Extreme rogue wave generation from narrowband partially coherent waves

Area of Science:

• Nonlinear physics
• Wave phenomena
• Statistical mechanics

Background:

• Partially coherent waves (PCW) are superpositions of uncorrelated linear waves.
• Long-time evolution of PCW leads to rogue waves and non-Gaussian statistics.
• Rogue wave frequency increases with narrower initial spectra.

Purpose of the Study:

• Investigate integrable turbulence from very narrow initial spectra in the focusing one-dimensional nonlinear Schrödinger equation.
• Analyze the emergence and statistics of rogue waves in this limiting case.
• Characterize the quasistationary state (QSS) and its properties.

Main Methods:

• Numerical simulations of the focusing one-dimensional nonlinear Schrödinger equation.
• Analysis of probability density functions (PDF) of intensity.
• Comparison of observed rogue wave amplitudes with rational breather solutions.

Main Results:

• Turbulence enters a long-lived quasistationary state (QSS) from very narrow initial spectra.
• The PDF of intensity in the QSS is Bessel function-approximated and independent of the initial spectrum.
• Rogue waves with amplitudes ten times the average are observed, matching rational breather solutions.

Conclusions:

• The QSS exhibits heavy-tailed, non-Gaussian statistics, significantly increasing rogue wave probability.
• The findings highlight the fundamental limiting case of PCW evolution and rogue wave formation.
• Rational breather solutions accurately describe the largest rogue waves observed.