{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,20]],"date-time":"2026-10-20T21:02:41Z","timestamp":1792530161142,"version":"4.5.0"},"reference-count":77,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2022,8,15]],"date-time":"2022-08-15T00:00:00Z","timestamp":1660521600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Russian Science Foundation","award":["19-19-00598"],"award-info":[{"award-number":["19-19-00598"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>The theory of singular perturbations in a unified formulation is used, for the first time, to study the propagation of two-dimensional periodic perturbations, including capillary and gravitational surface waves and accompanying ligaments in the 10\u22124&lt;\u03c9&lt;103\u2009\u2009s\u22121 frequency range, in a viscous continuously stratified fluid. Dispersion relations for flow constituents are given, as well as expressions for phase and group velocities for surface waves and ligaments in physically observable variables. When the wave-length reaches values of the order of the stratification scale, the liquid behaves as homogeneous. As the wave frequency approaches the buoyancy frequency, the energy transfer rate decreases: the group velocity of surface waves tends to zero, while the phase velocity tends to infinity. In limiting cases, the expressions obtained are transformed into known wave dispersion expressions for an ideal stratified or actually homogeneous fluid.<\/jats:p>","DOI":"10.3390\/axioms11080402","type":"journal-article","created":{"date-parts":[[2022,8,15]],"date-time":"2022-08-15T20:58:08Z","timestamp":1660597088000},"page":"402","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":31,"title":["Periodic Waves and Ligaments on the Surface of a Viscous Exponentially Stratified Fluid in a Uniform Gravity Field"],"prefix":"10.3390","volume":"11","author":[{"given":"Yuli D.","family":"Chashechkin","sequence":"first","affiliation":[{"name":"Laboratory of Fluid Mechanics, Ishlinsky Institute for Problems in Mechanics RAS, 119526 Moscow, Russia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0825-3507","authenticated-orcid":false,"given":"Artem A.","family":"Ochirov","sequence":"additional","affiliation":[{"name":"Department of Intelligent Information Radiophysical Systems, Physics Faculty, P.G. Demidov Yaroslavl State University, 150003 Yaroslavl, Russia"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2022,8,15]]},"reference":[{"key":"ref_1","unstructured":"Sumptibus, J.R. (1738). Hydrodynamica, Sive de Viribus et Motibus Fluidorum Commentarii, Opus Academicum, Argentorati."},{"key":"ref_2","unstructured":"D\u2019Alembert, J.-L.R. (1747). R\u00e9flexions sur la Cause G\u00e9n\u00e9rale des Vents, David."},{"key":"ref_3","first-page":"274","article-title":"Principes g\u00e9n\u00e9raux du mouvement des fluids","volume":"11","author":"Euler","year":"1757","journal-title":"M\u00e9m. L\u2019acad\u00e9mie Des. Sci. 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