How Are Sets Formed?

Tony Butt

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Updated 7d ago

One of the great things about surfing is that no two swells are the same. Even though ‘on paper’ they might look exactly the same, in reality they can turn out completely different. Apart from key parameters such as wave height, period and direction, there are other, more subtle factors that can give each swell its own unique signature. One of these is the way that swell is organised into groups, or sets.

This is extremely important, especially if it’s big. Things like the time between sets, the number of waves in a set and which wave in the set is the biggest can be crucial. On a big day it is usually a good idea to get an idea of the behaviour of the sets beforehand – while you are sitting on the clifftop studying the rips and other things. This can save you a lot of grief once you are out there.

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Oh when the sets come marching in.

Oh when the sets come marching in.

© 2019 - Trevor Murphy.

We can call this the groupodynamics of a swell. But despite the importance of the groupodynamics, we can only really predict it in broad, fairly imprecise terms. We know that, the further the swell propagates away from the storm centre, the more opportunity the waves have to form into groups.

Therefore, a long-travelled swell is more likely to have regularly spaced and clearly defined sets, whereas a locally generated swell will more likely be chaotic and continuous. But those subtle details, such as whether the fourth or the sixth wave is the biggest; or whether there are sets of three interspersed with sets of eight, or sets of eight interspersed with sets of three, usually only become apparent on the actual day the swell arrives.

Before we start to wonder how all that might work, let’s have a look at the most basic principles behind how wave groups are formed.

To begin to understand how waves form into groups, we can look at a very simple mechanism called linear superposition.

In reality, many different waves of different sizes, lengths and directions are generated in the storm centre. As these propagate away from the storm centre they all interact with each other, which, as you can imagine, is extremely complicated. So, just to start with, we’ll use a highly-simplified case of just two wave trains, and see what happens as they interact.

Forecast: UK + Ireland

The two wave trains are the same height, and they are travelling in the same direction, but each one has a slightly different wavelength. As they both start to propagate over the same stretch of ocean, one becomes superimposed upon the other. A resultant wave train emerges, which is the sum of the two original wave trains.

If they had been of equal wavelength, the resultant wave train would just be the same, only twice the height. However, since they have different wavelengths, the peaks and troughs corresponding to each wave train don’t simply coincide. You get peaks coinciding with peaks, peaks with troughs and every combination in between. This is called constructive and destructive interference, and is a very simple concept that you might remember from elementary physics.

In the end we can see that the resulting wave train is a primitive wave group (see diagram).

‘Snapshot’ of the simple case of two superimposed wave trains (the red and the blue) of slightly different wavelengths. Because of the different wavelengths, the peaks and troughs don’t exactly coincide at every point. Where they coincide, they add together making the result twice as big. Where a peak coincides with a trough, they cancel out making the result zero. The resultant wave train at the bottom contains a primitive grouping structure.

Now, there are one or two problems with the simple model above. Firstly, it is a snapshot – in other words the sea surface is frozen at one instant in time. If we could see how the situation evolves over time, it might reveal things that we couldn’t see before.

Secondly, as I already mentioned, in reality there are many, many wave trains combining together, all of different heights, wavelengths and directions. What's more, the combination of those factors is constantly changing as the swell propagates over the ocean. So, really, the model above is a pretty unrealistic simplification.

Finally, the model doesn’t take into account the fact that waves of different wavelengths travel at different velocities (radial dispersion – see my article here). This is really important and it affects the way the waves combine as they travel along.

In the diagram below is a slightly more realistic model. For a start the waves are moving. Also, there are three wave trains instead of two, and the wave trains are of different heights. And, crucially, radial dispersion is taken into account, with the longer waves travelling faster than the shorter ones. You can see how the grouping structure constantly changes as the waves move along.

Superposition of three wave trains each of a slightly different wavelength and height, and including the effects of radial dispersion: The resultant wave train is the dark blue one at the bottom. (Thanks to Kraaiennest for the original diagram upon which this was based).

Cover shot by Adam Cornick