{"title":"带有斯图尔特型漩涡的分层海洋涡旋","authors":"Qixing Ding, Luigi Roberti","doi":"10.1007/s10231-024-01469-5","DOIUrl":null,"url":null,"abstract":"<div><p>In the setting of the thin-shell approximation of the Euler equations in spherical coordinates for oceanic flows with variable density on the spinning Earth, we study a vorticity equation for a pseudo stream function <span>\\(\\psi \\)</span>, whereby the assumption of incompressibility allows us to express the density as a function of <span>\\(\\psi \\)</span>. Via an elliptic comparison argument, we show that, under certain assumptions, the (explicit) solution in the case of zero rate of rotation (i.e., on a fixed sphere) in a bounded region with smooth boundary contained either in the Northern or in the Southern Hemisphere is an approximation, in a suitable sense, of the corresponding solution of the equation with positive rate of rotation in the same region. This provides new insight into the dynamics of ocean gyres.</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":"203 6","pages":"2847 - 2862"},"PeriodicalIF":1.0000,"publicationDate":"2024-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10231-024-01469-5.pdf","citationCount":"0","resultStr":"{\"title\":\"Stratified ocean gyres with Stuart-type vortices\",\"authors\":\"Qixing Ding, Luigi Roberti\",\"doi\":\"10.1007/s10231-024-01469-5\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>In the setting of the thin-shell approximation of the Euler equations in spherical coordinates for oceanic flows with variable density on the spinning Earth, we study a vorticity equation for a pseudo stream function <span>\\\\(\\\\psi \\\\)</span>, whereby the assumption of incompressibility allows us to express the density as a function of <span>\\\\(\\\\psi \\\\)</span>. Via an elliptic comparison argument, we show that, under certain assumptions, the (explicit) solution in the case of zero rate of rotation (i.e., on a fixed sphere) in a bounded region with smooth boundary contained either in the Northern or in the Southern Hemisphere is an approximation, in a suitable sense, of the corresponding solution of the equation with positive rate of rotation in the same region. This provides new insight into the dynamics of ocean gyres.</p></div>\",\"PeriodicalId\":8265,\"journal\":{\"name\":\"Annali di Matematica Pura ed Applicata\",\"volume\":\"203 6\",\"pages\":\"2847 - 2862\"},\"PeriodicalIF\":1.0000,\"publicationDate\":\"2024-06-05\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://link.springer.com/content/pdf/10.1007/s10231-024-01469-5.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Annali di Matematica Pura ed Applicata\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s10231-024-01469-5\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annali di Matematica Pura ed Applicata","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s10231-024-01469-5","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
In the setting of the thin-shell approximation of the Euler equations in spherical coordinates for oceanic flows with variable density on the spinning Earth, we study a vorticity equation for a pseudo stream function \(\psi \), whereby the assumption of incompressibility allows us to express the density as a function of \(\psi \). Via an elliptic comparison argument, we show that, under certain assumptions, the (explicit) solution in the case of zero rate of rotation (i.e., on a fixed sphere) in a bounded region with smooth boundary contained either in the Northern or in the Southern Hemisphere is an approximation, in a suitable sense, of the corresponding solution of the equation with positive rate of rotation in the same region. This provides new insight into the dynamics of ocean gyres.
期刊介绍:
This journal, the oldest scientific periodical in Italy, was originally edited by Barnaba Tortolini and Francesco Brioschi and has appeared since 1850. Nowadays it is managed by a nonprofit organization, the Fondazione Annali di Matematica Pura ed Applicata, c.o. Dipartimento di Matematica "U. Dini", viale Morgagni 67A, 50134 Firenze, Italy, e-mail annali@math.unifi.it).
A board of Italian university professors governs the Fondazione and appoints the editors of the journal, whose responsibility it is to supervise the refereeing process. The names of governors and editors appear on the front page of each issue. Their addresses appear in the title pages of each issue.