Numerical simulation of modified nonlinear Schrodinger equation and turbulence generation

Abstract

This article presents a numerical model to study wave turbulence in fluids. The model equation is derived by incorporating energy conservation (along with the usual fluid equations of a compressible flow), and the source of nonlinearity is the rise in temperature due to the acoustic wave's high amplitude. The nonlinear Schrödinger (NLS) and modified nonlinear Schrödinger (MNLS) equations have been derived and then solved numerically. A numerical simulation of the MNLS equation is used for investigating the turbulence generation and a semi-analytical method to understand the physics of localized structures of nonlinear waves. The numerical simulation is based on a pseudo-spectral approach to resolve spatial regimes, a finite difference method for temporal evolution. The results show a periodic pattern viz. Fermi–Pasta–Ulam (FPU) recurrence for NLS, while turbulence generation breaks down the FPU recurrence in MNLS. The turbulent power spectrum in the inertial sub-range approximately follows the Kolmogorov–Zakharov scaling (∼k−1.2).