论文标题
指数渐近学和淹没线涡流的自由表面流产生
Exponential asymptotics and the generation of free-surface flows by submerged line vortices
论文作者
论文摘要
最近对水波的研究以及非零涡度的研究引起了重大兴趣。我们得出在以二维为单位生成的指数级别的自由表面波的分析近似，当以低弗洛德数字驱动时，通过一个或几个淹没点涡流。涡旋固定在适当的位置，沿表面的弧长中的边界综合公式可以研究非线性波和强点涡流。我们证明，对于单点涡流，指数渐近学中的技术规定了与来自涡流的Stokes线有关的波的形成。当将多点涡旋放置在流体中时，可能会发生被捕获的波，而这些波浪仅限于涡旋之间。我们还证明，对于两涡流问题，对于一组无限的弗洛德数值集，捕获波的现象发生。这项工作将为波浪结构相互作用的其他渐近研究构成基础，在这些相互作用中，涡度在表面波的形成中起着关键作用。
There has been significant recent interest in the study of water waves coupled with non-zero vorticity. We derive analytical approximations for the exponentially-small free-surface waves generated in two-dimensions by one or several submerged point vortices when driven at low Froude numbers. The vortices are fixed in place, and a boundary-integral formulation in the arclength along the surface allows the study of nonlinear waves and strong point vortices. We demonstrate that for a single point vortex, techniques in exponential asymptotics prescribe the formation of waves in connection with the presence of Stokes lines originating from the vortex. When multiple point vortices are placed within the fluid, trapped waves may occur, which are confined to lie between the vortices. We also demonstrate that for the two-vortex problem, the phenomenon of trapped waves occurs for a countably infinite set of values of the Froude number. This work will form a basis for other asymptotic investigations of wave-structure interactions where vorticity plays a key role in the formation of surface waves.
