Experiments on higher-order and degenerate Akhmediev breather-type rogue water waves

A possible mechanism that is responsible for the occurrence of rogue waves in the ocean is the Benjamin–Feir instability or modulation instability. The deterministic framework that describes this latter instability of Stokes waves in deep water is provided by the family of Akhmediev breather (AB) solutions of the nonlinear Schrödinger equation (NLS). It is indeed very convenient to use these exact pulsating envelopes particularly for laboratory experiments, since they allow to generate extreme waves at any location in space at any instant of time. As such, using this framework is more advantageous compared to the classical initialization of the unstable wave dynamics from a three wave system (main wave frequency and one pair of unstable sidebands). In this work, we report an experimental study on higher-order AB hydrodynamics that describe a higher-order stage of modulation instability, namely, starting from five wave systems (main wave frequency and two pairs of unstable sidebands). The corresponding laboratory experiments, that have been conducted in a large water wave facility, confirm the NLS wave dynamics forecast while boundary element method-based numerical wave tank simulations show a very good agreement with the experimental data.