### Abstract

The propagation properties of gravity waves in a vertically rotating compressible vertically sheared zonal flow are investigated. In slowly-varying shear flows the local dispersion relation is used to study the wave-normal surfaces and the possible types of ray trajectory. It is found that the relaxation of the Boussinesq approximation modifies the two critical levels present in the Boussinesq fluid in such a way that waves approaching them can exhibit valve-like behaviour. However, in a full wave treatment the valve behaviour, already known to be effected by variations in the basic state, is here modified by the neglect of the Boussinesq approximation. The influence of compressibility is shown to increase the number of singularities by two. The wave invariant of the system (which represents conservation of the vertical total wave-energy flux) is used to examine the influence of the singularities on the vertical propagation of the waves, and to conclude that energy absorption can only occur at the singularities present in a slowly varying basic state in an incompressible Boussinesq fluid.

Original language | English |
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Pages (from-to) | 313-330 |

Number of pages | 18 |

Journal | Quarterly Journal of Mechanics and Applied Mathematics |

Volume | 32 |

Issue number | 3 |

DOIs | |

Publication status | Published - Aug 1979 |

### ASJC Scopus subject areas

- Molecular Biology
- Statistics and Probability
- Computational Mathematics
- Condensed Matter Physics
- Applied Mathematics
- Mechanics of Materials
- Mechanical Engineering

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## Cite this

*Quarterly Journal of Mechanics and Applied Mathematics*,

*32*(3), 313-330. https://doi.org/10.1093/qjmam/32.3.313