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This article introduces a numerical model for examining wave turbulence in fluids. The model equation is derived by considering energy conservation and the standard fluid equations for compressible flow. The nonlinearity in the equation arises from the temperature increase caused by the high amplitude of the acoustic wave. The modified nonlinear Schrodinger equation (MNLS) is derived and solved using numerical methods. Artificial damping is added to the MNLS equation, and turbulence generation is investigated through a numerical simulation. The numerical simulation utilizes a pseudo-spectral method for spatial domains and a finite difference method for temporal evolution. The results demonstrate a periodic pattern resembling the Fermi-Pasta-Ulam (FPU) recurrence for the NLS equation. At the same time, turbulence generation disrupts the FPU recurrence in the case of the MNLS and damped MNLS equation. The energy spectrum in the inertial range follows a Kolmogorov-Zakharov (KZ) scaling of approximately \(k^{-1.2}\) in the inertial range and steeper than \(k^{-3}\) beyond the inertial range.

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Numerical Simulation of a Damped-Driven MNLS Equation to Study Turbulence Behavior

  • 会议论文

  • 发表日期：

    2026年

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  • Praveen Kumar,
  • R. Uma,
  • R. P. Sharma

摘要

This article introduces a numerical model for examining wave turbulence in fluids. The model equation is derived by considering energy conservation and the standard fluid equations for compressible flow. The nonlinearity in the equation arises from the temperature increase caused by the high amplitude of the acoustic wave. The modified nonlinear Schrodinger equation (MNLS) is derived and solved using numerical methods. Artificial damping is added to the MNLS equation, and turbulence generation is investigated through a numerical simulation. The numerical simulation utilizes a pseudo-spectral method for spatial domains and a finite difference method for temporal evolution. The results demonstrate a periodic pattern resembling the Fermi-Pasta-Ulam (FPU) recurrence for the NLS equation. At the same time, turbulence generation disrupts the FPU recurrence in the case of the MNLS and damped MNLS equation. The energy spectrum in the inertial range follows a Kolmogorov-Zakharov (KZ) scaling of approximately \(k^{-1.2}\) in the inertial range and steeper than \(k^{-3}\) beyond the inertial range.