{"title":"透水海床罗宾边界条件的面波阻尼作用","authors":"","doi":"10.1016/j.euromechflu.2024.10.010","DOIUrl":null,"url":null,"abstract":"<div><div>We investigate the damping of inviscid surface gravity waves when they propagate over a permeable seabed. Traditionally, this problem is solved by considering the wave motion in the upper water layer interacting with the Darcy flow in the porous bottom layer through matching of the solutions at the permeable interface. The novel approach in this study is that we describe the interaction between the upper fluid layer and the permeable bottom layer by the application of a Robin boundary condition. By varying the magnitude of the Robin parameter <span><math><mi>R</mi></math></span>, we can model the bottom structure of the fluid layer from rigid to completely permeable. In the case when the bottom is a porous medium where Darcy’s law applies, or composed by densely packed vertical Hele-Shaw cells, <span><math><mi>R</mi></math></span> is small, and can by determined by comparison with analytical results for a two-layer structure. In this case the wave damping is small. For larger values of <span><math><mi>R</mi></math></span>, the damping increases, and for very large <span><math><mi>R</mi></math></span>, the wave is almost critically damped. For the nonlinear transport in spatially damped shallow-water waves, increasing bottom permeability (larger <span><math><mi>R</mi></math></span>), reduces the magnitude of the horizontal Stokes drift velocity, while the drift profile tends to become parabolic with height. The vertical Stokes drift in the limit of large permeability is linear with height, with a magnitude that is larger than the horizontal drift. It is suggested that the implementation of a permeable bottom bed in some cases could prevent shorelines from damaging erosion by incoming surface waves.</div></div>","PeriodicalId":11985,"journal":{"name":"European Journal of Mechanics B-fluids","volume":null,"pages":null},"PeriodicalIF":2.5000,"publicationDate":"2024-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Surface wave damping by a Robin boundary condition at a permeable seabed\",\"authors\":\"\",\"doi\":\"10.1016/j.euromechflu.2024.10.010\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>We investigate the damping of inviscid surface gravity waves when they propagate over a permeable seabed. Traditionally, this problem is solved by considering the wave motion in the upper water layer interacting with the Darcy flow in the porous bottom layer through matching of the solutions at the permeable interface. The novel approach in this study is that we describe the interaction between the upper fluid layer and the permeable bottom layer by the application of a Robin boundary condition. By varying the magnitude of the Robin parameter <span><math><mi>R</mi></math></span>, we can model the bottom structure of the fluid layer from rigid to completely permeable. In the case when the bottom is a porous medium where Darcy’s law applies, or composed by densely packed vertical Hele-Shaw cells, <span><math><mi>R</mi></math></span> is small, and can by determined by comparison with analytical results for a two-layer structure. In this case the wave damping is small. For larger values of <span><math><mi>R</mi></math></span>, the damping increases, and for very large <span><math><mi>R</mi></math></span>, the wave is almost critically damped. For the nonlinear transport in spatially damped shallow-water waves, increasing bottom permeability (larger <span><math><mi>R</mi></math></span>), reduces the magnitude of the horizontal Stokes drift velocity, while the drift profile tends to become parabolic with height. The vertical Stokes drift in the limit of large permeability is linear with height, with a magnitude that is larger than the horizontal drift. It is suggested that the implementation of a permeable bottom bed in some cases could prevent shorelines from damaging erosion by incoming surface waves.</div></div>\",\"PeriodicalId\":11985,\"journal\":{\"name\":\"European Journal of Mechanics B-fluids\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":2.5000,\"publicationDate\":\"2024-10-18\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"European Journal of Mechanics B-fluids\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0997754624001493\",\"RegionNum\":3,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MECHANICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"European Journal of Mechanics B-fluids","FirstCategoryId":"5","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0997754624001493","RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MECHANICS","Score":null,"Total":0}
引用次数: 0
摘要
我们研究了不粘性表面重力波在透水海床上传播时的阻尼问题。传统上,解决这一问题的方法是考虑上水层中的波浪运动与多孔底层中的达西流之间的相互作用,通过在渗透界面上进行匹配求解。本研究的新方法是通过应用罗宾边界条件来描述上层流体层与渗透底层之间的相互作用。通过改变罗宾参数 R 的大小,我们可以模拟流体层从刚性到完全渗透的底部结构。当底层为适用达西定律的多孔介质或由密集的垂直海尔-肖单元组成时,R 值很小,可通过与两层结构的分析结果进行比较来确定。在这种情况下,波的阻尼很小。R 值越大,阻尼越大,当 R 值非常大时,波的阻尼几乎达到临界值。对于空间阻尼浅水波的非线性输运,增加底部渗透率(R 越大)会减小水平斯托克斯漂移速度的大小,同时漂移剖面随高度的增加呈抛物线趋势。在渗透率较大的情况下,垂直斯托克斯漂移与高度呈线性关系,漂移幅度大于水平漂移。这表明,在某些情况下,采用透水性底床可以防止海岸线被涌入的表面波侵蚀。
Surface wave damping by a Robin boundary condition at a permeable seabed
We investigate the damping of inviscid surface gravity waves when they propagate over a permeable seabed. Traditionally, this problem is solved by considering the wave motion in the upper water layer interacting with the Darcy flow in the porous bottom layer through matching of the solutions at the permeable interface. The novel approach in this study is that we describe the interaction between the upper fluid layer and the permeable bottom layer by the application of a Robin boundary condition. By varying the magnitude of the Robin parameter , we can model the bottom structure of the fluid layer from rigid to completely permeable. In the case when the bottom is a porous medium where Darcy’s law applies, or composed by densely packed vertical Hele-Shaw cells, is small, and can by determined by comparison with analytical results for a two-layer structure. In this case the wave damping is small. For larger values of , the damping increases, and for very large , the wave is almost critically damped. For the nonlinear transport in spatially damped shallow-water waves, increasing bottom permeability (larger ), reduces the magnitude of the horizontal Stokes drift velocity, while the drift profile tends to become parabolic with height. The vertical Stokes drift in the limit of large permeability is linear with height, with a magnitude that is larger than the horizontal drift. It is suggested that the implementation of a permeable bottom bed in some cases could prevent shorelines from damaging erosion by incoming surface waves.
期刊介绍:
The European Journal of Mechanics - B/Fluids publishes papers in all fields of fluid mechanics. Although investigations in well-established areas are within the scope of the journal, recent developments and innovative ideas are particularly welcome. Theoretical, computational and experimental papers are equally welcome. Mathematical methods, be they deterministic or stochastic, analytical or numerical, will be accepted provided they serve to clarify some identifiable problems in fluid mechanics, and provided the significance of results is explained. Similarly, experimental papers must add physical insight in to the understanding of fluid mechanics.