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Nonlinear Processes in Geophysics An interactive open-access journal of the European Geosciences Union

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https://doi.org/10.5194/npg-2017-32
© Author(s) 2017. This work is distributed under
the Creative Commons Attribution 4.0 License.
Research article
10 Jul 2017
Review status
This discussion paper is under review for the journal Nonlinear Processes in Geophysics (NPG).
Analytic Solutions for Long's Equation and its Generalization
Mayer Humi Department of Mathematical Sciences, Worcester Polytechnic Institute, 100 Institute Road, Worcester, MA 01609, USA
Abstract. Two dimensional, steady state, stratified, isothermal, atmospheric flow over topography is governed by Long's equation. Numerical solutions of this equation were derived and used by several authors. In particular these solutions were applied extensively to analyze the experimental observations of gravity waves. In the first part of this paper we derive an extension of this equation to non-isothermal flows. Then we devise a transformation that simplifies this equation. We show that this simplified equation admits solitonic type solutions in addition to regular gravity waves. These new analytical solutions provide insights about the propagation and amplitude of gravity waves over topography.

Citation: Humi, M.: Analytic Solutions for Long's Equation and its Generalization, Nonlin. Processes Geophys. Discuss., https://doi.org/10.5194/npg-2017-32, in review, 2017.
Mayer Humi
Mayer Humi
Mayer Humi

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Short summary
Derive a generalization of Long's equation to nonisothermal flow, shows that Long equation has (approximate) soliton like solutions, provides a transformation that linearizes Long's equation (and analytic solutions), provides analytic solutions for a base flow with shear.
Derive a generalization of Long's equation to nonisothermal flow, shows that Long equation has...
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