水波中结构系统的散射特性

IF 0.8 4区工程技术 Q3 MATHEMATICS, APPLIED

Quarterly Journal of Mechanics and Applied Mathematics Pub Date : 2014-11-01 DOI:10.1093/QJMAM/HBU021

M. Mciver

{"title":"水波中结构系统的散射特性","authors":"M. Mciver","doi":"10.1093/QJMAM/HBU021","DOIUrl":null,"url":null,"abstract":"A fixed, rigid structure is said to be cloaked in small amplitude, time-harmonic water waves if it is possible to surround it with other fixed or moving structures or variations in the sea-bed topography in such a way that there are no scattered waves in the far field. The resulting system of structures is said to be transparent to the incident wave field. By finding inequalities which the kinetic and potential energy in the total wave field for such a system must satisfy, it is shown that transparency is impossible for a system of structures which has non-zero volume and satisfies the condition that the free surface is connected and a vertical line drawn from every point on the free surface does not intersect another structure but intersects the sea bed at a point at which the bed is horizontal.","PeriodicalId":56087,"journal":{"name":"Quarterly Journal of Mechanics and Applied Mathematics","volume":"67 1","pages":"631-639"},"PeriodicalIF":0.8000,"publicationDate":"2014-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/QJMAM/HBU021","citationCount":"8","resultStr":"{\"title\":\"The scattering properties of a system of structures in water waves\",\"authors\":\"M. Mciver\",\"doi\":\"10.1093/QJMAM/HBU021\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"A fixed, rigid structure is said to be cloaked in small amplitude, time-harmonic water waves if it is possible to surround it with other fixed or moving structures or variations in the sea-bed topography in such a way that there are no scattered waves in the far field. The resulting system of structures is said to be transparent to the incident wave field. By finding inequalities which the kinetic and potential energy in the total wave field for such a system must satisfy, it is shown that transparency is impossible for a system of structures which has non-zero volume and satisfies the condition that the free surface is connected and a vertical line drawn from every point on the free surface does not intersect another structure but intersects the sea bed at a point at which the bed is horizontal.\",\"PeriodicalId\":56087,\"journal\":{\"name\":\"Quarterly Journal of Mechanics and Applied Mathematics\",\"volume\":\"67 1\",\"pages\":\"631-639\"},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2014-11-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1093/QJMAM/HBU021\",\"citationCount\":\"8\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Quarterly Journal of Mechanics and Applied Mathematics\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://doi.org/10.1093/QJMAM/HBU021\",\"RegionNum\":4,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Quarterly Journal of Mechanics and Applied Mathematics","FirstCategoryId":"5","ListUrlMain":"https://doi.org/10.1093/QJMAM/HBU021","RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}

引用次数: 8

摘要

如果一个固定的刚性结构有可能被其他固定的或移动的结构或海床地形的变化所包围，从而在远场中没有散射波，那么这个固定的刚性结构就被称为小振幅的时谐水波所掩盖。由此产生的结构体系对入射波场是透明的。通过找出总波场中动能和势能必须满足的不等式，证明了对于一个体积非零的结构系统来说，透明是不可能的，它满足自由表面连通的条件，并且从自由表面上的每一点所画的垂直线不与另一个结构相交，而是在海床水平的一点与海床相交。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

The scattering properties of a system of structures in water waves

A fixed, rigid structure is said to be cloaked in small amplitude, time-harmonic water waves if it is possible to surround it with other fixed or moving structures or variations in the sea-bed topography in such a way that there are no scattered waves in the far field. The resulting system of structures is said to be transparent to the incident wave field. By finding inequalities which the kinetic and potential energy in the total wave field for such a system must satisfy, it is shown that transparency is impossible for a system of structures which has non-zero volume and satisfies the condition that the free surface is connected and a vertical line drawn from every point on the free surface does not intersect another structure but intersects the sea bed at a point at which the bed is horizontal.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Quarterly Journal of Mechanics and Applied Mathematics 物理-力学

CiteScore

1.90

自引率

11.10%

发文量

审稿时长

>12 weeks

期刊介绍： The Quarterly Journal of Mechanics and Applied Mathematics publishes original research articles on the application of mathematics to the field of mechanics interpreted in its widest sense. In addition to traditional areas, such as fluid and solid mechanics, the editors welcome submissions relating to any modern and emerging areas of applied mathematics.