{"title":"Heat-source type atmospheric nonlinear flow patterns in zonal cloud bands","authors":"C.I. Martin","doi":"10.1016/j.jde.2025.113589","DOIUrl":null,"url":null,"abstract":"<div><div>We present a family of exact solutions to a set of recently derived nonlinear equations governing at leading order the dynamics of flows in zonal cloud bands that resemble those on Jupiter. These solutions are radial in the horizontal variables, present density and temperature that decrease with height, a pressure function that decreases in the radial direction, and allow heat flowing out into the environment: these are features that are also observed in the Jupiter's Red Spot. Using a WKB analysis we show that certain exact solutions are stable under a specific choice of the density distribution.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"445 ","pages":"Article 113589"},"PeriodicalIF":2.4000,"publicationDate":"2025-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Differential Equations","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0022039625006163","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
We present a family of exact solutions to a set of recently derived nonlinear equations governing at leading order the dynamics of flows in zonal cloud bands that resemble those on Jupiter. These solutions are radial in the horizontal variables, present density and temperature that decrease with height, a pressure function that decreases in the radial direction, and allow heat flowing out into the environment: these are features that are also observed in the Jupiter's Red Spot. Using a WKB analysis we show that certain exact solutions are stable under a specific choice of the density distribution.
期刊介绍:
The Journal of Differential Equations is concerned with the theory and the application of differential equations. The articles published are addressed not only to mathematicians but also to those engineers, physicists, and other scientists for whom differential equations are valuable research tools.
Research Areas Include:
• Mathematical control theory
• Ordinary differential equations
• Partial differential equations
• Stochastic differential equations
• Topological dynamics
• Related topics