Exact solutions for steadily travelling water waves with submerged point vortices
Exact solutions for steadily travelling water waves with submerged point vortices
复制标题
具有浸没点涡的稳定行进水波的精确解
DOI：
--
复制
发表时间：
2023
影响因子：
3.7
通讯作者：
D. Crowdy
中科院分区：
文献类型：
--
作者：
D. Crowdy
摘要本文提出了一个新的理论框架，基于波的施瓦茨函数的概念，理解在没有重力和毛细作用的情况下的水波与涡。该框架自然导致三个子情况下，在这里被称为情况1，2和3，落入其中的三个现有的研究水波纳入均匀涡和淹没点涡的分类。这为文献中几个看似无关的结果提供了理论上的统一。它还提供了一个路线，以寻找新的精确解，本文侧重于新的解决方案属于情况2类别。在这里提出的几个是一个淹没的点涡对同程与孤立的深水波，冯卡门点涡街道同程与周期性的深水波和一个点涡行同程与波在水中的有限深度。还构造了一些其他更奇特的波形。所有这些新的解决方案推广了Crowdy & Roenby（Fluid Dyn.结果：Vol.46，2014），他发现深水中的稳定波与淹没的点涡行共同行进，对于该点涡行，自由表面形状与Crapper（J.Fluid Mech.，第2卷，1957）。新的精确解可能提供一个有用的基础渐近或数值研究时，如重力和毛细作用的其他影响。
Abstract This paper presents a novel theoretical framework, based on the concept of the Schwarz function of a wave, for understanding water waves with vorticity in the absence of gravity and capillarity. The framework leads naturally to a taxonomy of three subcases, herein referred to as cases 1, 2 and 3, into which fall three existing studies of water waves incorporating uniform vorticity and submerged point vortices. This provides a theoretical unification of several seemingly unrelated results in the literature. It also provides a route to finding new exact solutions with this paper focussing on new solutions falling within the case 2 category. Among several presented here are a submerged point vortex pair cotravelling with a solitary deep-water wave, von Kármán point vortex streets cotravelling with a periodic deep-water wave and a point vortex row cotravelling with a wave in water of finite depth. Some other more exotic waveforms are also constructed. All these new solutions generalize those of Crowdy & Roenby (Fluid Dyn. Res., vol. 46, 2014) who found steady waves in deep water cotravelling with a submerged point vortex row for which the free surface shapes turn out to coincide with those of pure capillary waves on deep water found by Crapper (J. Fluid Mech., vol. 2, 1957). The new exact solutions are likely to provide a useful basis for asymptotic or numerical studies when additional effects such as gravity and capillarity are incorporated.
登录
查看更多内容
影响因子：
2.4
作者：
Hur, Vera Mikyoung;Wheeler, Miles H.
通讯作者：
Wheeler, Miles H.
行进的水波——两个世纪的潮起潮落
影响因子：
0.8
作者：
Haziot, Susanna V.;Hur, Vera Mikyoung;Strauss, Walter A.;Toland, John F.;Wahlen, Erik;Walsh, Samuel;Wheeler, Miles H.
通讯作者：
Wheeler, Miles H.
DOI：
10.1016/j.euromechflu.2012.09.007
发表时间：
2013
期刊：
European Journal of Mechanics - B/Fluids
影响因子：
--
作者：
Crowdy D
通讯作者：
Crowdy D
具有恒定涡度的斯托克斯波：一、数值计算
影响因子：
2.7
作者：
Dyachenko, Sergey A.;Hur, Vera Mikyoung
通讯作者：
Hur, Vera Mikyoung
影响因子：
2
作者：
Le, Hung
通讯作者：
Le, Hung