{"title":"On the onset of wave-breaking and the time evolution of the maximum of horizontal velocity in rotational equatorial waves","authors":"Calin I. Martin","doi":"10.1016/j.nonrwa.2025.104367","DOIUrl":null,"url":null,"abstract":"<div><div>We are concerned here with the time evolution of the maximal (modified) surface velocity for a rotational wave in the <span><math><mi>f</mi></math></span>-plane approximation. Using a parametric description of the wave surface, we show that the appearance of asymmetry in the wave profile is a necessary condition for the occurrence of a fluid velocity that exceeds the wave crest celerity, the latter occurence characterizing the inception of the wave-breaking phenomenon. This is achieved by means of an equation relating the time evolution of the maximum of the (modified) horizontal velocity to the horizontal component of the pressure gradient. Our analysis extends previous results concerning irrotational flows to the rotational situation of constant vorticity.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"85 ","pages":"Article 104367"},"PeriodicalIF":1.8000,"publicationDate":"2025-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Nonlinear Analysis-Real World Applications","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S1468121825000537","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
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Abstract
We are concerned here with the time evolution of the maximal (modified) surface velocity for a rotational wave in the -plane approximation. Using a parametric description of the wave surface, we show that the appearance of asymmetry in the wave profile is a necessary condition for the occurrence of a fluid velocity that exceeds the wave crest celerity, the latter occurence characterizing the inception of the wave-breaking phenomenon. This is achieved by means of an equation relating the time evolution of the maximum of the (modified) horizontal velocity to the horizontal component of the pressure gradient. Our analysis extends previous results concerning irrotational flows to the rotational situation of constant vorticity.
期刊介绍：
Nonlinear Analysis: Real World Applications welcomes all research articles of the highest quality with special emphasis on applying techniques of nonlinear analysis to model and to treat nonlinear phenomena with which nature confronts us. Coverage of applications includes any branch of science and technology such as solid and fluid mechanics, material science, mathematical biology and chemistry, control theory, and inverse problems.
The aim of Nonlinear Analysis: Real World Applications is to publish articles which are predominantly devoted to employing methods and techniques from analysis, including partial differential equations, functional analysis, dynamical systems and evolution equations, calculus of variations, and bifurcations theory.
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