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

摘要： 为了研究小尺度不可压缩周期流的稳定性，应用多尺度分析方法获得控制其扰动流的大尺度均场方程。对稳态平行流，根据均场方程得到控制大尺度扰动流稳定性的涡流粘性系数。为了验证多尺度理论预测的正确性，采用可以避免速度场和压力场失耦且具有高精度的时间分裂拟谱算法，对不同参数和初始条件下的均场方程以及原始扰动流控制方程进行了数值求解。

关键词: 稳定性, 多尺度分析, 均场方程, 拟谱算法