Nonlinear water waves driven by the motion of a solid body

由固体运动驱动的非线性水波

• 批准号: EP/H007830/1
• 负责人: John Billingham
• 金额: $ 64.56万
• 依托单位: University of Nottingham
• 依托单位国家: 英国
• 项目类别: Research Grant
• 财政年份: 2010
• 资助国家: 英国
• 起止时间: 2010 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=EP%2FH007830%2F1
• 关键词: Nonlinear; water; waves; driven; motion

Water waves have long been of interest to engineers, physicists and applied mathematicians. The generation of waves by the motion of partially immersed solid bodies is of obvious relevance in marine and naval engineering, as well as being important in wave power generation. Most theoretical studies in this area have been based on numerical solutions of the equations of motion. However, in flows where a free surface meets a solid body, the starting flow usually develops a generic inner asymptotic region where the flow evolves on a small scale. This region can dominate the calculation of the initial load on the body, and have a significant effect on the subsequent flow. Recently, Needham, Billingham and co-workers have been studying the initial development of free surface flow driven by a rigid, moving wall. In particular, for the case of an inclined plate with constant acceleration, we have shown that there is a critical plate angle at which a 120 degree corner is formed on the free surface within the inner region -- an aperiodic analogue of Stokes' highest periodic wave. For larger inclination angles, no solution is possible. When surface tension is taken into account and the contact angle is such that the free surface is initially horizontal, the solution exists for a finite time until the amplitude of the nonlinear capillary wave that forms on the free surface becomes large enough for a bubble to be pinched off. For general contact angles, there is a rich structure in the relevant parameter space, which we seek to elucidate in this project through a combination of analytical, numerical and experimental work. We will also extend our analyses to the case of a plate smoothly withdrawn from a fluid layer, and an impulsively-moved plate. This project is an investigation into a fundamental problem in fluid mechanics that is easy to state, but difficult to tackle. There are significant technical challenges involved in all aspects of the project -- asymptotic, numerical and experimental. Moreover, our recent results lead us to believe that the qualitative structure of the mathematical solutions, and the corresponding flows, is both intricate and interesting, and will allow us significant insight into the generation of water waves by moving solid bodies, and their subsequent propagation.

工程师、物理学家和应用数学家长期以来一直对水波感兴趣。部分浸没的固体运动产生波浪在海洋和船舶工程中具有明显的相关性，在波浪发电中也很重要。这一领域的大多数理论研究都是基于运动方程的数值解。然而，在自由表面与固体相遇的流动中，起始流动通常发展为一个一般的内渐近区域，在该区域内流动以小尺度发展。该区域可以主导机体初始载荷的计算，并对后续流量有显著影响。最近，尼德姆、比林汉姆和同事们一直在研究由刚性移动壁面驱动的自由表面流动的初步发展。特别是，对于具有恒定加速度的倾斜板的情况，我们已经表明，存在一个临界板角，在该临界板角处，内部区域内的自由表面上形成了一个120度角——这是斯托克斯最高周期波的非周期模拟。对于较大的倾角，没有解是可能的。当考虑表面张力，并且接触角使自由表面初始水平时，解存在有限时间，直到在自由表面上形成的非线性毛细波的振幅大到足以使气泡被捏掉为止。对于一般的接触角，在相关的参数空间中有丰富的结构，我们在这个项目中试图通过分析、数值和实验工作的结合来阐明。我们还将把我们的分析扩展到一个板块从流体层中平稳撤出的情况，以及一个冲动运动的板块。这个项目是对流体力学中一个基本问题的研究，这个问题很容易表述，但很难解决。在项目的各个方面都有重大的技术挑战——渐近、数值和实验。此外，我们最近的结果使我们相信，数学解的定性结构，以及相应的流动，既复杂又有趣，并将使我们对运动的固体产生水波及其随后的传播有重要的了解。

项目成果

The initial development of a jet caused by fluid, body and free surface interaction with a uniformly accelerated advancing or retreating plate. Part 1. The principal flow

由流体、物体和自由表面与均匀加速前进或后退板块相互作用引起的射流的初始发展。

• DOI: 10.1017/jfm.2018.4
• 发表时间: 2018
• 期刊: Journal of Fluid Mechanics
• 影响因子: 3.7
• 作者: Gallagher M

The initial development of a jet caused by fluid, body and free surface interaction with a uniformly accelerated advancing or retreating plate. Part 2. Well-posedness and stability of the principal flow

由流体、物体和自由表面与均匀加速前进或后退板块相互作用引起的射流的初始发展。

• DOI: 10.1017/jfm.2018.5
• 发表时间: 2018
• 期刊: Journal of Fluid Mechanics
• 影响因子: 3.7
• 作者: Gallagher M

A spectral boundary integral method for inviscid water waves in a finite domain

有限域内无粘性水波的谱边界积分方法

• DOI: 10.1002/fld.4225
• 发表时间: 2016
• 期刊: International Journal for Numerical Methods in Fluids
• 影响因子: 1.8
• 作者: Im J

The initial development of a jet caused by fluid, body and free surface interaction. Part 5. Parasitic capillary waves on an initially horizontal surface

由流体、物体和自由表面相互作用引起的射流的最初发展。

• DOI: 10.1017/jfm.2017.843
• 发表时间: 2017
• 期刊: Journal of Fluid Mechanics
• 影响因子: 3.7
• 作者: Billingham J