| 刘迪,王振.偶极子引起界面内波的线性解与非线性解[J].数学研究及应用,2024,44(2):269~284 |
| 偶极子引起界面内波的线性解与非线性解 |
| Linear and Nonlinear Solutions of Interfacial Waves Due to a Doublet |
| 投稿时间：2023-02-20 修订日期：2024-01-06 |
| DOI：10.3770/j.issn:2095-2651.2024.02.012 |
| 中文关键词: 界面波 偶极子 边界积分方程法 线性解 |
| 英文关键词:interfacial waves doublet boundary integral equation method linear solutions |
| 基金项目:国家自然科学基金(Grant Nos.52171251; U2106225). |
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| 中文摘要: |
| 本文考虑当下层具有浸没偶极子时的二维两层稳定势流,得到了线性解析解,同时基于边界积分方程法得到了完全非线性解.非线性强烈影响下游稳定波波高,并引起轻微相位差.Froude数较小时,随着Froude数增大波高很快达到极大值.若Froude较大则可以获得无波解.随后,本文比较了单点涡/涡对引起的界面波与偶极子引起的界面内波.发现如果适当设置涡旋对之间的距离,则由偶极子引起的非线性波与竖直放置的涡对引起的非线性波非常接近. |
| 英文摘要: |
| Steady two-dimensional potential flows of two-layer fluids with a submerged doublet in the lower layer are considered. Both linear analytical solutions and fully nonlinear solutions based on boundary integral equation methods are obtained. Nonlinearity strongly influences the downstream wave height and leads to a slight phase difference. When the Froude number is small, wave height fast gets its maximum as the Froude number increases. While wave-less solutions may be obtained if the Froude number is very large. Afterward, the interfacial waves due to one point vortex or a vortex pair are compared with those due to a doublet. It is found that the nonlinear wave profiles due to a doublet are quite close to those due to a vertical vortex pair if the distance between the vortex pair is set appropriately. |
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