Numerical modeling of wave turbulence: Stability analysis and energy spectrum evolution

This study investigates wave turbulence in fluids using a one-dimensional coupled model equation derived from conservation laws. Numerical simulations employing pseudo-spectral and finite difference methods reveal the intricate dynamics of turbulence evolution. The results reveal localized structures transitioning to chaotic patterns due to nonlinear interactions. The Fermi–Pasta–Ulam recurrence is disrupted in the coupled model due to nonlinearity, contrasting with the classical nonlinear Schrödinger equation, where recurrence is preserved. The inclusion of artificial damping demonstrates significant effects on turbulence, regularizing the energy transfer processes and steepening the energy spectra. Analytical studies of Benjamin–Feir instability confirm numerical growth rates and provide insights. These findings emphasize the role of damping (dissipation) in modulating turbulence and contribute to an understanding of nonlinear energy cascades.