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Nonlin. Processes Geophys., 24, 727-735, 2017
https://doi.org/10.5194/npg-24-727-2017
© Author(s) 2017. This work is distributed under
the Creative Commons Attribution 4.0 License.
Research article
05 Dec 2017
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 new insights into the propagation and amplitude of gravity waves over topography.

Citation: Humi, M.: Analytic solutions for Long's equation and its generalization, Nonlin. Processes Geophys., 24, 727-735, https://doi.org/10.5194/npg-24-727-2017, 2017.
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Short summary
Deriving a generalization of Long's equation to non-isothermal flow shows that Long's equation has (approximate) soliton-like solutions, provides a transformation that linearizes Long's equation (and analytic solutions), and provides analytic solutions for a base flow with shear.
Deriving a generalization of Long's equation to non-isothermal flow shows that Long's equation...
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