茶杯奇点的流体力学分析
A fluid mechanic's analysis of the teacup singularity
摘要：
研究了无粘有壁流体流动中奇异性的形成机理。在圆柱形容器中数值模拟了不可压欧拉方程。流动是轴对称的，有旋涡。模拟再现和证实方面的先前研究报告的强有力的证据有限时间奇点。这里的分析重点是惯性和压力之间的相互作用，而不是涡量。利用压力泊松方程的线性性将压力场分解成由湍流和旋流产生的独立贡献，并强制执行不可压缩性和强制执行流量限制。驱动速度梯度爆破的关键压力场是将流体限制在圆柱壁内。一个模型的基础上提出的连续变量制定的欧拉方程的气缸壁，关闭来自压力是如何确定的速度。该模型捕捉到了爆炸情景机制中的关键特征。
英文摘要：
The mechanism for singularity formation in an inviscid wall-bounded fluid flow is investigated. The incompressible Euler equations are numerically simulated in a cylindrical container. The flow is axisymmetric with swirl. The simulations reproduce and corroborate aspects of prior studies reporting strong evidence for a finite-time singularity. The analysis here focuses on the interplay between inertia and pressure, rather than on vorticity. Linearity of the pressure Poisson equation is exploited to decompose the pressure field into independent contributions arising from the meridional flow and from the swirl, and enforcing incompressibility and enforcing flow confinement. The key pressure field driving the blowup of velocity gradients is that confining the fluid within the cylinder walls. A model is presented based on a primitive-variables formulation of the Euler equations on the cylinder wall, with closure coming from how pressure is determined from velocity. The model captures key features in the mechanics of the blowup scenario.
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