Rogue Wave Observation in a Water Wave Tank

The conventional definition of rogue waves in the ocean is that their heights, from crest to trough, are more than about twice the significant wave height, which is the average wave height of the largest one-third of nearby waves. When modeling deep water waves using the nonlinear Schrödinger equation, the most likely candidate satisfying this criterion is the so-called Peregrine solution. It is localized in both space and time, thus describing a unique wave event. Until now, experiments specifically designed for observation of breather states in the evolution of deep water waves have never been made in this double limit. In the present work, we present the first experimental results with observations of the Peregrine soliton in a water wave tank.

Figure 1

Peregrine breather solution (5). The maximum amplitude, which occurs at $X=0$, $T=0$, is a factor of 3 higher than the background carrier wave. Note also the sharp drops in the amplitude (troughs) on either side of the maximum.

Figure 2

Schematic illustration of the water wave tank.

Figure 3

Temporal evolution of the water surface height at various distances from the wave maker.

Figure 4

Peregrine soliton measured at the growing, as well as decaying, stages of its evolution.

Figure 5

Comparison of measured surface height at the position of maximum rogue wave amplitude (solid line) with the theoretical Peregrine solution (dashed line) evaluated at $X=0$.