Exact Solutions Modelling Nonlinear Atmospheric Gravity Waves

Exact solutions to the governing equations for atmospheric motion are derived which model nonlinear gravity wave propagation superimposed on atmospheric currents. Solutions are explicitly prescribed in terms of a Lagrangian formulation, which enables a detailed exposition of intricate flow character...

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Published inJournal of mathematical fluid mechanics Vol. 26; no. 1; p. 6
Main Author Henry, David
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.02.2024
Springer Nature B.V
Subjects
Atmospheric models
Classical and Continuum Physics
Exact solutions
Flow characteristics
Fluid mechanics
Fluid- and Aerodynamics
Gravity waves
Lee waves
Mathematical Methods in Physics
Mountains
Physics
Physics and Astronomy
Theoretical mathematics
Wave propagation
76U60
Mountain waves
35Q86
86A10
Atmospheric waves
Exact solution
Online AccessGet full text

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Abstract Exact solutions to the governing equations for atmospheric motion are derived which model nonlinear gravity wave propagation superimposed on atmospheric currents. Solutions are explicitly prescribed in terms of a Lagrangian formulation, which enables a detailed exposition of intricate flow characteristics. It is shown that our solutions are well-suited to modelling two distinct forms of mountain waves, namely: trapped lee waves in the Equatorial f -plane, and vertically propagating mountain waves at general latitudes.
AbstractList Exact solutions to the governing equations for atmospheric motion are derived which model nonlinear gravity wave propagation superimposed on atmospheric currents. Solutions are explicitly prescribed in terms of a Lagrangian formulation, which enables a detailed exposition of intricate flow characteristics. It is shown that our solutions are well-suited to modelling two distinct forms of mountain waves, namely: trapped lee waves in the Equatorial f -plane, and vertically propagating mountain waves at general latitudes.
Exact solutions to the governing equations for atmospheric motion are derived which model nonlinear gravity wave propagation superimposed on atmospheric currents. Solutions are explicitly prescribed in terms of a Lagrangian formulation, which enables a detailed exposition of intricate flow characteristics. It is shown that our solutions are well-suited to modelling two distinct forms of mountain waves, namely: trapped lee waves in the Equatorial f-plane, and vertically propagating mountain waves at general latitudes.Exact solutions to the governing equations for atmospheric motion are derived which model nonlinear gravity wave propagation superimposed on atmospheric currents. Solutions are explicitly prescribed in terms of a Lagrangian formulation, which enables a detailed exposition of intricate flow characteristics. It is shown that our solutions are well-suited to modelling two distinct forms of mountain waves, namely: trapped lee waves in the Equatorial f-plane, and vertically propagating mountain waves at general latitudes.
Exact solutions to the governing equations for atmospheric motion are derived which model nonlinear gravity wave propagation superimposed on atmospheric currents. Solutions are explicitly prescribed in terms of a Lagrangian formulation, which enables a detailed exposition of intricate flow characteristics. It is shown that our solutions are well-suited to modelling two distinct forms of mountain waves, namely: trapped lee waves in the Equatorial f-plane, and vertically propagating mountain waves at general latitudes.
Exact solutions to the governing equations for atmospheric motion are derived which model nonlinear gravity wave propagation superimposed on atmospheric currents. Solutions are explicitly prescribed in terms of a Lagrangian formulation, which enables a detailed exposition of intricate flow characteristics. It is shown that our solutions are well-suited to modelling two distinct forms of mountain waves, namely: trapped lee waves in the Equatorial -plane, and vertically propagating mountain waves at general latitudes.
ArticleNumber 6
Author Henry, David
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  orcidid: 0000-0003-2170-822X
  surname: Henry
  fullname: Henry, David
  email: d.henry@ucc.ie
  organization: Faculty of Mathematics, University of Vienna, School of Mathematical Sciences, University College Cork
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Issue 1
Keywords 76U60
Mountain waves
35Q86
86A10
Atmospheric waves
Exact solution
Language English
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PublicationTitle Journal of mathematical fluid mechanics
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842_CR28
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JM Wallace (842_CR33) 2017
MG Wurtele (842_CR34) 1996; 28
G Shutts (842_CR26) 2018; 120
RB Smith (842_CR29) 2008; 65
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References_xml – reference: ShuttsGObservations and numerical model simulation of a partially trapped lee wave over the Welsh MountainsMon. Weather Rev.2018120205620661992MWRv..120.2056S10.1175/1520-0493(1992)120<2056:OANMSO>2.0.CO;2
– reference: ConstantinAMonismithSGGerstner waves in the presence of mean currents and rotationJ. Fluid Mech.20178205115282017JFM...820..511C365972010.1017/jfm.2017.223
– reference: ConstantinAJohnsonRSOn the modelling of large-scale atmospheric flowJ. Differ. Equ.20212857517982021JDE...285..751C423481010.1016/j.jde.2021.03.019
– reference: GrayAModern Differential Geometry of Curves and Surfaces With Mathematica2006Boca RatonChapman & Hall/CRC
– reference: Ionescu-KruseDExact viscous compressible flow describing the dynamics of the atmosphereJ. Math. Fluid Mech.202224Paper No. 432022JMFM...24...43I440066310.1007/s00021-022-00682-7
– reference: HealeCJBossertKVadasSLHoffmannLDörnbrackAStoberGSnivelyJBJacobiCSecondary gravity waves generated by breaking mountain waves over EuropeJ. Geophys. Res. Atmos.202012511810.1029/2019JD031662
– reference: ScorerRSTheory of waves in the lee of mountainsQ. J. R. Meteorol. Soc.19497541561949QJRMS..75...41S10.1002/qj.49707532308
– reference: SmithRBThe influence of mountains on the atmosphereAdv. Geophys.197921872301979AdGeo..21...87S10.1016/S0065-2687(08)60262-9
– reference: MarshallJPlumbRAAtmosphere, Ocean and Climate Dynamics: An Introductory Text2016LondonAcademic Press
– reference: BennettALagrangian Fluid Dynamics2007CambridgeCambridge University Press
– reference: HenryDExact equatorial water waves in the f\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$f$$\end{document}-planeNonlinear Anal. Real World Appl.201628284289342282510.1016/j.nonrwa.2015.10.003
– reference: ConstantinAExact nonlinear mountain waves propagating upwardsJ. Phys. A2023562023JPhA...56x5702C460230910.1088/1751-8121/acd429
– reference: HenryDInternal equatorial water waves in the f\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$f$$\end{document}-planeJ. Nonlinear Math. Phys.201522499506343407610.1080/14029251.2015.1113046
– reference: VosperSBInversion effects on mountain lee wavesQ. J. R. Meteorol. Soc.20041301723482004QJRMS.130.1723V10.1256/qj.03.63
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Snippet Exact solutions to the governing equations for atmospheric motion are derived which model nonlinear gravity wave propagation superimposed on atmospheric...
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SubjectTerms Atmospheric models
Classical and Continuum Physics
Exact solutions
Flow characteristics
Fluid mechanics
Fluid- and Aerodynamics
Gravity waves
Lee waves
Mathematical Methods in Physics
Mountains
Physics
Physics and Astronomy
Theoretical mathematics
Wave propagation
Title Exact Solutions Modelling Nonlinear Atmospheric Gravity Waves
URI https://link.springer.com/article/10.1007/s00021-023-00842-3
https://www.ncbi.nlm.nih.gov/pubmed/38144908
https://www.proquest.com/docview/2904233805
https://www.proquest.com/docview/2905781856
https://pubmed.ncbi.nlm.nih.gov/PMC10733203
Volume 26
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