Title: Viscous Strength of Water Show Chinese title

Title: 水的粘性强度

Abstract: In the laminar mode interactions among molecules generate friction between layers of water that slide with respect to each other. This friction triggers the shear stress, which is traditionally presumed to be linearly proportional to the velocity gradient. The proportionality coefficient characterizes the viscosity of water. Remarkably, the standard Navier-Stokes model surmises that materials never fail - the transition to turbulence can only be triggered by some kinematic instability of the flow. This premise is probably the reason why the Navier-Stokes theory fails to explain the so-called subcritical transition to turbulence with the help of the linear instability analysis. When linear instability analysis fails, nonlinear instability analysis is often resorted to, but, despite the occasional uses of this approach, it is intrinsically biased to require finite flow perturbations which do not necessarily exist. In the present work we relax the traditional restriction on the perfectly intact material and introduce the parameter of fluid viscous strength, which enforces the breakdown of internal friction. We develop a generalized Navier-Stokes constitutive model which includes a material failure description, and use it to analyze the Couette flow between two parallel plates to find that the lateral infinitesimal perturbations can destabilize the laminar flow. Furthermore, we use the results of the recent experiments on the onset of turbulence in pipe flow to calibrate the viscous strength of water. Specifically, we find that the maximal shear stress that water can sustain in the laminar flow is about one Pascal. We note also that the introduction of the fluid strength uncovers new prospects in the explanation of the remarkable phenomenon of the delay of the transition to turbulence due to an addition of a small amount of long polymer molecules to water. Show Chinese abstract

Abstract: 在层流模式中，分子之间的相互作用产生摩擦，这种摩擦发生在相对滑动的水层之间。 这种摩擦引发剪切应力，传统上认为该应力与速度梯度成线性比例。 比例系数表征了水的粘度。 值得注意的是，标准的纳维-斯托克斯模型假设材料永远不会失效——湍流的转变只能由流动的运动学不稳定性触发。 这一前提可能是纳维-斯托克斯理论无法借助线性不稳定分析解释所谓的亚临界湍流转变的原因。 当线性不稳定分析失效时，通常会采用非线性不稳定分析，但尽管偶尔使用这种方法，它本质上存在偏差，因为它要求存在有限的流动扰动，而这些扰动不一定存在。 在本研究中，我们放松了对材料完全完整性的传统限制，并引入了流体粘性强度参数，该参数促使内部摩擦的破坏。 我们开发了一个广义的纳维-斯托克斯本构模型，该模型包括材料失效的描述，并利用它来分析两块平行板之间的库埃特流动，结果发现横向的微小扰动可以导致层流的失稳。 此外，我们利用最近关于管道流动中湍流起始的实验结果来校准水的粘性强度。 具体而言，我们发现水在层流中所能承受的最大剪切应力约为1帕斯卡。 我们还注意到，流体强度的引入揭示了在解释由于向水中添加少量长聚合物分子而导致湍流转变延迟这一显著现象方面的新前景。