Shallow water waves

Have you ever noticed how, if you are at a shallow beach, no matter how choppy waves are further offshore, everything becomes nice and orderly on the beach?

Below you see where the water depth suddenly increases, both from the color of the water and from the wave pattern. While in deeper water waves propagate at all kinds of speeds depending on their wavelength, the moment the water becomes shallow enough, all waves propagate at the same speed (except for the really short waves for which the water is still deep, but let’s forget about those). If all waves propagate at the same speed, it means that the form of the wave that we observe stays constant over time and just moves as a whole. Hence it looks a lot more tidy than the choppy waves further out.

Funny that in all these years of wave watching, I have never thought about that before!

Watch the movie below to see for yourself

Watch the dispersion relation in action

Remember how we talked about how waves seem to propagate extremely slowly into that calm patch that occurs when a boat pulls away from a dock? Well, the other day I noticed that there is even more physics you can see when watching a similar situation: You see how long waves propagate much faster than short waves (that is for deep water waves, in shallow water the wave speed only depends on water depth, not on wave length)

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Here you see a formerly smooth patch of water where the Håkon Mosby was until a minute ago, and you see how long waves have already propagated into that smooth patch while shorter waves are everywhere in the choppy water around the smooth patch, but have yet to propagate into it. Now that I think of it I’ve seen this many times before, I just never noticed. It’s even visible in the video I posted with the other blog post.

And here is a video. Note how the long waves invade the smooth spot of water long before the shorter waves do: