伪湍流
Fake turbulence
AI总结：
针对高维动力系统降阶投影的非确定性问题，提出“无物理”随机马尔可夫模型，在确定性分量占优时能模拟真实湍流统计特性，而确定性模型则收敛至稳态。
摘要：
高维动力系统投影到降阶模型上后不再具有确定性，最好用状态空间中的概率分布来描述。其运动方程映射到一个演化算子上，该算子包含描述投影动力学的确定性分量，以及来自被忽略维度的随机分量。结果表明，对于确定性分量占主导的投影，可以构建“无物理”的随机马尔可夫模型，即使算子近似相当粗糙，这些模型也能模拟真实流动的许多统计特性。确定性模型会收敛到稳态。这与马尔可夫链的一般性质有关，并通过中等雷诺数湍流通道的数据驱动模型进行了说明。
英文摘要：
High-dimensional dynamical systems projected onto a reduced-order model cease to be deterministic and are best described by probability distributions in state space. Their equations of motion map onto an evolution operator with a deterministic component describing the projected dynamics, and a stochastic one from the neglected dimensions. It is shown that, for projections in which the deterministic component is dominant, `physics-free' stochastic Markovian models can be constructed that mimic many of the statistics of the real flow, even for fairly crude operator approximations. Deterministic models converge to steady states. This is related to general properties of Markov chains and illustrated with data-driven models for a moderate-Reynolds number turbulent channel.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
