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Nonlinear Processes in Geophysics An interactive open-access journal of the European Geosciences Union
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Volume 22, issue 2
Nonlin. Processes Geophys., 22, 133-138, 2015
https://doi.org/10.5194/npg-22-133-2015
© Author(s) 2015. This work is distributed under
the Creative Commons Attribution 3.0 License.
Nonlin. Processes Geophys., 22, 133-138, 2015
https://doi.org/10.5194/npg-22-133-2015
© Author(s) 2015. This work is distributed under
the Creative Commons Attribution 3.0 License.

Research article 06 Mar 2015

Research article | 06 Mar 2015

Time-dependent Long's equation

M. Humi M. Humi
  • Department of Mathematical Sciences, Worcester Polytechnic Institute, 100 Institute Road, Worcester, MA01609, USA

Abstract. Long's equation describes steady-state two-dimensional stratified flow over terrain. Its numerical solutions under various approximations were investigated by many authors. Special attention was paid to the properties of the gravity waves that are predicted to be generated as a result. In this paper we derive a time-dependent generalization of this equation and investigate analytically its solutions under some simplifications. These results might be useful in the experimental analysis of gravity waves over topography and their impact on atmospheric modeling.

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Short summary
Long's equation models the steady state of two-dimensional stratified flow over terrain. It has been used extensively to investigate the generation and properties of gravity waves and their impact on the structure constants of the atmosphere. In this paper we derive a time-dependent version of this equation which might be useful in the analysis of experimental data about gravity waves.
Long's equation models the steady state of two-dimensional stratified flow over terrain. It...
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