Special Session 51: Recent progress on the rogue waves and their applications

Numerical simulations of nonlinear evolution of modulational instabilities of Short-Crested Waves
Malek ABID
Aix-Marseille Universit\`e/IRPHE
France
Co-Author(s):    Marc Francius, and Christian Kharif
Abstract:
Understanding the formation of extreme waves in crossing seas remains a major challenge in ocean physics. In this work, we investigate the modulational instability of short-crested waves (SCWs), a fundamental mechanism through which energy localizes and potentially leads to rogue waves. Using the coupled nonlinear Schr\{o}dinger (CNLS) framework, we analyze how crossing angle and perturbation direction control the nature of unstable modes. A key result is the first explicit link between CNLS instability predictions and the resonance-based classification (Ia/Ib) derived from fully nonlinear theory. Through systematic numerical simulations, complemented by fully nonlinear Euler computations using a High-Order Spectral Method, we show that a single perturbation can trigger markedly different dynamical responses, including self-phase and cross-phase instabilities. These findings reveal strong sensitivity of instability growth and wave amplification to wave geometry. While the CNLS model provides an efficient and accurate description of early-stage dynamics, fully nonlinear effects become essential to capture long-term evolution and extreme wave amplification.