{"title":"Approximation à la Oberbeck-Boussinesq for fluids with pressure-induced stratified density","authors":"D. Grandi, A. Passerini","doi":"10.1080/03091929.2020.1817913","DOIUrl":null,"url":null,"abstract":"ABSTRACT We consider a model for convection in compressible fluids in two dimensions. A constitutive limit is studied in which both the mechanical compressibility and thermal expansion affect the buoyancy force. The motion is no longer isochoric as in the classical Boussinesq approximation but has a uniform expansion rate associated to the upward motion: . By using a perturbative approach, we study a Boussinesq-like approximation with pressure-dependent buoyancy force. The existence of weak solutions for the approximated system is proved and their stability is investigated.","PeriodicalId":56132,"journal":{"name":"Geophysical and Astrophysical Fluid Dynamics","volume":"22 1","pages":"412 - 435"},"PeriodicalIF":1.1000,"publicationDate":"2020-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Geophysical and Astrophysical Fluid Dynamics","FirstCategoryId":"89","ListUrlMain":"https://doi.org/10.1080/03091929.2020.1817913","RegionNum":4,"RegionCategory":"地球科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"ASTRONOMY & ASTROPHYSICS","Score":null,"Total":0}
引用次数: 3
Abstract
ABSTRACT We consider a model for convection in compressible fluids in two dimensions. A constitutive limit is studied in which both the mechanical compressibility and thermal expansion affect the buoyancy force. The motion is no longer isochoric as in the classical Boussinesq approximation but has a uniform expansion rate associated to the upward motion: . By using a perturbative approach, we study a Boussinesq-like approximation with pressure-dependent buoyancy force. The existence of weak solutions for the approximated system is proved and their stability is investigated.
期刊介绍：
Geophysical and Astrophysical Fluid Dynamics exists for the publication of original research papers and short communications, occasional survey articles and conference reports on the fluid mechanics of the earth and planets, including oceans, atmospheres and interiors, and the fluid mechanics of the sun, stars and other astrophysical objects.
In addition, their magnetohydrodynamic behaviours are investigated. Experimental, theoretical and numerical studies of rotating, stratified and convecting fluids of general interest to geophysicists and astrophysicists appear. Properly interpreted observational results are also published.
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