## coastal british columbia## Why are there sets of larger waves? by John Sidles |

Why are there sets of larger waves?

Author; John Sidles sidles@u.washington.edu

Time for Sidles to write! People first began to discover why waves appear in sets when they built a wave tank which launched an absolutely regular train of waves out of a little wave-making machine at one end of the tank.

Trouble was, when this train of waves reached the other end, it was no longer regular. It had organized itself into tiny litle "sets". Hey! said the engineers. Our wave machine must not be working smoothly. So they put a lot of effort into making the tank and the machine absolutely precise and regular. But no go .. the wave trains *still* organized themselves into sets, no matter how carefully and uniformly they were launched.

So the engineers sat down and studied the equations that govern wave motion. They found that certain (very tiny and usually neglected) nonlinear terms in the equations of motion of deepwater waves act to transfer energy (very slowly) from the leading and trailing edge of a set of waves, toward the center waves. Thus the central waves get bigger at the expense of leading and trailing waves.

As a result, even if the wind is blowing absolutely uniformly, waves will still organize their energy into sets. This organization happens slowly, which is why local windswells are less-well-organized than swells that have propagated thousands of miles. The mathematical name of the nonlinear interaction that creates sets in water waves is the "Benjamin-Feir Instability".

In any case, it is pretty cool that this obscure energy transfer mechanism, acting over thousands of miles, creates sets for us surfers!

The best place to learn more about waves is the very cool and accessible paperback book "Waves and Beaches" by Willard R. Bascombe. Take a copy on your next surfari! The photos of Bascombe surfing a 20-ton WWII amphibious landing vehicle, one mile offshore on a maxed-out 20' PNW beach break swell, are more than worth the price!

Cawabunga ... JAS

## The Math

Author; Timothy B. Maddux tbmaddux@gear.ucsb.eduA linear gravity wave with a phase speed of 40 mph (C = gT/2pi, so T = 2piC/g) has a period of 11 seconds. A linear gravity wave with a phase speed of 75 mph has a period of 21.5 seconds.

Feel free to check my math. We don't get many waves over 20-second periods from relatively closer storms, but we also don't get hurricane-force winds over the long fetches and durations required to produce fully developed seas.

Fetch/duration and wind speed, and that is all. The first two are grouped together as they're really expressions of the same thing: how long the wind acts over a wave as it travels. Waves care nothing for distinctions between reaching the end of a fetch or the wind dying off with time.

.-``'. Timothy B. Maddux .` .`~ santabarbarasurfing.com _.-' '._ "From the essence of pure stoke springs all creation."