Velocity gradient tensor, $A_{ij}\equiv \partial u_i/\partial x_j$ , in a turbulence flow field is modelled by separating the treatment of intermittent magnitude ( $A = \sqrt {A_{ij}A_{ij}}$ ) from that of the more universal normalised velocity gradient tensor, $b_{ij} \equiv A_{ij}/A$ . The boundedness and compactness of the $b_{ij}$ -space along with its universal dynamics allow for the development of models that are reasonably insensitive to Reynolds number. The near-lognormality of the magnitude $A$ is then exploited to derive a model based on a modified Ornstein–Uhlenbeck process. These models are developed using data-driven strategies employing high-fidelity forced isotropic turbulence data sets. A posteriori model results agree well with direct numerical simulation data over a wide range of velocity-gradient features and Reynolds numbers.

中文翻译：

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不可压缩湍流中速度梯度拉格朗日演化的数据驱动模型

速度梯度张量， $A_{ij}\equiv \partial u_i/\partial x_j$ ，在湍流流场中通过分离间歇幅度的处理来建模（ $A = \sqrt {A_{ij}A_{ij}}$ ）根据更通用的归一化速度梯度张量， $b_{ij} \等于 A_{ij}/A$ 。的有界性和紧性 $b_{ij}$ - 空间及其普遍的动力学允许开发对雷诺数相当不敏感的模型。幅度的近似对数正态性 $A$ 然后利用改进的 Ornstein-Uhlenbeck 过程导出模型。这些模型是使用数据驱动策略开发的，采用高保真强迫各向同性湍流数据集。后验模型结果与各种速度梯度特征和雷诺数的直接数值模拟数据非常吻合。