Rossby-Kelvin instability: a new type of ageostrophic instability caused by a resonance between Rossby waves and gravity waves

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Abstract
An ageostrophic version of Phillips’ model is studied. All instabilities found are systematically interpreted in terms of resonance of wave components. The instability occurs if there is a pair of wave components which propagate in the opposite direction to the basic flow and these wave components have almost the same Doppler-shifted frequency. A new instability, identified as a resonance between the Kelvin wave and the Rossby waves, is found at Froude number F ≈ 0.7. The Rossby waves are almost completely in geostrophic balance while the ageostrophic Kelvin wave is the same as in a one-layer system. Doppler shifting matches frequencies which would otherwise be very different. This instability is presumably the mechanism of the frontal instability observed by Griffiths & Linden (1982) in a laboratory experiment. Ageostrophic, baroclinic instability with non-zero phase speed is also observed in the numerical calculation. This instability is caused by resonance between different geostrophic modes.
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