Rogue Waves in Water and Optics
Date and time:
Friday, July 19, 2013 - 3:00pm
In recent years, large amplitude “rogue” waves have been studied in water and optical ﬁbers. These large waves occur more frequently than suggested by conventional linear models and there is widespread belief that nonlinear phenomena may be responsible for these waves.
The nonlinear Schrödinger equation models a slowly modulated, monochromatic, deep water wave train. Moreover, It is widely known that perturbed plane wave solutions of the nonlinear Schrödinger (NLS) equation experience growth due to modulational instability. Through repeated numerical simulations, wave height statistics are determined for both NLS and an equation which incorporates the full linear water wave dispersion relation. The latter technique prevents unbounded spectral broadening which is present in 2D NLS. All equations studied lead to non-gaussian wave statistics that are well described by Rayleigh distributions, and support rogue waves with amplitudes up to ﬁve times the initial amplitude. The differences between one and two dimensional results are small, with the two dimensional equations leading to slightly narrower wave height distributions with a higher mean. This suggests that it may be sufﬁcient to study the integrable, one dimensional Schrödinger equation to understand extreme rogue events, without having to turn to higher dimensional models.
Finally, NLS-type equations that model pulse propagation in zero dispersion nonlinear ﬁbers are also studied. In addition to modulational instability, it appears that certain parameter regimes are governed by a nonlinear instability. Both processes cause signiﬁcant growth that can lead to extreme amplitudes events.