In the previous article of this series we had a look at how waves are generated by the action of the wind blowing across the ocean surface, and how those waves grow in the storm centre. Now we’ll look at what happens to them once they leave the storm centre and are no longer under the influence of the wind.
Once the waves leave the generating area, they start to propagate away as free-travelling swell. Several different things happen to that swell as it gets further and further away from the generating area. Among these are (a) stretching out in the direction of propagation (radial dispersion), which I already covered in an earlier article (HERE) and (b) spreading out over a progressively wider area (circumferential dispersion), which I’m going to have a look at here.
You can track a swell by keeping an eye on the charts pages. Head HERE for more.
During their initial growth in the storm centre, a certain amount of energy was transferred into the waves. As the waves propagate away, most of that energy tends to be conserved, and swells can travel enormous distances without much loss of energy. This was proved in a famous 1963 experiment, when Walter Munk and colleagues tracked several swells from one end of the Pacific Ocean to the other.
However, even though the energy isn’t lost, it is effectively ‘thinned out’ as the swell gets further away from the storm centre and the swell spreads out over a progressively wider area. The spreading inevitably leads to a reduction in wave height. This is perhaps easier to understand if you think of the swell as a series of wave-fronts radiating out from a single point; the wave-fronts stretch out, getting wider but also getting lower at the same time.
So how much does the wave height actually decrease with distance from the storm centre? To explain, I’ll start off with a very simple model and then get more realistic as we go on. First of all, assume that the waves originate from a single point-source, and spread out from that source as a series of wave-fronts, just like when you throw a pebble into a pond. In this case, the total width of the wave-front is proportional to the distance it has travelled away from the source.
As I said earlier, the total wave energy is conserved; but the wave energy per metre width of wave-front diminishes in proportion to the distance from the source. In other words, for every doubling of the distance from the source, the energy per metre width of wave-front diminishes by half.
It follows that the wave height also diminishes. But it doesn’t diminish quite the same as the energy does. This is because the energy contained in ocean waves is proportional to the square of the wave height. As a result, an energy reduction of half means a height reduction of about 30 per cent. Or, for every doubling of the distance from the storm centre, the wave height is reduced by about 30 per cent. So, according to this simple model, if a swell that has propagated 500 km away from a storm is measured at 2 m, it will be 1.4 m high by the time it gets to 1,000 km and about 1 m high by the time it reaches 2,000 km.
Now, real storms are not singular point sources of swell like a pebble hitting a pond. In reality, the wind in the storm blows over an area of ocean (the fetch) that can be quite wide. As a result, the spreading out of the wave-fronts has less effect on the energy reduction with distance. The overall reduction in wave height for every doubling of distance from the storm centre could be as little as 15 to 20 per cent, depending on the width of the fetch.
I won’t go any further with that, because there is another thing that makes any calculation of wave-height reduction with distance from the storm centre a bit academic. This is the effect of the local bathymetry on wave height as the swell propagates over shallow water near the coast. Bathymetric focusing can sometimes increase wave heights so much that it more than compensates for any reduction due to circumferential dispersion. That is why, at places such as Puerto Escondido, you can get really big surfable waves from storms thousands of miles away, even from the other hemisphere.
More on this in my book Surf Science: an Introduction to Waves for Surfing.
Cover shot by Helio Antonio.