{"title":"Temperature Dependent Precipitation in Exact Nonlinear Mountain Waves","authors":"Tony Lyons, Jordan McCarney","doi":"10.1007/s00021-025-00946-y","DOIUrl":null,"url":null,"abstract":"<div><p>Lagrangian variables are used to develop an explicit description of nonlinear mountain waves propagating in a moist atmosphere. This Lagrangian description is used to deduce an integral representation of the atmospheric pressure distribution in terms of the temperature within the laminar flow layer. Kirchoff’s equation is used to determine a temperature dependent enthalpy which together with the Clausius-Clapeyron equation is used to obtain an explicit expression for temperature and vapour pressure profiles in a saturated atmosphere where mountain waves are prominent. Precipitation rates are computed from the first law of thermodynamics and compare favourably with meteorological field data at Feldberg, a mountain in Germany. The second law of thermodynamics is used to show that there is a subregion near the tropopause at which precipitation is prohibited within the laminar flow.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"27 3","pages":""},"PeriodicalIF":1.2000,"publicationDate":"2025-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00021-025-00946-y.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Mathematical Fluid Mechanics","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s00021-025-00946-y","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
Lagrangian variables are used to develop an explicit description of nonlinear mountain waves propagating in a moist atmosphere. This Lagrangian description is used to deduce an integral representation of the atmospheric pressure distribution in terms of the temperature within the laminar flow layer. Kirchoff’s equation is used to determine a temperature dependent enthalpy which together with the Clausius-Clapeyron equation is used to obtain an explicit expression for temperature and vapour pressure profiles in a saturated atmosphere where mountain waves are prominent. Precipitation rates are computed from the first law of thermodynamics and compare favourably with meteorological field data at Feldberg, a mountain in Germany. The second law of thermodynamics is used to show that there is a subregion near the tropopause at which precipitation is prohibited within the laminar flow.
期刊介绍：
The Journal of Mathematical Fluid Mechanics (JMFM)is a forum for the publication of high-quality peer-reviewed papers on the mathematical theory of fluid mechanics, with special regards to the Navier-Stokes equations. As an important part of that, the journal encourages papers dealing with mathematical aspects of computational theory, as well as with applications in science and engineering. The journal also publishes in related areas of mathematics that have a direct bearing on the mathematical theory of fluid mechanics. All papers will be characterized by originality and mathematical rigor. For a paper to be accepted, it is not enough that it contains original results. In fact, results should be highly relevant to the mathematical theory of fluid mechanics, and meet a wide readership.
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