Wave sets in the ocean

I USED TO SCOFF at the surfers’ notion that ocean waves arrive in sets of 7 or 9.  They could never explain why that should be. They were adamant, however, and later in life I discovered that there were many people with scientific training who agreed with them, although they had no explanation for it either.

I put the theory to test once on a tropical beach on the island of Fernando de Noronha, off Brazil, where ocean surf was pounding the only beach where we could land in our inflatable dinghy. I stood off, outside the line of breakers, and started counting swells.  I found it difficult to tell whether one breaker was bigger than another, but I certainly wanted to miss the biggest ones because I didn’t have any experience of landing an outboard dinghy on a beach through heavy surf.

But the swells did seem to arrive in sets, as my surfer friends had claimed. After each set there was a calmer patch, and that was the signal to gun it for the shore, riding the back of the last wave ahead.

We did this many times, of course, and the biggest problem seemed to be deciding whether the particular set you were watching comprised seven waves or nine. If it was a nine-wave set, and you started off on the seventh wave, you could be in trouble. There didn’t seem to be any pattern  that I could decipher. Sevens and nines rolled along in a totally random fashion.

Another problem was the variation of the size of individual waves in each set. You could never tell when one wave was going to be smaller than the others, which is what we would have liked to have known. But there were usually one or two that were bigger than the rest, sometimes one after the other, sometimes not. In the end, we mostly crossed our fingers and hoped we had timed it right, between sets.

It’s natural to be fascinated by waves if you sail on an ocean or a decent-sized lake and, indeed, there is an awful lot to be learned about them. One of the first things you learn about waves on the open ocean is that the water in them doesn’t move forward with the wave. The molecules in a deep-water wave merely move up, forward a tiny bit, and then down again.  You can achieve almost the same effect by laying out a line on the ground and snaking a wave through it.

Guy Murchie put it rather nicely when he wrote in The Seven Mysteries of Life:

What’s an ocean wave made of?

At first glance, nothing but salt water;

But keep your eyes on it ten seconds . . . twenty seconds . . .

You’ll notice that the water is roused

Only momentarily by the wave

Which passes it by,

That the wave leaves the molecules and bubbles behind,

That the wave in essence is a kind of ghost

Freed from materiality by the dimension of time,

Made not of substance

But energy.

Today’s Thought

There is no excellent beauty that hath not some strangeness in the proportion. — Francis Bacon

Tailpiece

“How much is a bottle of brandy? It’s my nephew’s birthday and he likes brandy.”

“Well, madam, it depends on the age. Seven-year-old is quite reasonably priced. Ten-year-old costs a bit more. Twelve-year-old can be quite expensive.”

“Gee, that’s terrible. My nephew is 25.”

(Drop by every Monday, Wednesday, Friday for a new Mainly about Boats column.)

Where the waves get started

WAVES ARE FASCINATING. If you’re out on the water, they’re all around you; waves everywhere. But how do they start?  What kick-starts a wave into motion?

Well, if you blow on a saucer of water, your breath will make a little dent. If you keep blowing, the pressure of your breath on the back of the dent will move it forward. It looks as if the molecules of water are trying to get away from you. But that’s deceptive.  In fact, the water in a wave just moves up and down, or in a slight circular motion. The wave you have created is in fact simply moving energy through the water, just as you can make loops snake through a length of rope. The rope itself doesn’t move forward.

Waves are visible energy, but they don’t move water forward either — at least not until they reach shallow water near shore and trip over their own feet. That having been said, a minimal amount of water moves forward when a whitecap breaks out at sea.

Out there, it’s the wind that dents the surface of the water, and the wind, as we know, is caused by unequal heating of the earth’s atmosphere by the sun’s rays; so we can safely say that waves are actually caused by radiation from the sun.

That still doesn’t explain how a little dent in the surface tension of a sheet of water can grow into a wave large enough to sink big ships. What’s going on here? How do little waves become big waves, and then swells?

Three phenomena make waves grow:  1. Wind speed. The harder the wind blows, the bigger the wave it forms. 2.  Wind duration. The longer the wind blows in the same direction, the larger the waves become. Roughly speaking, the biggest waves form after the wind has been blowing for the number of hours equalling the wind speed in knots. For example, a 20-knot wind needs to blow for 20 hours to form the biggest waves it’s capable of. And the maximum height of a wave in feet is roughly one half of the wind speed in knots. 3. Fetch. For waves to grow to their maximum size, a fetch of at least 600 miles is needed. (A fetch is a stretch of deep water with no intervening land masses.)

