High-frequency, finite-amplitude, acoustic traveling waves in bubbly liquids under the Crighton–Westervelt–Klein–Gordon equation

IF 5.7 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

International Journal of Engineering Science Pub Date : 2025-05-26 DOI:10.1016/j.ijengsci.2025.104295

N. Valdivia , P.M. Jordan

引用次数: 0

Abstract

Employing both analytical and numerical methodologies, we investigate the propagation of high-frequency, finite-amplitude, acoustic wave-forms in non-dissipative bubbly liquids under a (1D) PDE model, which we term the Crighton–Westervelt–Klein–Gordon (CWKG) equation. Exact traveling wave solutions (TWS)s for the pressure field are derived and analyzed. It is shown that the CWKG equation can admit both monotonic and periodic TWSs, but that only those of the latter type are bounded. Phase plane analyses of the traveling wave ODEs are performed, approximate expressions for the pressure field are derived, and special case results are identified and studied. We also point out a special/limiting case TWS that consists of (periodic) parabolic arcs with pointed peaks; discuss connections to three models, including the Korteweg–De Vries (KdV) equation, that describe well known types of water waves; and suggest possible follow-on studies.

查看原文本刊更多论文

crightton - westervelt - klein - gordon方程下气泡液体中的高频、有限振幅声波行波

采用解析和数值方法，我们在（1D） PDE模型下研究了非耗散气泡液体中高频、有限振幅、声波形式的传播，我们称之为Crighton-Westervelt-Klein-Gordon （CWKG）方程。推导并分析了压力场的精确行波解。结果表明，CWKG方程既可以承认单调tws，也可以承认周期tws，但只有后者是有界的。对行波ode进行了相平面分析，导出了压力场的近似表达式，并对特殊情况进行了识别和研究。我们还指出了一种特殊/极限情况TWS，它由尖峰的（周期）抛物弧组成；讨论与三个模型的联系，包括描述众所周知的水波类型的Korteweg-De Vries （KdV）方程；并建议可能的后续研究。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

International Journal of Engineering Science 工程技术-工程：综合

CiteScore

11.80

自引率

16.70%

发文量

审稿时长

45 days

期刊介绍： The International Journal of Engineering Science is not limited to a specific aspect of science and engineering but is instead devoted to a wide range of subfields in the engineering sciences. While it encourages a broad spectrum of contribution in the engineering sciences, its core interest lies in issues concerning material modeling and response. Articles of interdisciplinary nature are particularly welcome. The primary goal of the new editors is to maintain high quality of publications. There will be a commitment to expediting the time taken for the publication of the papers. The articles that are sent for reviews will have names of the authors deleted with a view towards enhancing the objectivity and fairness of the review process. Articles that are devoted to the purely mathematical aspects without a discussion of the physical implications of the results or the consideration of specific examples are discouraged. Articles concerning material science should not be limited merely to a description and recording of observations but should contain theoretical or quantitative discussion of the results.