论文标题
三维指数渐近学和Stokes表面，用于流过淹没点源
Three-dimensional exponential asymptotics and Stokes surfaces for flows past a submerged point source
论文作者
论文摘要
在研究低苏里德极限的流体体型相互作用时，传统的渐近理论可以预测每个顺序的小波自由表面。这是由于这一事实实际上是指数级的 - 超出了弗洛德数字的所有代数顺序。包含指数小术语的溶液表现出一种被称为Stokes现象的特殊性，因此波浪可以在所谓的Stokes线上瞬间“切换”，将流体域分隔为无波动区域和带有波浪的区域。在三个维度中，Stokes Line概念必须扩展到类似地称为“ Stokes-Surfaces”的概念。本文涉及到点源上均匀流动的原型问题---让人联想到著名的开尔文波问题，但分开了。从理论上讲，存在Stokes表面，即空间中的歧管，将无波浪区域与波浪区域分开。以前，在Lustri＆Chapman（2013）中，对于线性化点源阻塞的情况，发现Stokes表面与自由表面的交点是Z = 0。在这里，我们演示了如何在三维空间中计算stokes表面，尤其是以可以扩展到非线性体的方式。
When studying fluid-body interactions in the low-Froude limit, traditional asymptotic theory predicts a waveless free-surface at every order. This is due to the fact that the waves are in fact exponentially small---that is, beyond all algebraic orders of the Froude number. Solutions containing exponentially small terms exhibit a peculiarity known as the Stokes phenomenon, whereby waves can 'switch-on' seemingly instantaneously across so-called Stokes lines, partitioning the fluid domain into wave-free regions and regions with waves. In three dimensions, the Stokes line concept must extend to what are analogously known as 'Stokes-surfaces'. This paper is concerned with the archetypal problem of uniform flow over a point source---reminiscent of, but separate to, the famous Kelvin wave problem. In theory, there exist Stokes surfaces i.e. manifolds in space that divide wave-free regions from regions with waves. Previously, in Lustri & Chapman (2013) the intersection of the Stokes surface with the free-surface, z=0, was found for the case of a linearised point-source obstruction. Here we demonstrate how the Stokes surface can be computed in three-dimensional space, particularly in a manner that can be extended to the case of nonlinear bodies.
