Wave theory is quite extensive and complex, but only a very small amount of knowledge about waves is essential to sailors to anticipate the risks that can arise from waves for small crafts.
Waves are generated by the wind. There is a relation between fetch, wind speed and the maximum wave height that will result over time. Even with unlimited fetch and duration, the speed, length and height of the sea remain limited by wind speed. Sailors however have to contend with whatever gets dished out, and wave generation has little interest to us in the end.
There are two relations of critical interest to sailors in wave theory:
In order to propagate undisturbed, a deep water wave requires a depth at least equal to half of the distance separating the crests
If the sea bed rises, long waves can start “feeling the bottom”, slow down, become steeper and develop a tendency to break. This is very important. At the edge of the continental shelf, depth commonly changes abruptly from some 1000-1500 metres or more to less than 200 metres.
Long wavelengths in the sea react to this change and one can often feel it while sailing across the transition zone: the slow, sedate rhythm of the sea offshore changes, it feels restless. The sea can break very unexpectedly in this area.
The wind was fresh and the sea quite rough as I sailed off the coastal shelf and into ocean-deep water after leaving Iceland. I didn’t think conditions warranted changing course and kept going with a beam sea. Three times the same night, seas broke on the beam and rolled the sloop with the mast close to horizontal. The first two times, I thought we would soon be on the other side of the bad patch and kept going. The third time was enough and I changed course. Even though no consequences resulted, sailing over the edge with a beam sea is not something I would do today: far too dangerous.
I have found nervous, unstable seas on the edges of continental shelves all over the world. Off South Africa, full-size ships avoid remaining in that area due to the number of wave-induced accidents that have occurred in the past.
The velocity of the waves increases with the length of the sea
The velocity of the waves in deep water varies with the square root of the distance between the crests. This means it increases very quickly as the sea gets longer, and then much more gradually. Regardless of its height, a long sea travels faster. If it breaks, the water in the crest travels at a speed at least equal to the one of the wave, and higher if the crest comes crashing forward: it can equate to a very large sledgehammer. This is very important, because the kinetic energy in the crest increases with the square of the water velocity. A break in a long, fast sea can pack a phenomenal punch. This situation is typical of the high latitudes offshore: the sea is high, but in the same time so long that it creates false sense of security. People tend to think “it is just a harmless swell” and get caught.
A sea is nearly always formed of a system of waves of different lengths and amplitudes. There usually are one or two dominant components, such as a ground swell and wind-generated waves. When depth decreases, the long components in the sea will break first, even if they were hardly noticeable until then. This is how small vessels fishing on a shoal in calm weather can get capsized unexpectedly.
Because the sea is formed of different superimposed wavelengths, uneven heights are reached near-randomly. The phenomenon can create unstable waves unexpectedly even in deep water, especially when the dominant components are already steep. The worst scenario develops when different wave systems arrive from different directions; at the intersections of the crests, pyramidal waves that can reach considerable heights are created. This is also typical of high-latitude mid-ocean conditions, where frontal systems sweeping through can drag huge weather systems formed of northwest and southwest winds.
Besides this, there is some interesting trivia in wave theory, of limited usefulness to most sailors:
- Deep water waves become unstable and break when their height becomes close to 1/7th of the distance between crests.
- In deep water, wave length is linked to the time period T between crests: L = 1.56 x T^2 for T in seconds and L in metres; L = 5.12 x T^2 if L is to be obtained in feet.
- The velocity (in knots) of a deep water waves is linked to its length by the relation: V = 2.4 x √L with L in metres, or V = 1.33 x √L if L is taken in feet. As a result, we also have: V = 3 x T.
This means that by simply timing the sea offshore, one can calculate its length and velocity. A sea with a period of 10 seconds will have a length of 156 metres and a velocity of 30 knots. If the crest detaches and plunges forward into the trough, this mass of water can momentarily move faster than the wave itself. At that speed, it doesn’t take a very large crest at all to deliver a damaging blow to a vessel.
Regardless of wind conditions, one may consider being particularly cautious in the following situations:
When sailing over the edge of continental shelves especially, and near significant changes in water depth when there is a long swell present, even if the swell is low.
- When the sea is very long; long seas can hit unbelievably hard without being high.
- When the sea is steeper than usual and/or there is a known counter-current; this greatly increases the probability of a break.
- When there is a crossed sea running, with two significant wave systems interacting.