{"title":"A Free Surface Fluid with Two-Dimensional Periodic Disturbances in Various Models of the Fluid","authors":"Yu. D. Chashechkin, A. A. Ochirov","doi":"10.1134/s1028335823110022","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>The complete dispersion relations for periodic perturbations of a flat free surface with a positive definite frequency and a complex wavenumber describing spatial attenuation in a viscous stratified charged liquid were obtained in a linear approximation by methods of the theory of singular perturbations for the first time. Regular components of the complete solution describe plane gravitational-capillary waves. Singular components characterize ligaments, i.e., thin flows that are absent in the model of an ideal medium. The obtained dispersion relations in extreme cases uniformly transform into known expressions for inviscid stratified, viscous homogeneous and ideal liquids. The calculated dependencies of the wavelength and thickness of the ligament and the group and phase velocity of the components on the frequency at different values of the media parameters are given.</p>","PeriodicalId":533,"journal":{"name":"Doklady Physics","volume":null,"pages":null},"PeriodicalIF":0.6000,"publicationDate":"2024-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Doklady Physics","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1134/s1028335823110022","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MECHANICS","Score":null,"Total":0}
引用次数: 0
Abstract
The complete dispersion relations for periodic perturbations of a flat free surface with a positive definite frequency and a complex wavenumber describing spatial attenuation in a viscous stratified charged liquid were obtained in a linear approximation by methods of the theory of singular perturbations for the first time. Regular components of the complete solution describe plane gravitational-capillary waves. Singular components characterize ligaments, i.e., thin flows that are absent in the model of an ideal medium. The obtained dispersion relations in extreme cases uniformly transform into known expressions for inviscid stratified, viscous homogeneous and ideal liquids. The calculated dependencies of the wavelength and thickness of the ligament and the group and phase velocity of the components on the frequency at different values of the media parameters are given.
期刊介绍：
Doklady Physics is a journal that publishes new research in physics of great significance. Initially the journal was a forum of the Russian Academy of Science and published only best contributions from Russia in the form of short articles. Now the journal welcomes submissions from any country in the English or Russian language. Every manuscript must be recommended by Russian or foreign members of the Russian Academy of Sciences.
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