Statistical calculations, broadly confirmed by observation, tell us that in a chaotic sea one wave in every 20 ought to be twice the average height; one in every thousand three times the average height; and that one in every 300,000 waves is four times as big as usual.
Ancient tradition, on the other hand, had it that each tenth wave, or sometimes each seventh , is always bigger than its fellow. Tennyson believed the number should be nine ; in The Coming of Arthur he records:
And then the two
Dropt to the cove, and watched the great sea fall,
Wave after wave, each mightier than the last;
Till last, a ninth one, gathering half the deep
And full of voices, slowly rose and plunged
Roaring, and all the wave was in a flame.
The development of waves is very complex. It often happens that a strong wind, having created a train of waves moving in a certain direction, begins to blow from a different quarter. The original train of waves survives as swell - waves no longer driven by the wind, slowly decaying, but sometimes surviving by their own momentum for a surprisingly long time.
The "new" wind, on the other hand, creates its own new train of waves, which interferes with the first - the individual waves sometimes reinforcing each other to create a wave of exceptional height, at other times cancelling each other out. Any number of individual wave trains may coexist in this way as components of a complex pattern. Let me tell you how a colleague once described it:
"As the components continually get into and out of step with each other they produce groups of high waves, followed by the brief intervals of relatively quiet water which are characteristic of even the stormiest of seas. Every now and then, just by chance, it so happens that a large number of these components get into step at the same place, and an exceptionally high wave ensues. The life of such a wave is transient, being not much more than a minute or two.
"Because each wave component is travelling at its own characteristic speed, the faster ones escape from the others and the monster wave just dies away as swiftly as it was born. But somewhere else in the storm, at some other time, some other wave trains will again just by chance coincide, and produce another large wave which will have its brief moment of glory before disappearing forever into the random jungle of the sea."