Super Rogue Waves: Observation of a Higher-Order Breather in Water Waves

Click the image for a video of an experimentally-generated
rogue wave capsizing a Lego boat.

Phys. Rev. X 2, 011015
(2012) -
Oceanic rogue waves are relatively large surface waves that appear spontaneously far at sea. They can suddenly develop from very calm and apparently safe sea states, cause serious damage to ships or offshore structures, and then disappear without a trace. Where these apparent anomalies come from is still a puzzle for scientists. A simple theoretical model for describing the evolution of these waves is a nonlinear Schrödinger equation. This equation, due to its nonlinearity, has a set of hierarchically ordered solutions known as rational breathers, or evolving solitons growing out of, and amplifying, a small localized wave perturbation. Recently, we created the lowest order rational breather, also known as the Peregrine soliton, in a laboratory-scale water tank. One open question was then: Could higher-order strongly amplifying breathers, or super rogue waves, be generated also in such a water tank? In this paper, we combine an experiment with the theory to show that the answer is an affirmative “yes.”

To generate these solutions in an open water tank, we start with a carrier wave that is a wave-tank analogue of the stable small ocean waves. The mathematical initial conditions describing small localized perturbations for the generation of the higher-order breathers are simulated exactly with a computer controlled paddle and stage-wise experiments are carefully designed to remove artifacts or get around the constraints imposed by the limited size of the tank. Indeed, large localized waves with an amplification factor of 5—super rogue waves in this laboratory setting—grow out of the small perturbation in the manner predicted by the equation.

We believe that our work not only suggests an easily accessible platform for exploring extreme water-wave dynamics, but may also stimulate similar experimental studies on high-order breather solutions in other fields such as optics, plasma physics, and superfluidity where nonlinear dynamics rules.