论文标题
圆形液压跳跃的流体动力白孔中的表面张力和不稳定性
Surface tension and instability in the hydrodynamic white hole of a circular hydraulic jump
论文作者
论文摘要
我们在液体（水）的稳定，浅，径向流出上施加了线性化的欧拉扰动，其局部压力函数既包括静液压和拉普拉斯压力项。所得波方程带有流体力学度量的形式。从波方程中提取的分散关系由于表面张力和圆柱流对称性而产生不稳定。使用分散关系，我们还得出了三个已知关系，这些关系扩展了流出中圆形液压跳跃的半径。前两个关系是通过粘度和重力来缩放的，其依赖于毛细血管的交叉与第三关系相关，并通过粘度和表面张力来缩放。作为高频行驶波的扰动，径向向内散发出散装流出，就在圆形液压跳跃外面被阻塞。由于奇异性，波浪的振幅在这里也有分歧。该阻滞与表面张力有关，这使圆形液压跳动是流体动力的白孔。
We impose a linearized Eulerian perturbation on a steady, shallow, radial outflow of a liquid (water), whose local pressure function includes both the hydrostatic and the Laplace pressure terms. The resulting wave equation bears the form of a hydrodynamic metric. A dispersion relation, extracted from the wave equation, gives an instability due to surface tension and the cylindrical flow symmetry. Using the dispersion relation, we also derive three known relations that scale the radius of the circular hydraulic jump in the outflow. The first two relations are scaled by viscosity and gravity, with a capillarity-dependent crossover to the third relation, which is scaled by viscosity and surface tension. The perturbation as a high-frequency travelling wave, propagating radially inward against the bulk outflow, is blocked just outside the circular hydraulic jump. The amplitude of the wave also diverges here because of a singularity. The blocking is associated with surface tension, which renders the circular hydraulic jump a hydrodynamic white hole.
