Numerical Validation of the Inverse Cascade of Surface Gravity Wave Action

Area of Science:

• Fluid dynamics
• Wave phenomena
• Computational physics

Background:

• Surface gravity waves are fundamental in geophysical flows.
• Weakly nonlinear wave interactions can lead to energy transfer across scales.
• Previous studies lacked the scale separation to confirm theoretical predictions.

Purpose of the Study:

• To numerically simulate surface gravity waves forced at small scales.
• To investigate the inverse cascade of wave action.
• To validate theoretical predictions of wave spectra in the inverse cascade regime.

Main Methods:

• Spectral simulations of weakly nonlinear surface gravity waves.
• Utilizing modern graphics processing units (GPUs) for high-performance computing.
• Achieving large scale separation between forcing and domain scales.

Main Results:

• Observed an inverse cascade of wave action from small to large scales.
• Established a broad inertial range in the wave spectrum.
• Unambiguously confirmed theoretical predictions for the spectral index.
• Validated the dependence of the spectral level on the action flux.

Conclusions:

• The study provides strong numerical evidence for the inverse cascade of surface gravity waves.
• Confirms the validity of spectral theories for weakly nonlinear wave dynamics.
• Highlights the power of GPU-accelerated simulations for studying large-scale phenomena.