Ninth wave theory

By chance I came across this web site today that asks the question “What are the most popular cruise ship destinations?” I am not interested in the answer to this question, but on this page there is a sidebar entitled “Rogue waves common in Gulf of Mexico” that caught my attention because it has this excerpt:

...the ninth wave theory. As these waves converge occasionally the ninth wave of the ninth wave from one ongoing movement of water hits another one at the exact same time in a certain place into this causes a huge wave ...

Click on this sidebar led to another web page that has this caveat:

Now rogue waves caused from the ninth wave theory are not proven and it is highly skeptical that this is even true. However if you ask a surfer about such scenarios they often consider this theory to be very viable. Oceanographers and wave research specialists disagree and do not believe that this ninth wave thing is possible with rogue waves scenarios.

Not being a surfer myself and never has the opportunity to know one, I have no idea what do the surfers think. But I am intrigued about this ninth wave thing, where does it come from?

I found two reliable sources that can attest to the fact they did not made it up. One source may be more pleasing to the water wave aficionados -- it is actually come from George Gabriel Stokes (1819-1903). In this 2005 Annual Review of Fluid Mechanics article by Alex Craik which included this story recalled by Stokes' daughter, Mrs. Laurence Humphry,

There was a cave called the Land Cave which we always visited after storms had been ploughing up the Atlantic. It had a sort of window opening into it from the land, so that we could see the great waves come in. . . He made a good many wave-observations there, not about steep sea-waves, for that was much earlier, but I think he was trying to find out the relation of the waves to one another and why the ninth wave was so much larger than the others. He told me that he was nearly carried away by one of these great waves when bathing as a boy off the coast of Sligo, and this first attracted his attention to waves.

I added the bold italic emphasize. So this ninth wave thing must be a widely known depiction in Stokes time.

Another source is more literary, it is from the Idylls of the King: The coming of Arthur by Lord Alfred Tennyson (1809-1892) as:

. . . 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: . . .

So if any, this ninth wave thing is likely to be at least an old British legend. Somehow the number seems to have been reduced through out the years. The one I heard most frequently has been the seventh. At any rate the description in that sidebar that "As these waves converge occasionally the ninth wave of the ninth wave from one ongoing movement of water hits another one at the exact same time in a certain place into this causes a huge wave" is just about the most understandable explanation of linear superposition principle for freaque waves one can pass along. For a more academical account of the current state of the art of freaque waves research, however, I highly recommend this web article by Prof. Dysthe and his collaborators.