Waves Upon, and Within, Waves
Date Posted: February 6, 2024
Source: Vincent Pica Commodore, 1st District, Southern Region (D1SR) USC

There was a rogue wave incident involving the cruise ship Viking Polaris on November 29, 2022, at 22:40 local time, while the ship was sailing towards Ushuaia, Argentina. But what is a "rogue wave incident"?  Rogue, freak, or killer waves have been part of marine folklore for centuries but have only been accepted as real by scientists over the past few decades.

A rogue wave estimated at 18.3 meters (60 feet) in the Gulf Stream off Charleston, South Carolina. At the time, surface winds were light at 15 knots. The wave was moving away from the ship after crashing into it moments before this photo was captured. Courtesy: NOAA

"Surf Happens" – But How Do I Gauge It?

For the more scientifically inclined, the energy within a wave is proportional to the square of the wave's height.  Like many things in nature, a 4' wave isn't four times as powerful as a 1' wave.  Four-foot seas are 16 times as energetic as one-foot seas, all else being equal.  How much energy is in one of those 100' "grey beards" passing by Cape Horn, compared to a 4' wave in Moriches Inlet?  Do the math.  Not 25 times more powerful (100' / 4') but 625 times more powerful!  (100 squared / 4 squared)

But things are rarely equal.  A long, slow, four-foot sea is one of life's great pleasures at sea.  What matters is how close together and how steep those waves are.  A good way to compare wave steepness is to divide the wave height by the frequency period squared. This is essentially how fast your sleigh ride is going to be – or the beating you are going to take.  Halving the frequency period (from, say, 10 seconds to 5 seconds) of a wave quadruples the acceleration of your sleigh ride, and more than likely multiplies the sea sickness aboard the boat. Another way to gauge what awaits you at sea is a Severity measurement.  This indicates the amount of energy carried by each bit of wave and is proportional to the energy of a wave (the square of its height) divided by its wavelength (how much distance the waves are apart, measured from peak to peak.)  As you can probably do in your head, 6' waves that are 6'(distance, not time) apart are more severe than 6' waves that are 12' apart.  We don't need the Cray computer for that one…

Continuing our discussion about waves, we all know that anyone who has stood by the seashore and watched the waves roll in must have wondered at least once, "when is the next big one coming?"  And, sure enough, just out in the offing, you can see one that just seems head and shoulders above the others.  This column is about that.

Traditions Die Hard at Sea

You've seen me make that observation before and it will always be true, by my reckoning.  One of those traditions is that waves come in sets of seven, meaning that every 7th wave will be like the prior wave that passed earlier.  Another view is that once a big one has crashed ashore, the next one is but seven waves behind.

Do the Math

Of course, that isn't true – but it is sort of true, meaning that waves are part of a hydrodynamic system and there are statistical probabilities that do apply.  One of the more quoted oceanographers in this regard is Walter Munk, who began the systemization of waves, weight heights and predictability (and measurement) of waves.  He started his work during World War II and won international awards and acclaim for his work in the field for many decades after.  Waves, or perhaps better said, "sets of waves", are categorized by the "significant wave height" or HsigHsig was intended to mathematically express the height estimated by a "trained observer".  

In oceanography, the Hsig is defined traditionally as the mean wave height (trough to crest) of the highest third of the waves.  But once you do that, you start to tease out the statistics of waves of varying heights arriving – and if you are a mariner out upon God's Great Sea, this can be of intense interest.

Now this can get pretty intense, mathematically, but if you focus on the message and not on the technology, you'll get all the information you need.  Generally, the statistical distribution of the individual wave heights is well approximated by a "Rayleigh Distribution." For example, given that Hsig = 1 meter, or 3.3 feet, statistically:

  • 1 in 10 will be larger than 1.2 m (3.6 ft)
  • 1 in 100 will be larger than 1.5 m (5.1 ft)
  • 1 in 1000 will be larger than 1.9 m (6.2 ft)

This implies that one might encounter a wave that is roughly double the significant wave height.

And remember what Hsig is – an expression of the highest 1/3rd of the waves.  This means that 2/3rd are less than that.  Perhaps lulling the mariner into a false sense of security?

Converting that distribution into time at sea, where a wave passes your 25' vessel every 6 seconds, the table would look like this:

  • 1 every minute will be larger than 1.2 m (3.6 ft)
  • 1 every 10 minutes will be larger than 1.5 m (5.1 ft)
  • 1 in 100 minutes (1.7 hours) will be larger than 1.9 m (6.2 ft)

And this is when 2/3rd of the waves are less than ~3'…  And, statistically, when two significant waves come into "phase", it is possible to encounter a wave that is much larger than the significant wave. 

Groups of 7?  No. But the big'uns are out there. "Both in safety and in doubt, always keep a good look-out."

If you have questions on this column or you are interested in being part of USCG Forces, email me at JoinUSCGAux@aol.com or go directly to the US Coast Guard Auxiliary "Flotilla Finder" at  http://www.cgaux.org/units.php and we will help you "get in this thing."

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