宽带湍流的随机SPOD-Galerkin模型
A stochastic SPOD-Galerkin model for broadband turbulent flows
摘要：
探讨了利用谱本征正交分解（SPOD）来构造宽带湍流的低阶模型。SPOD模式作为基向量的选择是出于它们的最优性和统计平稳流的时空相干性。本文遵循复杂非线性流体动力学可以近似为随机受迫线性系统的建模范式。所提出的随机两层SPOD-Galerkin模型控制由模态展开系数和强迫系数组成的复合状态。在第一层中，在线性时不变假设下，通过强迫线性化的Navier-Stokes算子得到模态展开系数。第二层控制强迫系数，补偿线性近似和真实状态之间的偏移。在这个层次上，最小二乘回归是用来实现封闭模式之间的非线性相互作用建模。剩余残差的统计数据用于构建去白化滤波器，该滤波器便于使用白噪声来驱动模型。如果将数据残差用作唯一输入，则模型可以准确地恢复所有时间的原始流量轨迹。如果残差被建模为随机输入，则模型生成准确再现原始数据的二阶统计和动态的替代数据。通过分析和蒙特卡罗模拟，量化了随机模型的不确定性、可预测性和稳定性。该模型在马赫数$M=0.9$和雷诺数$Re_D\approx 10^6$的湍流射流的大涡模拟数据上进行了验证。
英文摘要：
The use of spectral proper orthogonal decomposition (SPOD) to construct low-order models for broadband turbulent flows is explored. The choice of SPOD modes as basis vectors is motivated by their optimality and space-time coherence properties for statistically stationary flows. This work follows the modeling paradigm that complex nonlinear fluid dynamics can be approximated as stochastically forced linear systems. The proposed stochastic two-level SPOD-Galerkin model governs a compound state consisting of the modal expansion coefficients and forcing coefficients. In the first level, the modal expansion coefficients are advanced by the forced linearized Navier-Stokes operator under the linear time-invariant assumption. The second level governs the forcing coefficients, which compensate for the offset between the linear approximation and the true state. At this level, least squares regression is used to achieve closure by modeling nonlinear interactions between modes. The statistics of the remaining residue are used to construct a dewhitening filter that facilitates the use of white noise to drive the model. If the data residue is used as the sole input, the model accurately recovers the original flow trajectory for all times. If the residue is modeled as stochastic input, then the model generates surrogate data that accurately reproduces the second-order statistics and dynamics of the original data. The stochastic model uncertainty, predictability, and stability are quantified analytically and through Monte Carlo simulations. The model is demonstrated on large eddy simulation data of a turbulent jet at Mach number $M=0.9$ and Reynolds number of $Re_D\approx 10^6$.
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