A nonequilibrium expression of the turbulent viscosity in the Reynolds stress is proposed with the aid of the results from a two‐scale direct‐interaction approximation. The usual turbulent‐viscosity model based on the turbulent kinetic energy K and its dissipation rate ε is extended to include their nonequilibrium effects DK/Dt and Dε/Dt (D/Dt is the Lagrange derivative based on the mean velocity). The validity of the proposed model is confirmed through the test in homogeneous shear turbulence that is in a state of nonequilibrium in time. The relationship with the similar model presented by Taulbee [Phys. Fluids A 4, 2555 (1992)] is also discussed.

中文翻译：

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基于二阶湍流理论的湍流粘度非平衡表示

的非平衡表达 湍流的 黏度 在里面 雷诺应力借助两尺度直接交互近似的结果提出了。通常湍流粘度 模型 根据 湍流的动能K及其耗散率ε扩展为包括其非平衡效果 DK /申和d ε/申（d /申是基于平均速度拉格朗日衍生物）。提议的有效性模型 通过均质剪切测试确定 湍流在时间上处于非平衡状态。与相似的关系模型由Taulbee提出[Phys。流体A 4，2555（1992）]进行了讨论。