Floquet scattering of shallow water waves by a vertically oscillating plate

IF 2.1 3区 物理与天体物理 Q2 ACOUSTICS
Magdalini Koukouraki , Philippe Petitjeans , Agnès Maurel , Vincent Pagneux
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引用次数: 0

Abstract

We report on the scattering of a plane wave from a vertically oscillating plate in the low frequency approximation by means of Floquet theory. In the case of a static plate, the scattering coefficients are evaluated via mode matching method for the full two-dimensional linearized water wave problem and are compared with the coefficients obtained from a reduced one-dimensional model in the shallow water approximation. The main part of the analysis is the extension of this 1D shallow water approximation to the case of a vertically oscillating plate, where time modulation is only encapsulated in the blockage coefficient. We show that the incident wave is scattered into Floquet sidebands and extract the scattering coefficients for each harmonic using a Floquet scattering formalism. Finally, considering a slowly oscillating plate, we propose a quasistatic approximation which appears to be particularly accurate.
垂直振动板对浅水波的絮状散射
本文用Floquet理论研究了垂直振动平板平面波在低频近似下的散射。在静板的情况下,通过模式匹配方法计算了全二维线性化水波问题的散射系数,并与浅水近似下的一维简化模型得到的系数进行了比较。分析的主要部分是将这种一维浅水近似扩展到垂直振荡板的情况,其中时间调制仅封装在阻塞系数中。我们证明了入射波被分散到Floquet边带中,并使用Floquet散射形式提取了每个谐波的散射系数。最后,考虑到一个缓慢振荡的板块,我们提出了一个准静态近似,它似乎特别准确。
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来源期刊
Wave Motion
Wave Motion 物理-力学
CiteScore
4.10
自引率
8.30%
发文量
118
审稿时长
3 months
期刊介绍: Wave Motion is devoted to the cross fertilization of ideas, and to stimulating interaction between workers in various research areas in which wave propagation phenomena play a dominant role. The description and analysis of wave propagation phenomena provides a unifying thread connecting diverse areas of engineering and the physical sciences such as acoustics, optics, geophysics, seismology, electromagnetic theory, solid and fluid mechanics. The journal publishes papers on analytical, numerical and experimental methods. Papers that address fundamentally new topics in wave phenomena or develop wave propagation methods for solving direct and inverse problems are of interest to the journal.
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