### Abstract

The propagation properties of hydromagnetic-inertial-gravity waves riding a basic state which varies slowly in two independent coordinates are examined in the Boussinesq approximation. The amplitudes of the waves are governed by an equation representing conservation of wave action. A study of the dispersion relation shows that the existence of critical surfaces (i.e. the analogue of critical levels in two-dimensions) is governed by nonlinear partial differential equations for the phase function of the waves. Although a solution of these equations is not readily obtainable, the geometric representation of the dispersion relation indicates the existence of critical surfaces for certain types of basic state. These are composed of magnetic field lines and, in contrast to the non-magnetic case, they are associated with energy propagation.

Original language | English |
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Pages (from-to) | 187-202 |

Number of pages | 16 |

Journal | Quarterly Journal of Mechanics and Applied Mathematics |

Volume | 34 |

Issue number | 2 |

DOIs | |

Publication status | Published - May 1981 |

### ASJC Scopus subject areas

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