Generalized modulation theory for strongly nonlinear gravity waves in a compressible atmosphere

M. Schlutow, E. Wahlén
{"title":"Generalized modulation theory for strongly nonlinear gravity waves in a compressible atmosphere","authors":"M. Schlutow, E. Wahlén","doi":"10.1515/mcwf-2020-0105","DOIUrl":null,"url":null,"abstract":"Abstract This study investigates strongly nonlinear gravity waves in the compressible atmosphere from the Earth’s surface to the deep atmosphere. These waves are effectively described by Grimshaw’s dissipative modulation equations which provide the basis for finding stationary solutions such as mountain lee waves and testing their stability in an analytic fashion. Assuming energetically consistent boundary and far-field conditions, that is no energy flux through the surface, free-slip boundary, and finite total energy, general wave solutions are derived and illustrated in terms of realistic background fields. These assumptions also imply that the wave-Reynolds number must become less than unity above a certain height. The modulational stability of admissible, both non-hydrostatic and hydrostatic, waves is examined. It turns out that, when accounting for the self-induced mean flow, the wave-Froude number has a resonance condition. If it becomes 1/1/21/\\sqrt 2, then the wave destabilizes due to perturbations from the essential spectrum of the linearized modulation equations. However, if the horizontal wavelength is large enough, waves overturn before they can reach the modulational stability condition.","PeriodicalId":106200,"journal":{"name":"Mathematics of Climate and Weather Forecasting","volume":"62 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2019-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematics of Climate and Weather Forecasting","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1515/mcwf-2020-0105","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 2

Abstract

Abstract This study investigates strongly nonlinear gravity waves in the compressible atmosphere from the Earth’s surface to the deep atmosphere. These waves are effectively described by Grimshaw’s dissipative modulation equations which provide the basis for finding stationary solutions such as mountain lee waves and testing their stability in an analytic fashion. Assuming energetically consistent boundary and far-field conditions, that is no energy flux through the surface, free-slip boundary, and finite total energy, general wave solutions are derived and illustrated in terms of realistic background fields. These assumptions also imply that the wave-Reynolds number must become less than unity above a certain height. The modulational stability of admissible, both non-hydrostatic and hydrostatic, waves is examined. It turns out that, when accounting for the self-induced mean flow, the wave-Froude number has a resonance condition. If it becomes 1/1/21/\sqrt 2, then the wave destabilizes due to perturbations from the essential spectrum of the linearized modulation equations. However, if the horizontal wavelength is large enough, waves overturn before they can reach the modulational stability condition.
查看原文
分享 分享
微信好友 朋友圈 QQ好友 复制链接
本刊更多论文
可压缩大气中强非线性重力波的广义调制理论
摘要本文研究了从地球表面到大气深处的可压缩大气中的强非线性重力波。格里姆肖耗散调制方程有效地描述了这些波,为寻找固定解(如背风山波)和以解析方式测试其稳定性提供了基础。假设能量一致的边界和远场条件,即没有通过表面的能量通量,自由滑移边界和有限的总能量,导出了一般的波解,并在实际背景场中进行了说明。这些假设还暗示,在一定高度以上,波的雷诺数必须小于1。研究了非静水和静水容许波的调制稳定性。结果表明,在考虑自诱导平均流时,波-弗劳德数具有共振条件。如果它变成1/1/21/\sqrt 2,那么由于线性化调制方程的基本谱的扰动,波不稳定。然而,如果水平波长足够大,波在达到调制稳定条件之前就会翻转。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 去求助
来源期刊
自引率
0.00%
发文量
0
期刊最新文献
Expanding Grids for Efficient Cloud Dynamics Simulations Across Scales On strongly nonlinear gravity waves in a vertically sheared atmosphere Shallow-cloud impact on climate and uncertainty: A simple stochastic model Pattern formation in clouds via Turing instabilities Estimation of seasonal boundaries using temperature data: a case of northwest part of Bangladesh
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
0
微信
客服QQ
Book学术公众号 扫码关注我们
反馈
×
意见反馈
请填写您的意见或建议
请填写您的手机或邮箱
已复制链接
已复制链接
快去分享给好友吧!
我知道了
×
扫码分享
扫码分享
Book学术官方微信
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术
文献互助 智能选刊 最新文献 互助须知 联系我们:info@booksci.cn
Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。
Copyright © 2023 Book学术 All rights reserved.
ghs 京公网安备 11010802042870号 京ICP备2023020795号-1