Random conditions in the ocean occasionally produce mammoth waves. A wave must be at least 2.2 times the height of the so-called significant wave height to qualify as a freak wave. The significant wave height is the average height of the largest 33% of waves. Some freak waves are caused by strong currents or the chance reinforcement of two large waves, but scientists recently found that a 'self-focusing' effect could also create outsized waves.

The JONSWAP power spectrum - named after the Joint North Sea Wave Project that monitored a huge expanse of ocean in 1973 - describes typical sea conditions. The range of wave heights at different frequencies is a smooth hump that extends from about 0.7 to 0.2 hertz. But Onorato and colleagues found that a so-called 'enhancement factor' in the JONSWAP spectrum has an unexpectedly powerful effect on the profile. When the enhancement factor is 1 the profile is a smooth peak spanning a wide frequency range. But when it rises to 5, the profile becomes much sharper, leading to waves nearly ten times higher. Transforming the frequency-based JONSWAP relation into a time-based Schrödinger-like equation enabled Onorato and colleagues to map the motion of waves over the whole portion of sea under consideration.

"We believe our results provide important new physical insights into the generation of freak waves", says Onorato. His team hopes to verify its findings by employing higher-order equations that take into account finer details about the motion of wave trains. "Wave tank experiments will also be very useful", he adds.