非线性尾流相互作用研究

王程英; 张建生

doi:10.11993/j.issn.2096-3920.2020.06.014

非线性尾流相互作用研究

doi: 10.11993/j.issn.2096-3920.2020.06.014

西安工业大学理学院, 陕西西安, 710021

基金项目: 陕西省教育厅专项科研计划项目(2010JK585) 西安市未央区科技计划项目(201843).

详细信息

作者简介:
王程英(1993-), 女, 在读硕士, 主要研究方向为水下信息光学、光学测试研究.

中图分类号: U661.1 O175.29
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出版历程
- 收稿日期: 2020-05-12
- 修回日期: 2020-07-21
- 刊出日期: 2020-12-31

Study on Nonlinear Wake Interaction

School of Sciences, Xi’an Technological University, Xi’an 710021, China

摘要

摘要: 在限制水域中, 快速船舶的尾迹最重要的特征是在船舶前方能产生孤立波。文中基于Korteweg-de Vries型方程和Hirota双线性形式的符号和辅助结果, 得到不同相位变化中的双孤子解。利用Mathematica软件仿真得到了KP(Kadovtsev-Petviashvili)方程双孤子解在不同相位变化中的所有可能波型以及双孤子解分解结构与线性叠加的波形, 为理解KP方程双孤子解、双孤子相互作用及其形态结构特征奠定了基础。基于无量纲KP方程的双孤子解, 仿真得到标准坐标下等振幅和非等振幅入射孤子相互作用区域的表面高度。结果表明, 等振幅入射孤子的振幅与参考孤子的振幅相差0.01%比相差1%的相互作用波峰空间范围大非等振幅的2个入射孤子的相互作用主要导致了2种入射孤子波峰的弯曲。利用Matlab软件仿真得到入射孤子和相互作用中心双孤子解的不同波峰, 通过调节参数k对比相互作用孤子的坡度, 结果表明沿波峰的传播方向, k值越大, 相互作用孤子的轮廓越窄, 坡度越大。
- 船舶尾流 /
- 双孤子解 /
- 孤子相互作用 /
- 表面高度 /
- 坡度
Abstract: The most important feature of the wakes of fast ships in restricted waters is that solitary waves can be generated ahead of the ship. Using the Korteweg de Vries equation and the sign and auxiliary results of the Hirota bilinear form, this study derives a two-soliton solution with different phase changes. All possible waveforms of the two-soliton solution of the Kadovtsev-Petviashvili(KP) equation for different phase changes and the waveforms of the decomposition structure and linear superposition of the two-soliton solution are obtained using Mathematica. This establishes a foundation for understanding the two-soliton solution of the KP equation, two-soliton interaction, and its morphological characteristics. Based on the two-soliton solution of the dimensionless KP equation, the study simulates the surface height of the interaction region of equal and unequal amplitude incident solitons with standard coordinates. The results show that the amplitude difference between the equal amplitude incident soliton and the amplitude of the reference soliton is 0.01% larger than that of the 1% difference in the space of the interaction peak. The interaction of two incoming solitons with unequal amplitudes results in the bending of their wave humps. The different wave humps of the incoming soliton and two-soliton solution at the center of interaction area are obtained using MATLAB. Finally, the slopes of the interacting solitons are compared by adjusting the parameter k. Results show that for a higher value of k, the profile of the interacting soliton is narrower and the slope along the propagation direction of the wave crest is greater.
- ship wake /
- two-soliton solution /
- soliton interaction /
- surface height /
- slope

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