论文标题
毛细血管粘度波的粘性阻尼的数值估计值：宏观深度依赖性滑移长度模型
Numerical estimate of the viscous damping of capillary-gravity waves: A macroscopic depth-dependent slip-length model
论文作者
论文摘要
我们提出了一种数值方法，以使粘性毛细血管刺激波在圆柱容器中具有移动接触线的计算中出现的接触线奇异性正常。线性化的Navier-Stokes方程在容器侧壁上具有宏观的Navier样滑动条件，并具有深度不同的滑移长度在接触线上桥接自由滑滑条件，到远离十周期的无滑动条件。根据文献的建议，选择该特征性的渗透深度是与特征频率有关的典型Stokes层厚度。由于后者尚不清楚，因此首先使用Inviscid特征频率简化了所得的非线性特征值问题，以估计Stokes层厚度。然后，该溶液被证明与使用Inviscid eigenmodes的文献相比，可以提供一致的结果，以估计耗散的不同来源，除了被忽视的角区域外。这表明这种数值正则化方案适合检索物理上有意义的结果。
We propose a numerical approach to regularize the contact line singularity appearing in the computation of viscous capillary-gravity waves with moving contact line in cylindrical containers. The linearized Navier-Stokes equations are complemented by a macroscopic Navier-like slip condition on the container side wall, with a depth-varying slip-length bridging a free-slip condition at the contact line to a no-slip condition further away from the meniscus. In accordance with suggestions from the literature, this characteristic penetration depth is chosen as the typical Stokes layer thickness pertaining to the eigenfrequency. Since the latter is unknown, the resulting nonlinear eigenvalue problem is first simplified using the inviscid eigenfrequency to estimate the Stokes layer thickness. The solution is then shown to provide consistent results when compared to the asymptotic approaches of the literature using the inviscid eigenmodes to estimate the different sources of dissipation with the exception of the neglected corner regions. This demonstrates that such numerical regularization scheme is suitable to retrieve physically meaningful results.
