Instability of Neutral Eady Waves and orography

A quasigeostrophic Eady model is used to study the instability properties of finite-amplitude Eady waves and relate them to the disturbances generated by isolated bottom topography. It is found that when the amplitude of the primary wave is small the unstable perturbations are slightly deformed three-dimensional Eady modes, with growth rates and phase speed near the values obtained for the instability of the mean zonal state only. When the amplitude of the primary wave is large the most unstable modes are frontal waves, with growth rates increasing with the amplitude of the primary wave and locked in phase with it. The transition between the two regimes occurs for amplitudes of the primary wave around 10 mb. When a wave packet is generated by the interaction of a large-amplitude primary wave with orography, the character of the instability is absolute—that is, the local perturbation grows exponentially—while in the small amplitude, as well as in the zonal, case, the perturbation is advected downstream while growing, so that at any fixed spatial point only the base state remains as t → infinity.