Amplification of coherent streaks in the turbulent Couette flow: an input–output analysis at low Reynolds number
Amplification of coherent streaks in the turbulent Couette flow: an input–output analysis at low Reynolds number
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湍流库埃特流中相干条纹的放大：低雷诺数下的输入输出分析
DOI：
10.1017/s0022112009992151
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发表时间：
2010
影响因子：
3.7
通讯作者：
C. Cossu
中科院分区：
文献类型：
--
作者：
Y. Hwang;C. Cossu
我们计算了 Re = 750 时湍流库埃特平均流对初始条件、谐波和随机强迫的最佳响应。相干扰动方程在湍流平均流附近线性化，并包括相关的涡粘性。研究发现平均流量是线性稳定的，但它有可能放大流向涡流中的流向条纹。放大最大的结构是流向均匀的，初始条件能量和随机强迫方差的最大放大是通过展向波长分别为4.4h和5.2h的大尺度条纹实现的。这些展向尺度与在实验实现和湍流库埃特流的直接数值模拟中观察到的相干大尺度条纹的尺度很好地比较。对谐波强迫的最佳响应与边界条件和人工强迫的敏感性相关，可以非常大，并且通过具有较大展向波长（7.7h）的结构的稳定强迫来获得。此外，还发现最佳的大尺度条纹与粘性子层直至缓冲层的平均湍流剖面成正比。
We compute the optimal response of the turbulent Couette mean flow to initial conditions, harmonic and stochastic forcing at Re = 750. The equations for the coherent perturbations are linearized near the turbulent mean flow and include the associated eddy viscosity. The mean flow is found to be linearly stable but it has the potential to amplify steamwise streaks from streamwise vortices. The most amplified structures are streamwise uniform and the largest amplifications of the energy of initial conditions and of the variance of stochastic forcing are realized by large-scale streaks having spanwise wavelengths of 4.4h and 5.2h respectively. These spanwise scales compare well with the ones of the coherent large-scale streaks observed in experimental realizations and direct numerical simulations of the turbulent Couette flow. The optimal response to the harmonic forcing, related to the sensitivity to boundary conditions and artificial forcing, can be very large and is obtained with steady forcing of structures with larger spanwise wavelength (7.7h). The optimal large-scale streaks are furthermore found proportional to the mean turbulent profile in the viscous sublayer and up to the buffer layer.