Abstract Within the framework of the Navier–Stokes equations, the Weissenberg effect of turbulence is investigated. We begin with our investigation on the elastic effect of homogeneous turbulent shear flow. First, in the sense of Truesdell (Physics of Fluids, 1964) on the natural time of materials, we derive the natural time of turbulence, and use it together with the natural viscosity of turbulence derived in the article of Huang et al. (Journal of Turbulence, 2003) to define the natural Weissenberg number of turbulence as a measure of the elastic effect of homogeneous turbulence. Second, we define a primary Weissenberg number of turbulence, which in laminar flow reduces to the Weissenberg number widely applied in rheology to characterize the elasticity of visco-elastic fluids. Our analysis based on the experimental results of Tavoularis and Karnik (Journal of Fluid Mechanics, 1989) indicates that the larger is the Weissenberg number of turbulence, the more elastic becomes the turbulent flow concerned. Furthermore, we put forth a general Weissenberg number of turbulence, which includes the primary Weissenberg number of turbulence as a special case, to measure the overall elastic effects of turbulence. Besides, it is shown that the general Weissenberg number can also be used to characterize the elastic effects of non-Newtonian fluids in laminar flow.

中文翻译：

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关于湍流的魏森伯格效应

摘要在Navier–Stokes方程的框架内，研究了湍流的Weissenberg效应。我们从对均匀湍流剪切流的弹性效应的研究开始。首先，在Truesdell（流体物理学，1964年）的意义上，我们推导了湍流的自然时间，并将其与Huang等人的文章中得出的湍流的自然粘度一起使用。（湍流杂志，2003年）定义了湍流的自然Weissenberg数作为均质湍流弹性效应的量度。其次，我们定义了湍流的主要Weissenberg数，该数在层流中减小为在流变学中广泛应用的Weissenberg数，以表征粘弹性流体的弹性。基于Tavoularis和Karnik（流体力学杂志，1989年）的实验结果进行的分析表明，魏森伯格湍流数越大，所涉及的湍流弹性就越大。此外，我们提出了一个一般的魏森伯格湍流数，其中包括特例的主要魏森伯格湍流数，以测量湍流的整体弹性效应。此外，证明了一般的魏森伯格数也可用于表征非牛顿流体在层流中的弹性效应。其中包括湍流的主要Weissenberg数作为特例，以测量湍流的整体弹性效应。此外，证明了一般的魏森伯格数也可用于表征非牛顿流体在层流中的弹性效应。其中包括湍流的主要Weissenberg数作为特例，以测量湍流的整体弹性效应。此外，证明了一般的魏森伯格数也可用于表征非牛顿流体在层流中的弹性效应。