{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,20]],"date-time":"2026-10-20T21:02:42Z","timestamp":1792530162171,"version":"4.5.0"},"reference-count":91,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2022,6,20]],"date-time":"2022-06-20T00:00:00Z","timestamp":1655683200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>This study presents the detailed experimental results of fine structures and dynamics in a stratified flow past a sphere, which is towed with constant velocity in a transparent basin. We developed experimental procedures based on the complete solutions of the truncated fundamental fluid equations. These complete solutions describe the waves and fine accompanying ligaments, as well as the vortices and other flow structures. To visualize the flow, a variety of classical schlieren and electrolytic precipitation procedures were used. Ligaments appear in the schlieren images of the flow as fine interfaces and fibers. They strengthen the influence of the relatively weak density gradient in a continuously stratified fluid (CSF). The symmetry in the wake is discrete at small Froude numbers with the domination of buoyancy effects. At increased velocity and high Froude numbers, when the inertial and non-linear effects turn out to be significant, an axial symmetry becomes continuous.<\/jats:p>","DOI":"10.3390\/sym14061278","type":"journal-article","created":{"date-parts":[[2022,6,22]],"date-time":"2022-06-22T23:11:19Z","timestamp":1655939479000},"page":"1278","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Discrete and Continuous Symmetries of Stratified Flows Past a Sphere"],"prefix":"10.3390","volume":"14","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"}]}],"member":"1968","published-online":{"date-parts":[[2022,6,20]]},"reference":[{"key":"ref_1","unstructured":"Popov, N.I., Fedorov, K.N., and Orlov, V.M. (1979). Sea Water, Nauka. 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