Fourier amplitude distribution and intermittency in mechanically generated surface gravity waves.

Area of Science:

• Fluid dynamics
• Oceanography
• Wave physics

Background:

• Surface gravity waves are fundamental in many natural phenomena.
• Understanding their statistical evolution is crucial for predicting complex wave behaviors.
• Previous studies often focused on linear wave properties or strong nonlinear regimes.

Purpose of the Study:

• To investigate the spatial evolution of statistical properties in mechanically generated surface gravity wave fields.
• To analyze the impact of nonlinear interactions on wave energy distribution and statistical distributions.
• To identify the emergence of non-Rayleigh distributions in wave spectra.

Main Methods:

• Initialization of wave fields with specific spectral energy, phase, and amplitude distributions.
• Analysis of nonlinear interactions driving energy cascades.
• Examination of probability density functions of Fourier mode amplitudes at varying distances from the wave generator.

Main Results:

• Nonlinear interactions cause an energy cascade towards high-frequency modes.
• A directional spread in wave energy is observed.
• Localized intermittent bursts are triggered by nonlinear effects.
• A heavy-tailed distribution emerges in the high-frequency wave spectrum with increasing distance from the generator.
• The emergent distribution deviates from the initial Rayleigh distribution.

Conclusions:

• Nonlinear interactions significantly alter the statistical properties of surface gravity waves.
• Intermittent bursts and energy cascades are key mechanisms driving spectral evolution.
• The departure from Rayleigh distributions highlights the importance of nonlinear effects even in weakly nonlinear conditions.