Nonconservative higher-order hydrodynamic modulation instability

Abstract

The modulation instability (MI) is a universal mechanism that is responsible for the disintegration of weakly nonlinear narrow-banded wave fields and the emergence of localized extreme events in dispersive media. The instability dynamics is naturally triggered, when unstable energy side-bands located around the main energy peak are excited and then follow an exponential growth law. As a consequence of four wave mixing effect, these primary side-bands generate an infinite number of additional side-bands, forming a triangular side-band cascade. After saturation, it is expected that the system experiences a return to initial conditions followed by a spectral recurrence dynamics. Much complex nonlinear wave field motion is expected, when the secondary or successive side-band pair that are created are also located in the finite instability gain range around the main carrier frequency peak. This latter process is referred to as higher-order MI. We report a numerical and experimental study that confirm observation of higher-order MI dynamics in water waves. Furthermore, we show that the presence of weak dissipation may counter-intuitively enhance wave focusing in the second recurrent cycle of wave amplification. The interdisciplinary weakly nonlinear approach in addressing the evolution of unstable nonlinear waves dynamics may find significant resonance in other nonlinear dispersive media in physics, such as optics, solids, superfluids and plasma.

References in corpus (12)

• Instabilities, breathers and rogue waves in optics
• Modulation instability, Akhmediev Breathers and continuous wave supercontinuum generation
• Observation of an Inverse Energy Cascade in Developed Acoustic Turbulence in Superfluid Helium
• Vector Rogue Waves and Baseband Modulation Instability in the Defocusing Regime
• Optical Rogue Waves in integrable turbulence
• Triggering rogue waves in opposing currents
• Theory of weakly damped free-surface flows: a new formulation based on potential flow solutions
• Universal nature of the nonlinear stage of modulational instability
• Universal Peregrine soliton structure in nonlinear pulse compression in optical fiber
• Damped-Driven Granular Crystals: An Ideal Playground for Dark Breathers and Multibreathers
• Enhancement of the Benjamin-Feir instability with dissipation
• Frequency downshift in a viscous fluid

Cited by in corpus (11)

• Nonlinear spectral analysis of Peregrine solitons observed in optics and in hydrodynamic experiments
• Observation of modulation instability and rogue breathers on stationary periodic waves
• Growth rate of modulation instability driven by superregular breathers
• Modulation instability and non-degenerate Akhmediev breathers of Manakov equations
• Higher-order modulation instability and multi-Akhmediev breathers of Manakov equations: Frequency jumps over the stable gaps between the instability bands
• A Comparison of Frequency Downshift Models of Wave Trains on Deep Water
• Spatio-temporal observation of higher-order modulation instability in a recirculating fiber loop
• Statistics of Vector Manakov Rogue Waves
• Excitation of Peregrine-type waveforms from vanishing initial conditions in the presence of periodic forcing
• Wigner instability analysis of the damped Hirota equation
• Separatrix crossing and symmetry breaking in NLSE-like systems due to forcing and damping