论文标题
在Euler方程的流动中孤立波的数值稳定性
Numerical stability of solitary waves in flows with constant vorticity for the Euler equations
论文作者
论文摘要
多年来，对恒定涡度的欧拉方程的研究引起了许多研究人员的好奇心。在稳定流动的假设下，已经对该主题进行了许多研究。在这项工作中，我们提供了一种数值方法，该方法使我们能够以恒定的涡度计算孤立波，并分析其稳定性。通过共形映射技术，我们计算稳定的Euler方程的解决方案，然后将它们作为时间依赖性的Euler方程作为初始数据。我们专注于分析在时间依赖性框架内稳定的孤立波在多大程度上稳定。我们的数值模拟表明，尽管有可能在具有巨大涡度值的流量中计算稳定的Euler方程的孤立波，但对于绝对值大得多的涡度而言，这种波在数值上并不稳定。此外，我们注意到，即使对于少量的涡度值，大波浪也是不稳定的。
The study of the Euler equations in flows with constant vorticity has piqued the curiosity of a considerable number of researchers over the years. Much research has been conducted on this subject under the assumption of steady flow. In this work, we provide a numerical approach that allows us to compute solitary waves in flows with constant vorticity and analyse their stability. Through a conformal mapping technique, we compute solutions of the steady Euler equations, then feed them as initial data for the time-dependent Euler equations. We focus on analysing to what extent the steady solitary waves are stable within the time-dependent framework. Our numerical simulations indicate that although it is possible to compute solitary waves for the steady Euler equations in flows with large values of vorticity, such waves are not numerically stable for vorticities with absolute value much greater than one. Besides, we notice that large waves are unstable even for small values of vorticity.
