Hobie Surf: Surf Science 101: Wave Speed

Last week’s blog focused on the genesis of ocean waves. This weeks I will attempt to breakdown the often lengthy journey open ocean waves take on before reaching the coastline. We know that from low-pressure storm activity, strong winds can create waves that can exceed 50-feet in height. Waves of these immense heights are common within the fetch and just outside the area of storm activity but decay rapidly during the initial distance traveled. kind of like how a brand-new car driven off the car lot instantly loses value, waves generally lose between 80 – 90 per cent of their energy in the first 100 miles traveled away from the area of storm activity. So, an initial wave height of 30-feet will be reduced to 6-feet, soon after traveling away from the area of propagation.

Once waves travel out of the fetch, or area where the wind is the generating force, they are no longer wind waves and in-turn identified as free waves, or what we understand as ground swell.

Wave Speed

For me, the most intriguing characteristic of waves is wave speed. As waves travel away from the storm’s influence they begin to organize into groups of waves with similar period and wave length called wave trains or wave groups.

Wave period is the amount of time that passes between successive wave crests (or troughs) at a stationary point. Try this; the next time you are out surfing, sit outside and wait for a set. When the crest of the first wave of the set passes underneath you, stay where you are and start counting,… one Mississippi, two Mississippi… until the next wave crest passes beneath you, and try it again for the following wave. Better yet, count the seconds between each wave crest for the entire set. The seconds that pass between each wave is the wave period. You will notice that the period will change daily. Generally speaking, the shorter wave periods (8 – 11 seconds) are waves that have formed relatively close to the coast, what surfers refer to as wind swell. Waves with longer periods (12 – 18 seconds) are traveling much farther distances before reaching the coast. Shorter wave periods do not equate to faster moving swell. Short period equates to short wavelengths (the distance between successive crests or troughs) and long period equates to long wavelengths.

Short period swells equate to short wave lengths and low energy. Long period swells have long wave lengths and high energy.  A swell originating in the south Pacific that reaches the coast of Southern California has to travel upwards of 5,000 miles and only longer period, longer wavelength swells can make that journey.

So how does all this relate to wave speed? Well, longer wavelength swell groups travel much faster than shorter wavelength swell. Longer wavelengths have much more energy due to the fact that wave motion depth is equal to one-half the wavelength. For example, a south Pacific swell, in deep water, with an 18-second period and significant wave height of 35 feet will have a significant wave speed of about 62mph*. This would equate to each wave crest moving at about 92 feet per-second, therefore, with an 18-second period, the wavelength would equal about 1652 feet. So, referring back to deep-water particle motion of one-half of the wave length, the depth of each wave in the swell group to be about 826 feet. This means that at an ocean depth of 826 feet, the swell group begins to feel the bottom and slow down, but it is very important to know that the wave period remains the same. For comparison, a swell group with a 7 second wave period and wave height of 10-feet will have a significant wave speed of about 25mph*.

To make things even more confusing, significant wave speed does not equal the wave group speed. Wave groups, or what we might refer to as a “set”, move at one-half the significant wave speed. So, that significant wave speed of 62mph with an 18-second period is moving within a wave group moving only 31mph. So, what’s the deal?

The best analogy I can come up with is to think of each wave group as a pack of cyclists in the Tour de France. In a typical bike race, cyclists group themselves into riders that can maintain similar speeds, the group being referred to as a peloton. When you watch a peloton in action, the group of cyclists are working together to keep the entire peloton moving at the fastest possible pace. The leading edge of the peloton is encountering the most wind resistance while the back of the peloton is drafting, or being pulled by the group because they are essentially in the slipstream of the cyclists in front of them. Eventually the leading cyclist will tire and begin to fall-off and the following cyclists will speed-up to move into the leading edge. So, back to the wave group, although the entire wave group is moving at about 31mph, the speed of the wave at the end of the group needs to move at 62mph in order to eventually reach the leading edge before falling-off to the back of the pack before moving forward again. Think of it as a conveyor-belt operating within a moving sidewalk.

I’m sure this is enough to wrap your mind around until next week but if you want to do wave-speed conversions of your own, here is the formula:

*Wave speed, C, = L/T, where L = Wavelength and T, the wave period, is conserved.

C² = (g/2π) L Tanh[(2π/L)D], where g = earth’s gravity,

D = water depth, L = wavelength, and Tanh[ø] = the hyperbolic tangent of angle[ø]. Here ø equals (2π/L)D in radians.

Deep-water approximation:

When D>L/2, Tanh[(2π/L)D] ≈ 1.0. C² = (g/2π)L

Shallow-water approximation (when the wave begins to feel the bottom of the ocean).

When D<L/20, Tanh[(2π/L)D] ≈ (2π/L)D. C = √gD

Use a calculator.

Gary Larson

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