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Hydrodynamic modulation instability triggered by a two-wave system.

Chaos

October 2024

Disaster Prevention Research Institute, Kyoto University, Uji, Kyoto 611-0011, Japan.

Article Synopsis
  • Modulation instability (MI) causes regular nonlinear wave trains to break down, potentially resulting in localized phenomena like rogue waves across various nonlinear dispersive media, including hydrodynamics and optics.
  • The classical MI dynamics can start with small-amplitude sidebands around a main wave peak, often visualized as a three-wave interaction setup in experiments, but more complex patterns can emerge through breather solutions of the nonlinear Schrödinger equation (NLSE).
  • This study explores MI in deep-water surface gravity waves, demonstrating that it can be initiated by just a single unstable sideband, yielding experimental results that align closely with nonlinear simulations, while also indicating shifts in focusing cycle behavior observed in longer-term wave evolution.
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We present the experimental finding of multiple simultaneous two-fold degeneracies in the spectrum of a Kerr oscillator subjected to a squeezing drive. This squeezing drive resulting from a three-wave mixing process, in combination with the Kerr interaction, creates an effective static two-well potential in the phase space rotating at half the frequency of the sinusoidal drive generating the squeezing. Remarkably, these degeneracies can be turned on-and-off on demand, as well as their number by simply adjusting the frequency of the squeezing drive.

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Evolution of resonant three-wave interaction is governed by quadratic nonlinearities. While propagating localized modes and inverse scattering mechanisms have been studied, transient states such as rogue waves and breathers are not fully understood. Modulation instability modes can trigger growth of disturbances and the eventual development of breathers.

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