It seems to me that waves also grow bigger by eating other waves. Big ones bite and swallow little ones, but, as you’ll know if you’ve ridden out a gale at sea, the little ones don’t disappear. They ride along on the backs of the bigger ones.

It reminds me of what the Victorian-era mathematician Augustus De Morgan once wrote:

“Great fleas have little fleas upon their backs to bite 'em,

“And little fleas have lesser fleas, and so ad infinitum.

“And great fleas themselves, in turn, have greater fleas to go on,

“While these again have greater still, and greater still, and so on."

­ Eventually the wind will die down, but the energy in the waves will carry on. The waves flatten out, round off, and turn into what we call swells; and swells can travel for thousands of miles from the areas where storms created them. Thus, what started off as a tiny ripple in a calm sea can turn into a pack of energy capable of upsetting stomachs on ocean liners and cruise ships far, far away.

Incidentally, if you have any questions about waves, the University of California at Santa Cruz (UCSC) has some answers for you:  

http://wwwcatsic.ucsc.edu/~kudela/OS101/LectureNotes_07/OS101_020907/OS101_020907_notes.pdf

Today’s Thought

The waves came shining up the sands,

As here today they shine;

And in my pre-pelasgian hands

The sand was warm and fine.

— Frances Cornford, Preëxistence

Tailpiece

There was a young lady of Natchez
Whose garments were always in patchez.
When comment arose
On the state of her clothes
She drawled: “Where Ah itchez Ah scratchez.”

(Drop by every Monday, Wednesday, Friday for a new Mainly about Boats column.)

The mystery of waves

I SOMETIMES WONDER how different sailing would be if there were no waves. I mean, imagine a surface like sheet of mercury that would just dent slightly when the wind blew on it.  We would just glide serenely everywhere, all over the world. There would be no pounding, no spray flying back to soak the helmsman, and perhaps best of all, no seasickness.

I have a hard time understanding how a wave forms and why the scientists insist that the water in a wave doesn't actually move forward. I have a faint recollection of reading somewhere that a wave starts when a dimple forms on a flat sheet of water.  The wind blows on the back of the dimple and pushes it forward turning it into a wave that grows bigger and longer as the wind blows longer and harder. But what starts the dimple?

The Oxford Companion to Ships and the Sea says quite categorically that "the water in a wave does not move forward in a horizontal direction but rises and falls below the surface, unless the force of the wind is enough to cause the crest of the wave to overbalance and break, when the water in the crest does move forward."

 It also moves forward when a wave reaches a shallowing shoreline, of course, and the bottom of the wave is retarded by friction against the sea bed.  I have no problem understanding that.

Interestingly, the relationship between wind speed, in miles per hour, and the height of the wave it generates, in feet, is approximately 2 to 1.  This ratio from the U.S. Hydrographic Office suggests that a wind of 50 mph should raise a 25-foot sea.

In fact, however, there are many reports of waves 40 and 50 feet high in heavy gales in some oceans , which would require sustained winds of 80 to 100 mph, which seems unlikely outside of hurricane season. Perhaps these rogue waves are formed when one huge wave happens to ride on the back of another huge wave, thereby doubling its height.

The length of a wave, from crest to crest, is reckoned to be about 20 times the height, after the wind has been blowing steadily for some time and when there is no opposing current. Thus, a wave 25 feet high would be about 500 feet long and would race through the water at about 30 knots, because the speed of a wave (in knots) is the square root of the length from crest to crest (in feet) times 1.34.

For the sea to become fully developed, the wind must blow in the same direction for a certain minimum time, and the rule of thumb here is that the time in hours equals the wind speed in knots. In other words, a 20-knot wind will take about 20 hours to form the biggest waves it can.

Another little mystery for me is how a little oil can calm a nasty sea. I always imagine the tiny molecules of seawater swallowing the oil and experiencing the same relaxing effect that a glass of single-malt Scotch brings to a human being, but I'm not sure that's scientifically acceptable. So it will remain for me one of the many mysteries that makes sailing such a fascinating pastime.

Today's Thought
The longest wave is quickly lost in the sea.
— Emerson, Representative Men: Plato.

Tailpiece

“You’ve got to lose weight. “I’m putting you on soup and salad for a month.”
“OK, doc. Before or after meals?”

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