April 15, 2012

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.

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

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


ben said...

Though you make reference to a lot of "rules of thumb" there are a few things I remember about waves from highschool physics that I thought I slept through.

Namely, waves on average don't move. But any particular wave molecule is moving in a circle, and returns to it's starting point. That's why a wave can crash. After all, the water at each crest and trough have to go and come from somewhere.

As for the height problem, when two waves coming from different directions meet, their heights add together. So when two crests of equal height meet, the resulting crest is double high. When their troughs meet, they will be doubly low. That double high and double low can add up to scary. Fortunately, when a crest and trough meet, they cancel each other out.

As for what starts a wave, don't try and tell us you have never sneezed in your coffee (and experienced the resulting splashes.)

Don P said...

Wow, this..
"the speed of a wave (in knots) is the square root of the length from crest to crest (in feet) times 1.34." explains where the formula for maximum hull speed comes from. Max speed through the water being obtaind when the crest following the bow wave moves back to the stern of the boat.

Thanks John!
As always a font of knowledge and wisdom.

Adam said...

Thanks again for the rules of thumb. Hopefully some day I will remember them all :)

Here's something for you:


It's a video of a bowed violin string in slow motion. Initially you see just a small vibration, but no coherent "movement". After about thirty seconds, and increasingly throughout the video, you can really see the traveling wave--traveling along the string even though the string itself is not moving along its own length.

One interesting thing is that the traveling wave is really only obvious while the string is being bowed. Once the bow lifts off the string, that component of the wave is a lot harder to notice, and instead you mostly see a standing wave. I wonder if this has any analogy in ocean waves?