{"title":"Wave Structures in Ideal Gas Flows with an External Energy Source","authors":"","doi":"10.1134/s0081543823040193","DOIUrl":null,"url":null,"abstract":"<span> <h3>Abstract</h3> <p> We consider the propagation of plane waves in an ideal gas in the presence of external sources of energy inflow and dissipation. Using the Whitham criterion, we obtain conditions under which small perturbations of a constant solution are transformed into nonlinear quasiperiodic wave packets of finite amplitude that move in opposite directions. The structure of these wave packets is shown to be similar to roll waves in inclined open channels. We perform numerical calculations of the development of self-oscillations and the nonlinear interaction of waves. The calculations show that under a small harmonic perturbation of the initial equilibrium state, two types of wave structures can develop: roll waves and periodic two-peak standing waves. </p> </span>","PeriodicalId":54557,"journal":{"name":"Proceedings of the Steklov Institute of Mathematics","volume":"12 1","pages":""},"PeriodicalIF":0.4000,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the Steklov Institute of Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1134/s0081543823040193","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
We consider the propagation of plane waves in an ideal gas in the presence of external sources of energy inflow and dissipation. Using the Whitham criterion, we obtain conditions under which small perturbations of a constant solution are transformed into nonlinear quasiperiodic wave packets of finite amplitude that move in opposite directions. The structure of these wave packets is shown to be similar to roll waves in inclined open channels. We perform numerical calculations of the development of self-oscillations and the nonlinear interaction of waves. The calculations show that under a small harmonic perturbation of the initial equilibrium state, two types of wave structures can develop: roll waves and periodic two-peak standing waves.
期刊介绍：
Proceedings of the Steklov Institute of Mathematics is a cover-to-cover translation of the Trudy Matematicheskogo Instituta imeni V.A. Steklova of the Russian Academy of Sciences. Each issue ordinarily contains either one book-length article or a collection of articles pertaining to the same topic.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
