yes, we see pictures of surfers on Hawaii or of ships in waves occasionally, but usually we don’t really think about how large waves out in the ocean actually are. Which makes it easy to underestimate the force that the ocean holds within, not only on days when natural disasters like storm surges or tsunamis occur, but on a daily basis, just in the swell of distant storms. So sometimes it is quite healthy to look at waves on the beach and compare them to other buildings.

For example here, waves and Hastings Pier:

Those aren’t even particularly large waves, yet we see that their wavelength, peak to peak, is easily a lot more than 20m. This is what coastal structures deal with on a daily basis!

# Hair-dryer driven surface waves

Looking at wave length, frequency and speed. (deutscher Text unten)

The wave group played with a tank and a hair dryer (the hair dryer safely away from the water, obviously) and different modes of recording. high definition, slow motion and what have you. They also did a really cool data-model comparison, which is still top-secret, but we might reveal it tomorrow. Stay tuned!

Die Wellengruppe hat mit einem Fön (der natürlich in sicherer Entfernung vom Tank war!) Wellen erzeugt und sich die Wellenlänge, Frequenz und Geschwindigkeit angesehen. Sie haben außerdem mit unterschiedlichen Modi der Kamera gespielt: High Definition, Zeitlupe und noch mehr. Sie arbeiten außerdem an einem geheimen Daten-Modellvergleich, von dem wir wahrscheinlich morgen schon berichten werden. Stay tuned!