{"title":"A Lorenz model for an anelastic Oberbeck-Boussinesq system","authors":"Diego Grandi, Arianna Passerini, Manuela Trullo","doi":"10.1016/j.ijnonlinmec.2024.104968","DOIUrl":null,"url":null,"abstract":"<div><div>In an Oberbeck–Boussinesq model, rigorously derived, which includes compressibility, one could expect that the onset of convection for Bénard’s problem occurs at a higher critical Rayleigh number with respect to the classic O–B solutions. The new partial differential equations exhibit non constant coefficients and the unknown velocity field is not divergence-free. By considering these equations, the critical Rayleigh number for the instability of the rest state in Lorenz approximation system is shown to be higher than the classical value, so proving increased stability of the rest state as expected.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"169 ","pages":"Article 104968"},"PeriodicalIF":2.8000,"publicationDate":"2024-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Non-Linear Mechanics","FirstCategoryId":"5","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0020746224003330","RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MECHANICS","Score":null,"Total":0}
引用次数: 0
Abstract
In an Oberbeck–Boussinesq model, rigorously derived, which includes compressibility, one could expect that the onset of convection for Bénard’s problem occurs at a higher critical Rayleigh number with respect to the classic O–B solutions. The new partial differential equations exhibit non constant coefficients and the unknown velocity field is not divergence-free. By considering these equations, the critical Rayleigh number for the instability of the rest state in Lorenz approximation system is shown to be higher than the classical value, so proving increased stability of the rest state as expected.
期刊介绍：
The International Journal of Non-Linear Mechanics provides a specific medium for dissemination of high-quality research results in the various areas of theoretical, applied, and experimental mechanics of solids, fluids, structures, and systems where the phenomena are inherently non-linear.
The journal brings together original results in non-linear problems in elasticity, plasticity, dynamics, vibrations, wave-propagation, rheology, fluid-structure interaction systems, stability, biomechanics, micro- and nano-structures, materials, metamaterials, and in other diverse areas.
Papers may be analytical, computational or experimental in nature. Treatments of non-linear differential equations wherein solutions and properties of solutions are emphasized but physical aspects are not adequately relevant, will not be considered for possible publication. Both deterministic and stochastic approaches are fostered. Contributions pertaining to both established and emerging fields are encouraged.
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