Modulation instability and convergence of the random-phase approximation for stochastic sea states

Agissilaos Athanassoulis*, Irene Kyza

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

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Abstract

The nonlinear Schrödinger equation is widely used as an approximate model for the evolution in time of the water wave envelope. In the context of simulating ocean waves, initial conditions are typically generated from a measured power spectrum using the random-phase approximation, and periodized on an interval of length L. It is known that most realistic ocean waves power spectra do not exhibit modulation instability, but the most severe ones do; it is thus a natural question to ask whether the periodized random-phase approximation has the correct stability properties. In this work, we specify a random-phase approximation scaling, so that, in the limit of L→∞ ,the stability properties of the periodized problem are identical to those of the continuous power spectrum on the infinite line. Moreover, it is seen through concrete examples that using a too short computational domain can completely suppress the modulation instability.
Original languageEnglish
Number of pages23
JournalWater Waves
DOIs
Publication statusPublished - 22 Mar 2024

Keywords

  • Stochastic sea state
  • Random-phase approximation
  • Nonlinear Schrödinger equation
  • Modulation instability
  • Alber equation

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