Statistically accurate low-order models for uncertainty quantification in turbulent dynamical systems
Statistically accurate low-order models for uncertainty quantification in turbulent dynamical systems
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DOI：
10.1073/pnas.1313065110
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发表时间：
2013-08-20
影响因子：
11.1
通讯作者：
Majda, Andrew J.
中科院分区：
文献类型：
--
作者：
Sapsis, Themistoklis P.;Majda, Andrew J.
本文提出了一个湍流动力系统低阶预测统计建模和不确定性量化的框架。这些降阶，修改后的准线性高斯（ROMQG）算法适用于湍流动力系统，其中有显着的线性不稳定性或线性非正常动态的未扰动系统和能量守恒的非线性相互作用，将能量从不稳定的模式转移到稳定的模式，耗散发生，导致统计稳定状态，这样的湍流动力系统是无处不在的地球物理和工程湍流。ROMQG方法涉及到构建一个低阶的，非线性的，动态系统的平均值和协方差统计在减少的子空间，具有未扰动的统计作为一个稳定的不动点，并最佳地结合了非高斯三阶统计的间接影响的未扰动系统在系统的校准阶段。这种校准过程是通过只涉及未扰动平衡的均值和协方差统计信息来实现的。ROMQG算法的性能在两个严格的测试用例上进行了评估：40模Lorenz 96模型模拟中纬度大气湍流和两层斜压模型模拟高纬度海洋湍流，自由度超过125，000。在Lorenz 96模式中，ROMQG算法只使用一个模式来捕捉随机或确定性强迫的瞬态响应。对于斜压海洋湍流模式，廉价的ROMQG算法有252个模式，不到总数的0.2%，捕获的能量，热通量，甚至一维能量和热通量谱的非线性响应。
A framework for low-order predictive statistical modeling and uncertainty quantification in turbulent dynamical systems is developed here. These reduced-order, modified quasilinear Gaussian (ROMQG) algorithms apply to turbulent dynamical systems in which there is significant linear instability or linear nonnormal dynamics in the unperturbed system and energy-conserving nonlinear interactions that transfer energy from the unstable modes to the stable modes where dissipation occurs, resulting in a statistical steady state; such turbulent dynamical systems are ubiquitous in geophysical and engineering turbulence. The ROMQG method involves constructing a low-order, nonlinear, dynamical system for the mean and covariance statistics in the reduced subspace that has the unperturbed statistics as a stable fixed point and optimally incorporates the indirect effect of non-Gaussian third-order statistics for the unperturbed system in a systematic calibration stage. This calibration procedure is achieved through information involving only the mean and covariance statistics for the unperturbed equilibrium. The performance of the ROMQG algorithm is assessed on two stringent test cases: the 40-mode Lorenz 96 model mimicking midlatitude atmospheric turbulence and two-layer baroclinic models for high-latitude ocean turbulence with over 125,000 degrees of freedom. In the Lorenz 96 model, the ROMQG algorithm with just a single mode captures the transient response to random or deterministic forcing. For the baroclinic ocean turbulence models, the inexpensive ROMQG algorithm with 252 modes, less than 0.2% of the total, captures the nonlinear response of the energy, the heat flux, and even the one-dimensional energy and heat flux spectra.