论文标题
随机Navier-Stokes方程的输入输出分析：应用于湍流通道流
Input-output analysis of the stochastic Navier-Stokes equations: application to turbulent channel flow
论文作者
论文摘要
在Tessot，Mémin和Cavalieri中提出的随机线性建模（J. Fluid Mech。，第912、2021卷，A51）是基于经典的保护法，但要经过随机运输。一旦围绕平均流量进行线性性并在傅立叶域中表达，该模型就证明了其效率，可以预测湍流通道流中流速度条纹的结构。特别是证明，未解决的不一致的湍流随机运输可以通过提升机构更好地再现条纹。在本文中，我们关注的是对流向流向的结构的研究，在缓冲液和对数层中进行了能量。在缓冲层中，伸长的流向涡旋（称为rolls）被认为是由连贯的波波非线性相互作用造成的，这些相互作用是在随机线性框架中忽略的。我们提出了一种通过引入随机强迫来替代缺失的非线性项的随机模型中这些相互作用的方法。此外，我们提出了一种迭代策略，以确保自随机噪声从溶液中脱离，如建模假设所规定的那样。我们在$re_τ= 180 $，$re_τ= 550 $和$re_τ= 1000 $的通道流的缓冲区和对数层中探索了这种更完整的模型的预测能力。与涡流粘度的分辨分析相比，我们显示了预测的改善，尤其是在对数层中。
Stochastic linear modelling proposed in Tissot, Mémin & Cavalieri (J. Fluid Mech., vol. 912, 2021, A51) is based on classical conservation laws subject to a stochastic transport. Once linearised around the mean flow and expressed in the Fourier domain, the model has proven its efficiency to predict the structure of the streaks of streamwise velocity in turbulent channel flows. It has been in particular demonstrated that the stochastic transport by unresolved incoherent turbulence allows to better reproduce the streaks through lift-up mechanism. In the present paper, we focus on the study of streamwise-elongated structures, energetic in the buffer and logarithmic layers. In the buffer layer, elongated streamwise vortices, named rolls, are seen to result from coherent wave-wave non-linear interactions, which have been neglected in the stochastic linear framework. We propose a way to account for the effect of these interactions in the stochastic model by introducing a stochastic forcing, which replace the missing non-linear terms. In addition, we propose an iterative strategy in order to ensure that the stochastic noise is decorrelated from the solution, as prescribed by the modelling hypotheses. We explore the prediction abilities of this more complete model in the buffer and logarithmic layers of channel flows at $Re_τ=180$, $Re_τ=550$ and $Re_τ=1000$. We show an improvement of predictions compared to resolvent analysis with eddy viscosity, especially in the logarithmic layer.
