## Abstract

Resonant interactions between a marginally unstable wave and one or two pairs of slightly damped waves in a quasi geostrophic two layer flow on a beta plane were investigated. It was found that a system of waves that is stable under strictly inviscid conditions is destabilized by slight viscosity provided the initial energy of the participating waves exceed a certain threshold value. In the linear phase viscosity can trigger parametric instability. When weakly non-linear interactions are considered viscosity can lead to explosive instability, whereby the amplitudes of the waves grow without bound at a finite time. The unbounded growth is not always halted by increasing the number of participating waves or by considering higher order non-linear effects. The phenomenon of explosive instability whose significance lies in the rapid growth of the amplitudes of the waves on the approach to the singularity may explain the rapid growth of certain events of cyclogenesis recently observed. (A)

Original language | English |
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Pages (from-to) | 313-339 |

Number of pages | 27 |

Journal | Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences |

Volume | 395 |

Issue number | 1809 , Oct. 8, 1984 |

State | Published - 1984 |