关键词: 稳定性, 多尺度分析, 均场方程, 拟谱算法

Abstract: In order to study the stability of the incompressible small-scale periodic flow，the multiscale analysis method is developed to derive the mean-field equations which govern the transport of large-scale perturbations.On the basis of the mean-field equations，the eddy viscosity for stabilities of large scale perturbations is obtained for the parallel time-independent flow.And then，the time-splitting pseudospectral algorithm is used to solve the mean-field equations and the original linearized equations for different parameters and initial conditions.The agreements between the direct numerical simulations and the multiscale theoretic predictions demonstrate the multiscale method and the numerical algorithm are effective.

Key words: stability, multiscale analysis, mean-field equations, pseudospectral algorithm