Numerical investigation of turbulence generation using Zakharov-like model equation

Abstract

This study investigates the turbulence generation behavior with a Zakharov-like (ZL) equation in a fluid system. The model equation is derived using conservation equations (mass and momentum conservation), and the source of nonlinearity is the high amplitude of the acoustic wave. The Zakharov-like equation has been derived and then solved numerically, then turned into a modified nonlinear Schrödinger equation. Furthermore, modulation instability, or Benjamin–Feir instability, of the model equations, which leads to the emergence of Akhmediev breathers, is discussed. The numerical simulation uses a finite difference method for temporal evolution and a pseudo-spectral approach to determine spatial regimes. The outcomes indicate that the situation involving the nonlinear Schrödinger equation case displays a periodic pattern in space and time. The findings also demonstrate that the localization of structure and the Fermi, Pasta, and Ulam (FPU) recurrences are disrupted for the modified nonlinear Schrödinger equation and Zakharov-like equation cases. The energy spectrum exhibits a power law behavior that approximately follows k−1.65 in the ZL model equation case, and it is steeper than Kolmogorov's spectrum within the inertial sub-range.